[biomedical, chemical] In biology there is cell-to-cell interaction, which can be divided into four types of receptors: Cadherins, selectins, integrins, and immunoglobulin superfamily. Cadherins rely on the abundance of Ca^{2+} ions to provide a platform for temporary adhesion. The adhesion is homotype, using the Cadherin molecules to bind to each other spanning the extracellular space.
[biomedical, chemical] In biology there is cell-to-cell interaction, which can be divided into four types of receptors: Cadherins, selectins, integrins, and immunoglobulin superfamily. Cadherins rely on the abundance of Ca^{2+} ions to provide a platform for temporary adhesion. The adhesion is homotype, using the Cadherin molecules to bind to each other spanning the extracellular space.
[nuclear] Element: ${}_{48}{}^{112}\text{C}\text{d}$
. Semiconductor material.[biomedical, fluid dynamics, general] Decompression disease, formation of embolisms resulting from the release of gas bubbles from tissue into the bloodstream, primarily nitrogen, when the external pressure applied to the body is reduced too quickly. This phenomenon is connected to osmotic pressure, the partial pressure associated with dissolved gases, which can occur during scuba-diving expeditions on return to the sea level, while surfacing too rapidly. Originally the disease was associated with the exodus from a closed compartment, a caisson (when returning from underwater efforts while enclosed in the caisson under compressed air). One example is the use of caissons while working on the New York Brooklyn Bridge in the 1870s. The compressed air was necessary to compensate for the external hydrostatic pressure applied by the resting water column, where each 10 m of water corresponds to approximately 1 atmosphere, or 101.325 kPa, also called “the bends” or “divers disease” (see Figure C.1).
Figure C.1 Decompression chamber used to mitigate and treat decompression sickness after deep-sea diving, used by the United States Navy. (Courtesy of Jayme Pastoric, Mass Communication Specialist 2nd Class, US Navy.)
[atomic, biomedical] The adhesion of calcium to surfaces of implanted devices in biological organisms. Another form of calcification is in the formation of plaques in the lumen of blood vessels, making it tougher and harder than fatty plaques. Other mineralization effects of calcium are in diseased tissues, causing the biological material to become more rigid and hence fragile for tearing and fracture. During osteoporosis, bone calcium level decreases due to metabolic inequilibrium and a deficiency in the supply chain, primarily due to eating habits. Calcium deposition on heart valves gradually evolves into hardening of the valves, resulting in a diminished efficacy of the pump function due to regurgitation and seepage (see Figure C.2).
Figure C.2 Calcification of a water heater element due to “hard water” with calcium content.
[atomic, biomedical] Element used in the formation of bone and teeth as well as in the communication between cells $\left({}_{20}{}^{40}\text{C}\text{a}\right)$
. Biological cell have special calcium channels that carry the calcium ion (Ca^{2+}) charges for the creation of an action potential in combination with sodium and potassium ions. The calcium ion electropotential is described by the Nernst equation. The calcium ions and atoms also play a role in the Gibbs free energy calculations for biological cells. Calcium is a major catalyst in skeletal muscle contraction. Another implication of calcium is in the formation of plaque in the blood vessels. About 1% of calcium is dissolved in blood, and the remaining 99% is in cellular structures and muscular processes.[nuclear] Radioactive unstable element, classified as a metal in the element category of Actinide with a half-life of 898 years. Californium was synthesized at the University of California, Berkeley, in the 1950. The metal is artificially generated as a result of colliding Curium $[{}_{96}{}^{247}\text{C}\text{u}]$
with alpha particles $[{}_{2}{}^{4}\text{h}{\text{e}}^{2+}]$ . Other isotopes have a much shorter half-life with aggressive radiation. The disintegration process of Californium generates neutron emission and also produces alpha decay, which results in the production of isotopes of Curium. Californium possesses a simple hexagonal crystal structure.[computational, general] Measuring device that is designed for analog measurements of size with relative accuracy, generally in the order of 0.01 — 0.05 mm. In geometry this refers to a mechanism of calculating the configuration of a polygon, expressed by its antipodal points forming pairs and vertices. The computational rotating caliper respectively aligns a “caliper line” with the edges of a polygon, thus defining the corners or antipodal pairs while successively moving the caliper Une around the polygon. Also used to describe the disk-break pressure clamp for the wheels of an automobile or motorcycle, also called “calliper” (see Figure C.3).
Figure C.3 (a) Brake calipers on a Mercedes automobile front axle and (b) close up of disk brake calipers. (Courtesy of Daimler AG.)
[computational, thermodynamics] Physicist from the United States who made significant contributions to the theoretical formulation of thermodynamic concepts.
[energy, mechanics] Physicist and engineer from the United Kingdom, coinventor of the modern concept of the steam engine in 1712 with Thomas Newcomen (1663–1729). The other, more well-known, inventor related to the stem engine is James Watt (1736–1819).
[general, thermodynamics] Hypothetical concept of heat as a fluid, named caloric, introduced in 1809 by Horatio Gates Spafford (1778–1832) in his General Geography, and Rudiments of Useful Knowledge: In Nine Sections [Illustrated with an Elegant Improved Plate of the Solar System. A Map of the World. A Map of the United States], propounds the idea of heat being a subsystem of matter that is indestructible and self-repellent is incorrect. This concept was intended to replace kinetic theory, the idea that atomic/molecular motion is the foundation for the transfer of heat and was not introduced until Count Rumford (Benjamin Thompson [1753–1814]) described the equivalence of work and rising temperature in 1798. However, the principle of heat and “molecular motion” was introduced in a rudimentary form by Plato (427–347 BC) and later reaffirmed by Galileo Galilei (1564–1642) (see Figure C.4).
Figure C.4 Horatio Gates Spafford (1778–1832), thermodynamics engineer who introduced the caloric concept in 1809.
[general, thermodynamics] The concept of a physical medium that transfers energy, also referred to as theory of caloric. The fluidic medium involved in the energy transfer in question was named “caloric,” supposedly indestructible (see conservation of energy) and self-repellent (this statement comes back in a different format with respect to a concept loosely connected to energy: entropy).
[general, thermodynamics] Concept of heat transfer introduced by Professor Joseph Black (1728– 1799) in 1760. This concept is based on Black’s theoretical interpretation of the energy transfer between two systems; he also introduced the concept and unit of Calorie into the process of raising the temperature of a body.
[biomedical, general, thermodynamics] The amount of heat necessary to raise the temperature of 1 g of water by 1°C (from 14.5°C to 15.5°C ) under atmospheric pressure (1 atm = 1.013 × 10^{5}N/m^{2}= 1.013 × 10^{5}Pa). Abbreviated unit: cal = 4.186 j; kilocalorie is expressed as Cal (also see heat capacity ).
[general, thermodynamics] Device used to determine the caloric value of a substance, insulated to avoid exchange of heat with the exterior media (see Figure C.5).
Figure C.5 A calorimeter.
[biomedical, energy, thermodynamics] Indication of the interchange of energy: energy loss by hot object = energy gain by colder object. Additionally, in biological applications calorimetry describes the process of converting one form of energy, specifically the caloric value of fuel (i.e., food) involved in metabolic activity, for example, body temperature, cell division, and muscle action. In general, thermodynamic applications calorimetry is an indication of the energy consumption of pyrotechnic activity, combustion as well as phase transitions (e.g., melting, vaporization, and general heating and cooling, such as the Carnot process). The process of melting and vaporization introduces the latent heat of fusion and the latent heat of vaporization.
[biomedical, chemical] Protein in the proteolytic enzyme family, calcium-dependent with symmetric peptidase core. This type of protein is found in the connective tissues of the brain, eye lens, and skeletal muscle. The proteolytic nature identifies the use of peptide bonds for binding to amino acids, forming a polypeptide chain.
[biomedical, chemical, thermodynamics] Photosynthetic carbon reaction in biological cellular metabolism energy transfer. The “dark reactions” pathway in photosynthesis. In this chemical reaction pathway, the free energy obtained from cleaving phosphor bonds within ATP is applied to fix CO_{2} and chemically reduce, in order to form carbohydrate. The enzymes and their intermediates involved in the Calvin cycle are located in the cellular chloroplast stroma. The stroma forms a compartment that is equivalent to the mitochondrial matrix. This metabolic cycle was characterized by Melvin Ellis Calvin (1911–1997), with the support from James Bassham (1922–2012) and Andrew Benson (1917–), for which Melvin Calvin received the Nobel Prize in Chemistry in 1961 (see Figure C.6).
Figure C.6 The Calvin cycle. (Courtesy of Mike Jones.)
[fluid dynamics] The asymmetric surface contours of the upper and lower surfaces of an aerofoil. Because of a difference in camber between the upper and lower surface, the air-flow velocity over the top will be greater than under the bottom, providing a pressure difference between the top (lower) and the bottom (higher) based on the Bernoulli equation. The definition of camber ensures the maximum lift coefficient for the object in-flight. This principle is defined numerically by the line connecting the front and the tail end of the wing described by the camber line ( z (x)) with a path length for the air to travel: for the upper portion, Z _{up} (x) = Z(x) + (1/2)T(x), where T(x) is the “thickness function,” which varies with location (x) from front to rear, and for the bottom of the aerofoil, Z _{low}(x) = Z(x) − (1/2)T(x). The thickness curve can be of any formulations, for instance
T(x) = −(t _{ r }/0.2)[–a _{1} x ^{1/2} + b _{1} x + c _{1} x − (c _{1} − 1)x ^{3} + d _{1} x ^{4}], where t _{ r } is the thickness ratio. In supersonic design the camber can also be negative (see Figure C.7).
Figure C.7 Camber of model plane wing on profile.
[fluid dynamics] On an aerofoil the camber line indicates the partition line separating the upper and lower curved surfaces of the wing. The camber of the respected curved surfaces provide the in-flight lift. An aerofoil that curves upward at the tail end of the wing has a chamber line that curves up as well. An example of a curved chamber line is Z(x) = D _{2}[b _{2} x − c _{2} x ^{2} + (c _{2} − 1)x ^{3}], which varies with location (x) from front to rear and a and b are constants.
[general, optics] Optical instrument used for collecting still images or moving footage on a solid-state or digital format recording mechanism. The early cameras used photographic film to record single still images for still photography and a sequence of still images in high frame-rate acquisition for movies. Later photography relied on a charge-coupled device (CCD) array to record matrix elements of grayscale or red–green–blue (RGB) values in electronic format with a variable dynamic range and in a range of pdcel magnitudes. The camera has a simple or complex set of lenses (or only a single lens, for low-end quality imaging) that correct for distortions and color aberrations resulting from diffraction. The early mode solid-state camera used silver-chloride-coated plastic strips for the photographic effect. The silver chloride oxidizes and is later processed by chemical interactions to form a fixed chemical structure that covers the surface of the photographic plate. This mechanism will result in a negative image, since more light will result in an increase of the oxidation process, making the chemical darken respectively. The final process in the solid-state design requires the production of a print on a paper that is chemically treated to respond to the exposure to light in a similar manner, this presents the hues in the same relative distribution as when observed in real life. The image formation system uses a thin lens combination with a range of lenses with various optical configurations to provide wide-angle or zoom image capture possibilities. The image formation relies on magnification for both capture and hard-copy reproduction (see Figure C.8).
Figure C.8 (a) Picture of an old-fashioned Kodak camera, (b) Picture of a new age digital camera.
[general, optics] Imaging device using a pinhole as the Fourier lens that provides an inverted spatial DECONVOLUTION of a light pattern generated by a source distribution on a screen or photographic plate. The image has an optimal resolution depending on the diameter of the pinhole depending on the Rayleigh diffraction mechanism and the wavefront. The image formation is based on the paraxial image formation approach. The pinhole image formation was first described by Aristotle (384–322 BC) (see Figure C.9).
Figure C.9 Camera obscura.
[nuclear] In gas-filled tube with anode and cathode this represents the ions released from the anode, and are called anode ray or canal ray. The positive ions migrate toward the anode under the applied electric field. The canal rays migrate in the opposite direction from the cathode (electron) ray. The exact nature of the positive canal ray depends on the gas and hence the ions formed by surrendering any number of electrons at the positive anode. The discovery of the positive particle stream was made in 1886 by Eugen Goldstein (1850–1930).
[fluid dynamics, geophysics] Canals have a specific tidal flow pattern due to forced oscillation induced by the ebb and flood conditions. In some places the riverbed topography can create spectacular flow conditions, primarily resulting from the changes in propagation velocity with respect to long versus short waves. One example is the surf in the Kampar River in Sumatra and another is in Girdwood, Alaska, with a succession of tidal waves running for 8 km along the riverbed (see Figure C.10).
Figure C.10 Canal wave examples, (a) Sumatra, Indonesia. The “Seven Ghosts” wave can have a crest of up to 3 m and travels the distance of the Kampar River for up to 50 km, (b) Sumatra; tidal bore, (c) Kampar River; Bono wave, and (d) Alaska. (Courtesy of Bono Surf.)
[fluid dynamics] See tidal waves.
[biomedical] Spongy bone with internal structure similar to a honeycomb (“trabecular”) found for instance in ball joints, pelvis (ilium), skull (cranium), and the scapula (i.e., shoulder blade). Cancellous bone constitutes approximately 20% of the bone structure in the human anatomy. The Young’s modulus for cancellous bone is E _{ Y } = 1 GPa, whereas the cortical bone found in the skeletal structure such as the tibia has a Young’s modulus of E _{ Y } = 18 GPa. Cancellous bone is rich in bone marrow and is an essential supplier of red blood cells.
[computational, thermodynamics] A thermodynamic arrangement with two components: one component is a system at constant temperature and the second system a heating bath to maintain the temperature in system 1. The ensemble will still have fluctuations in energy (E). The ensemble consists of a fixed number of particles (N), a constant volume (V), and at constant temperature (T), which defines the canonical ensemble at N;V;T. Note that the temperature is related to entropy (S) as (1/T) = (∂S∕∂E). The distribution of the Hamiltonian (H _{ s }) and the Entropy (S _{ s }) for the ensemble is defined by a normalized Boltzmann distribution, or canonical energy distribution (ρ_{ c } ({q _{ i }}, {p _{ i }}), where {q _{ i }}, {p _{ i }} represent the degrees of freedom for the system) as
where k _{ b } = 1.3806488 × 10^{−23} m^{2}kg/s^{2}K is the Boltzmann coefficient.
[computational] When compared to Hamiltonian transform (with operator H _{tr}) and Lagrangian formulation, the canonical transform (with operator C _{tr}) implicitly does not have time as a parameter. The canonical transform requires an additional factor to conform to a Hamiltonian expressed as H _{tr} = C _{tr} + (∂F _{ a }/∂t), where F _{tr} is a generating or transform function.
[computational, fluid dynamics, geophysics] Elaborating on the work by Ludwig Prandtl (1875–1953) on boundary layers published in 1904, the features in a zero pressure gradient in the streamlined high Reynolds number flow of an incompressible medium are described in a pipe where the flow phenomena are not affected by wall curvature or surface roughness. In the formation of the canonical turbulent boundary layer the conditions also mandate that there are no obstruction upstream. The high Reynolds number (Re > 350 – 730 range) in the shear layer will be the instigator for canonical condition. One way of achieving the conditions for canonical turbulent boundary layer flow are through “shock” flow, jets of high velocity.
[biomedical, electronics, general] Electrical capacitance [C] specific to alternating current [ac] conditions; in general the capacitance of a device changes from direct current (steady-state) to alternating current operations. Specifically, the resistance, inductance, reactance, and capacitance under alternating current become complex; frequency (v = ω/2π, where ω is the angular frequency) dependent; and parameters that have crossover properties, meaning the parameters are no longer linear and singular defined. Consider the current (z), a sinusoidal function with time (t) = I _{max}cos(ωt), where I _{max} represents the maximum current (i.e., amplitude). For the charging process of a capacitor this current now transforms into a function of the capacitance (C) and the applied voltage (V _{max}),i = ωCV _{max} cos(ωt), which translates to a current–voltage relationship defined by V = (1/ωC)I, which yields a new parameter identified as the reactance, X _{ c } = 1/ωC,a derived capacitance. The frequency dependence will induce retardation in the current with respect to the driving voltage and can lag in phase. Indication of the amount of charge (Q) that can be “steady-state” stored on a capacitor when a voltage (V) is applied, C = Q/V. The value of the capacitance is expressed in Farad [F], in actuality the value of capacitors in general use has a denomination of pF or μF. For a plate capacitor the capacitance is a function of the surface area (A), and the separation between the plates (d), C = [ε(N − 1)A]/d, where ε is the dielectric permeability and N the number of plates while E = V ∕ d = σ_{elec} ∕ ε = Q/Aε indicates the electric field between the plates, with σ_{elec} the plate charge density. Because of the repulsive force between like charges, the charge distribution on a conductor or semiconductor will be uniform, which does not hold true for an insulator. Any object has a complex impedance, for instance the capacitance of a horse with respect to soil is approximately 150 – 200 pF, the hooves act as the insulation between “ground” or better, the dielectric separating the two sides of the capacitor. The storage of electric charge has many experimental observations culminating in the final description. Two concurrent but separate events are notable in this historical development, around 1745 the world was pursuing the collection of what was thought to be “electric fluid,” now known as electric current. Both Pieter van Musschenbroek (1692–1761) and Ewald JUrgens von Kleist (1700–1748) performed experiments that illustrated the storage and respective discharge of charge in a container, mediated by the conductive interface of a wet hand holding the device, providing the means to discharge.
[biomedical, chemical, electronics] See membrane capacitance.
[biomedical, electronics, general] Because of time lag under alternating current charge distribution in an electronic circuit the capacitive charging requires introduction of a new complex parameter representing resistance. As described under capacitance (ac), V = (1/ωC)I, which introduces the parameter defined as the capacitive reactance, X _{ c } = (1/ωC).
[biomedical, electronics, imaging] Particle counting under microfluidic conditions, specifically when the channel diameter is relatively large with respect to the particle diameter, put severe constraints on the equipment design. Polarizable micropillars can be used to provide a LIGAND-based capacitive system that specifically responds to certain molecular configurations. For instance, the use of polydimethylsiloxane can allow for such capacitive coupling counting system design. When an external electric field ( e ) is applied the capacitance (C) changes under the influence of the passage of the quantity of specific molecules. The current in the capacitive system will adhere to the equation of continuity, Δ · J = 0, where J is the current density, and Ohm’s law (constitutive Ohm’s law), J = (σ+ iωε_{ r }ε_{0})E, with ε_{ r } the relative permttvity and ε_{0} = 8.854187817 × 10^{−12} F/m the absolute permittivity of vacuum, σ the conductivity per unit length of medium, and ω = 2πv the angular frequency of alternating applied voltage with frequency v.The impedance (i.e., capacitance) can be calculated and plotted as a function of frequency in a Bode diagram (also referred to as a Bode plot) to derive the capacitive spectrum and hence the chemical composition of the fluid passing through the “lab-on-a-chip.” This sensing technology is also referenced under impedance spectroscopy.
[biomedical, electronics, general] Device capable of storing and releasing electrical charge, expressed in Farad (F). The capacitor design uses two conductors that are spaced apart by an insulating medium, such as glass, paper, polycarbonate, polyester (PET film), polystyrene, polypropylene, PTFE or teflon, silver mica, electrolytes, polymer, printed circuit board, and vacuum. Next to conductors semiconductor materials are also used. A charge applied on a capacitor will be equal but opposite in value for the two respective plates. The capacitance (C) of the capacitor represents the ability to hold charge (Q) and is defined by the electric field between the two charge layers or the electrical potential (V) associated with this electric field, C = Q/V. Capacitors are made with various media, such as metal plates separated by air (tuning capacitor, used in early radio design), electrolysis (oxidized metal foil emerged in conducting gel), and ceramics. The energy stored on a capacitor is the result of transferring a charge over an average potential (1/2)V, applying the capacitance yields E = (1/2)CV ^{2}. Placing capacitors in parallel equate to increasing the surface area for the capacitive charge storage thus adding the individual capacities, whereas in series the total charge is equal for each capacitor and the combined capacitance equates: C _{equivalent} = C _{1} C _{2}/(C _{1} + C _{2}) or (1/C _{equivalent}) = (1/Q) + (1/C _{2}) + (1/C _{ i }). A capacitor discharges its electrical charge while the voltage applied (V _{suppl}) over the external resistor (R) (i.e., impedance: X _{electric}) will drop accordingly, resulting in a time decay of the current (I) (i.e., charge released per unit time: t) expressed as dQ/dt = I = C(dV/dt) = C(dIR/dt) = RC(dI/dt); solving for the charging phenomenon or respectively the time release of charge yields Q(t) = CV _{suppl} [1 − e^{−RC/t } ]; or discharge, Q(t) = Q _{0}e^{−rc/ t }, or for the charging current I(t) = (V _{suppl}/R)e^{−rc/t}. When the capacitor is charged and discharged resulting from an alternating current (I _{cap} (t) = I _{max} sin(ωt)), where ω is the angular frequency indicating the change in direction of the current through the capacitor (I _{cap}) per unit time; there will be a lag between the voltage and the current of precisely 90° or π/2 in phase, the current leading over the voltage with respect to time (see Figure C.11).
Figure C.11 Capacitor.
[electronics, general] See parallel plate capacitor.
[general] Variable capacitance plate capacitor used in early design FM and am radio receiver and analog television receivers. The value of the capacitor determines the resonance frequency of the receiving circuit, hence locking on to one specific radio transmitter signal only.
[fluid dynamics, thermodynamics] The surface interaction between a fine gauge hollow tube inserted into a liquid surface and the resulting surface shape and level height with respect to the surrounding free liquid inside a narrow column. The height of the liquid surface inside the tube with respect to the level liquid surface is a function of the density (ρ) of the liquid and the “adhesive forces.” For instance, the height (h) as a function of tube diameter (d) for the following liquids is as follows: mercury falls below the surface h = −10/d, water h = 30/d, or alcohol h = 11.6/d. The surface curvature will make an angle θ with the wall of the tube that is directly dependent on the tension (F _{ T }) between the liquid and the surface material of the tube (or the lining of the tube, e.g., oil), h = 4F _{ T } cos θ/ ρgd, where g is the gravitational acceleration (see Figure C.12).
Figure C.12 Capillarity.
[biomedical, biophysics, general] Small diameter tubing that results in hemodynamic conditions where residual forces become apparent in the flow mechanism of action as well as under steady-state conditions revealing the influence of forces between the wall and the medium. One specifically notable situation is blood flow in capillary systems of the circulatory vasculature under mechanical contraction of the heart. The capillary flow is confined by the fact that the red blood cells will flow through with minimal gradient force, which entails that the red blood cells line up as stacked parachutes, resulting in what is known as Rouleaux formation. In case the red blood cells are tilted there will be a gradient in force making the cell straighten out with the edge of the circumference of the disk-shaped cell in cross-sectional contact with the wall of the tube, that is, capillary vessel. The full-circumference contact of the red blood cells results in a full mechanical contact with high friction and frequently resulting in both vascular and red blood cell deformation, emphasizing the viscoelastic properties of blood flow.
[fluid dynamics] (Greek: capilla: hair, i.e., hollow tube) Surface forces in the operational environment between a fluid and a solid that are dominated by either cohesive or adhesive forces. The surface tension for a certain liquid adheres to the wall and wets the surface because of a polar attraction greater than the internal Van der Waals forces of the liquid. This phenomenon may cause the fluid to rise inside a narrow tube. The radius of curvature of the meniscus of the liquid in a tube with radius R is defined as r = R/cos θ, where θ is the angle with the wall outside the liquid. The height (h) with which the liquid may rise depends on the density of the liquid ρ, expressed as the pressure of the column of liquid under gravitational attraction (g the gravitational acceleration): p = ρgh compared to the force per unit area resulting from the surface tension over the curved surface, 2(σ_{surface}/r), yielding h = 2σ_{surface} cosθ/ρgR.
[fluid dynamics] Flow is expressed as the integral of the velocity of medium over the cross-sectional area of a conduit with diameter 2R. The velocity is the result of the pressure gradient ( p _{1} − p _{2} ) over a length of a passage way (L), while the velocity can be a function of the radius (r) to the center of the conduit, $Q=\left(2\text{\pi /4\eta}\right)\left[\left({P}_{1}-{P}_{2}\right)\text{/}L\right]{\displaystyle {\int}_{0}^{\text{R}}\left[{R}^{2}-{\left({r}^{\prime}\right)}^{2}\right]rd{r}^{\prime}}$
, known as Poiseuille’s law.[biomedical, fluid dynamics] Ratio of viscous force to elastic force, $\text{Ca}=\text{\mu}\dot{\text{\gamma}}a/bE$
, when applied to vascular wall where μ is the viscosity, $\dot{\text{\gamma}}$ is the shear rate, a is the radius, h is the membrane thickness, and E is the membrane Young’s modulus. For large diameter vessels the shear rate can still be large near the wall. The shear rate on the surface of the wall concomitantly leads to deformation of red blood cells, and attributes to the formation of a flow-free layer at the vessel wall.[fluid dynamics] γ_{ s } Surface tension, η viscosity, v velocity. In the description of capillary flow, the capillary number ties together with the Bond number to describe conditions where the viscous stress between a bubble and the wall will be ruled by viscous lubrication. Under capillary flow transporting a bubble the friction forces across the surface of the bubble can vary locally. Under certain conditions the bubble may be elongated and hence in close contact with the wall of the tube, which may be identified by a low, nonzero capillary number. Under these circumstances the surface of the bubble can be divided in regions that are subject to specific force diagrams, respectively locally unique from tip to tail. The capillary number may additionally influence approximations and reductions in the Navier–Stokes equation (see Figure C.13).
Figure C.13 The relation for the capillary number in bubble growth.
[energy, fluid dynamics, mechanics] Ripples occurring at an interface between two liquids. One circumstance is the ripple wave resulting from wind on the surface of a liquid. Because of the size or magnitude, capillary wave grow and extinguish rapidly when the source (i.e., wind) engages or disengages. The wave process is confined primarily by the surface tension (T _{ s }). The breaking wave causes the fluid pressure to become discontinuous at the surface in the crest. Assuming two curves are forming the crest, each with respective radius R _{ i }, the discontinuity in the fluid surface pressure (P) can be defined as P − P′ = T _{ s } [(1/R_{1}) + (1/R_{2})]) where P and P′ represent the pressure at the surface on either side of the crest. In the case of negligible influence of gravity the velocity potential (ϕ _{ v }) of the wave propagation in the x-direction with amplitude in the y-direction can be represented as ϕ _{ v } = Ce^{ky} cos(kx)cos(ψt + φ) and ϕ _{ v }′ = C′e^{−ky} cos(kx)cos(ψt + φ), respectively, where C and C′ are constants and k = 2π/λ the wave number, ψ the imposed velocity, and φ a phase shift. This translates in a varying pressure under external force defined for one side respectively, (P/ρ) = (∂ϕ_{ v }/∂t) = (ψ^{2} a/k)e^{ky} cos(kx)sin(ψt + φ), in case of a fluid density ρ. The surface deformation velocity is defined by $\text{\psi}=\sqrt{\left[{T}_{s}{k}^{3}/\left(\text{\rho}+{\text{\rho}}^{\prime}\right)\right]}$
, where ρ′ the density on the “opposite side of the crest.” The wavelength is not a singular value, but rather forms a spectrum, ranging from low to high frequencies. The higher frequencies will be subject to dispersion and will cause the sharp crest to “break” eventually (on large scale this corresponds to braking wave at the beach in Hawaii, for instance). The driving force and the associated energy of motion (KE) will determine the wavelength spectrum based on the velocity potential, $KE=\left(1\text{/}2\right)\text{\rho}{\displaystyle {\int}_{0}^{\text{\lambda}}{\text{\varphi}}_{v}{\left(\partial {\text{\varphi}}_{v}/\partial y\right)}_{y=0}dx}-\left(1/2\right){\text{\rho}}^{\prime}{\displaystyle {\int}_{0}^{\text{\lambda}}{{\text{\varphi}}^{\prime}}_{v}{\left(\partial {{\text{\varphi}}^{\prime}}_{v}/\partial y\right)}_{y=0}dx}$ for waves at the interface of two fluids. Under capillary wave motion the surface tension has an overpowering force influence on the wave description, acting as a restoring force. Generally, water waves with a wavelength less than 0.0173 m can be considered capillary waves. Both the phase velocity and group velocity increase with decreasing wavelengths. The group velocity for capillary waves is greater than the phase velocity. At the crossover wavelength the phase velocity has a minimum value, approximately 0.231 m/s in a water–air fluid surface interface. Capillary waves can generally be recognized as small ripples, and result from a fresh wind blowing over smooth water. These waves have curved crowns and v-shaped troughs. Capillary waves are extinguished by molecular “viscosity.” For gravitational waves, in contrast, generally the crests are sharp and the troughs are rounded (see Figure C.14).Figure C.14 Capillary wave.
[computational, thermodynamics] Mathematician from Germany. The work of Dr. Carathéodory made significant changes in the computational approach to thermodynamic axiomas. In axiomatic thermodynamics, the solution mechanism for the second law of thermodynamics relies on how to interpret the geometric configuration of a specific differential equation and the appropriate solutions, known as the Pfaffian. Carathéodory made significant strides in formulating thermodynamic laws in proper mathematical expressions. Carathéodory made statements with respect to the second law of thermodynamics concerning the mathematical definition of thermal concepts for a system (S _{ y }), such as temperature (T) and heat (Q = Δu + W _{ y } with the change of internal energy u and the work W performed), described in mechanical terms of displacement (i.e., momentum: p = mv, with mass m and velocity v), volume (k)> and pressure (P). Each system will consist of different phases (e.g., liquid, solid), where the total energy of the system is the sum of the energy constituents of the various phases ε = Σε_{ i } (V _{ i }, p _{ i }, m _{ ik }), where k denotes the respective constituents, for the respective phase i. This has analogies with Lord Kelvin’s (1824–1907) definition of temperature as the average kinetic energy (E) of a system, E = (1/2)mv ^{2} (3/2)k _{ b } T, where k _{ b } = 1.3806488 × 10^{−23}m^{2}kg/s^{2} k the Boltzmann constant.
[biomedical, chemical] Molecular structure principally consisting of carbon, hydrogen, and depending on the full macromolecular definition, including oxygen as an organic compound. Also referred to as saccharide. Examples of carbohydrates are sugars, wheat, and lactose. The carbohydrate designation is further subdivided in monosaccharides (e.g., glucose), polysaccharides (e.g., starch), disaccharides (e.g., lactose, sucrose), and oligosaccharides (e.g., inulin, also found specifically in AB blood and on the membrane of cells where they form a marker in cell to cell communications).
[atomic, biomedical, chemical, imaging] Organic element. Part of molecular structures such as graphite and diamond as well as carbohydrates and organic fuels. Major atomic building block in organic structures, biological organism are composed of molecular chains containing carbon in a large percentage. This stable element has by definition the atomic weight of 12.00000 atomic mass units (u). Stable carbon consists of 6 protons, 6 neutrons, and 6 electrons. Additionally, carbon isotopes are used in imaging applications since they will seamlessly integrate with the biological structure. Some of the available isotopes are ^{11}C and ^{14}C (see Figure C.15).
Figure C.15 Carbon is the building block of organic structures, as well as a fundamental ingredient for construction, (a) Log cabin made completely out of wood; (b) a tree; (c) a chameleon, biological life form; and (d) graphite tip of a pencil and a diamond earring.
[biomedical, chemical, imaging] This unstable carbon isotope has a half-life of 20.4 min and is used in positron emission tomography as a tracer in order to label physiological processes. The decay process of ^{11}C is by one positron.
[biomedical, chemical] Major atomic building block in organic structures, biological organism are composed of molecular chains containing carbon in a large percentage. The decay process of ^{4}C is by two electrons with a half-life of τ_{1/2} = 5,730years. The radioactive isotope ^{14} C occurs in normal living carbon structures as a common “cousin” with a ratio of 1.3 × 10^{−12} to stable carbon-12 (same as the atmospheric ratio), and is used as a standard tool for radioactive dating of organic structures. During normal metabolism the standard ratio of ^{14} C to ^{12}C is maintained while after cell death the ^{14}C will start to decay. Determining the remaining ratio provides the quantitative tools for radioactive dating.
[general, nuclear] Carbon isotope; 14C is produced in the upper atmosphere as 14N is bombarded by cosmic rays. (Note: standard carbon has atom mass 12.) The 14C drops to the Earth where it is absorbed by plants and animals. The 14C levels in an organism are constant throughout the organism’s life (since it continuously adds and removes 14C through nutrition and respiration). When an organism dies it can no longer replenish its 14C levels and the 14C begins to decay. Using the fact that the half-life for 14C is 5730 years, radioactivity levels of 14C are measured and the level of decay from the original value is used to estimate the organism’s age. This type of radioactive dating only applies to objects that have carbon as a base (primarily a metabolic base), not stones and such. There are however limitations to the accuracy and time range (see Figure C.16).
Figure C.16 Carbon dating of human skull.
[biomedical, fluid dynamics] Blood flow principle recognized by Adolf Eugen Fick (1829–1901) as the total volume ejected by the contracting heart per minute of time, expressed in liters per minute. The cardiac output (CO) is thus a function of both the volume of the ventricles and the heart rate (HR): heart rate multiplied by stroke volume (SV): CO = HR × SV. The heart ejects a volume of blood based on the muscular function of the cardiac muscle as well as the fluid dynamic constraints resulting from the vascular resistance and compliance in the whole body circulation. The circulation system comprises the aorta on the left ventricular side and the pulmonary artery on the right ventricular side, branching out into a web of arteries, arterioles, and capillaries, flowing under a combination of venules and veins, leading back to the left and right atrium by means of the pulmonary veins from the lungs (carrying oxygen-rich blood) and the hollow vein (superior vena cava), carrying oxygen-depleted blood, respectively. During exercise the cardiac output can increase by more than fivefold, depending on the training and general health of the individual.
[biomedical] See pacemaker.
[computational, thermodynamics] French physicist who provided essential insight on the practical applications of the second law of thermodynamics in 1824 and may be credited as one of the cultivating founders of the essence of thermodynamics. Carnot’s most remarkable asset is the theoretical description of a process that relies on the exchange of heat and the performance of work. The process has four (4) stages in an ideal mechanism; isothermal expansion during delivery of heat ( q _{ H }) at high temperature, followed by adiabatic expansion, with the third-stage isothermal compression, with heat exchange (i.e., loss) at low temperature heat ( q _{ L }); and the fourth phase adiabatic compression, ending up in the exact same energetic point in pressure and volume (pv plot) as where it left off. Work (w) is performed during the isothermal expansion of stage 1 as well as the adiabatic expansion of stage 2. Inertia or other stored energy mechanism provides for the stroke in stage 3. Since the described Carnot process is ideal there is a reality associated with the efficiency of working devices and hence an associated efficiency: e _{ c } = output of useful energy/delivered energy for the process = w/q = (Q _{ H } − q _{ L })/ q _{ h } . Examples of the efficiency of specific devices are as follows: electric motor 50%–95%; gas furnace for domestic heating 70%–85%; hydrogen-oxygen fuel cell 60%; nuclear power-plant 30%–35%; incandescent lamp 5% (see Figure C.17).
Figure C.17 Nicolas Leonard Sadi Carnot (1796–1832).
[thermodynamics] Identification parameter for the distribution of the energy “consumption” of a system, divided in two components: work performed on the external system and the disposal of the entropy received from both the external heat source and the entropy generated by the engine. The Carnot engine primarily operates based on internal temperature (T _{in}) and the external temperature that drives the process (T _{out}), yielding the Carnot coefficient, η_{Carnot} = (T _{out} − T _{in} )/T _{out}. This provides the entropy (S) generated by an irreversible process as S _{irr} = η_{Carnot} (Q _{out}/T _{in}), where Q _{ aix } represents the energy transferred out of the system.
[energy, general, thermodynamics] (syn.: work) {use: cooling, heating, thermodynamics} A four-stage process where a gas is expanded and contracted in two isothermal stages and two isentropic stages in interchangeable order. The Carnot cycle and Carnot engine principle were conceived by Nicolas LÉonard Sadi Carnot, a French scientist (1796–1832). The principles of the thermodynamics and the associated efficiency of energy exchange processes and resulting work were first described in 1824 (see Figure C.18).
Figure C.18 (a,b) Pressure-volume diagram for a Carnot cycle at a specific temperature.
[energy, thermodynamics] (syn.: work) {use: cooling, heating, thermodynamics} The Carnot engine consists of a cylinder and a piston, the compartment sealed off by the piston is filled with gas and the reservoir is exposed to either low or high temperature resulting in a heat exchange process. Alternating the heat exchange (cooling/heating) results in the periodic expansion and contraction of the sealed-off gas, moving the piston up and down.
[biomedical] Vascular surgeon from France, who invented the mechanism of blood oxygen exchange outside of the human body for which he received the Nobel Prize in Physiology and Medicine in 1912. This mechanism was adapted and incorporated in the first heart–lung machine developed by Dr. John Heysham Gibbon (1903–1973). Together with Charles Lindbergh (1902–1974) Carrel developed the first heart–lung machine in 1935.
[biomedical] Protein chains that facilitate the transport of molecules through the biological cell membrane at specific receptor sites. The respective individualized protein chains are highly specialized in the selection of molecules to transport. This transport system is classified as facilitated diffusion, an active process.
[general] Electromagnetic or acoustic wave in analog format that can be frequency or amplitude modulated to encrypt information for transmission to a remote receiver location. In digital format the mechanism of transfer is in bit rate, not in modulation. For television the transfer mechanism in the United States (in 2009) and in various other countries has changed from frequency modulation to digital encoding (using the same carrier wave for the respective channels/television stations). The carrier wave can be chosen to promote long distance propagation, whereas the modulation can be in the audible range or in a range that can be analyzed with some kind of spectral mechanism of action after the carrier wave has been removed by a demodulation scheme. In electromagnetic radiation amplitude modulation is used in am radio (150 kHz–26 MHz), whereas frequency modulation is used in FM radio (87.5 MHz– 108 MHz). General FM radio is transmitted in stereo. Radio stations perform the audio encoding for the transmission across the air ways to the audience. The stereo modulation is obtained at two separate audio frequencies: V _{left} and V _{right} (i.e., multiplexing) with respect to the pilot tone (V _{ p }), expressed as {0.9([(V _{left} + V _{right})/2] + [((v _{left} − v _{right})/2)sin(4πv_{ p } t)]) + 0.1sin(2πv _{ p } t)} × 75 kHz.The audio signal in FM radio transmission is between 30 Hz and 15 kHz, defined as HiFi, or high-fidelity. The HiFi standard was introduced in 1966 to set the standards for accuracy in frequency transfer (reproduction of the input signal to the consumer) and low signal-to-noise ratio. The converted multiplexed signal is recombined in a decoder, which is part of the radio receiver unit, and the output is transferred to an amplifier and relayed to speakers for the listening pleasure. Amplitude modulated radio waves generally have a short range, up to 200 km, whereas frequency modulated waves reaching into very short waves can travel extreme distances due to reflection from the ionosphere ranging from the opposite side of the world.
[general, mechanics] Coordinate system named after René descartes (1596–1650), using two planes (two-dimensional) or three orthogonal planes (three-dimensional [coordinates: x,y,z]).
[astronomy, general, geophysics] Mathematician, astronomer, and engineer from Italy, and geophysicist. He completed the work of Jean Picard (1620–1682) on the longitude and latitude angular division scale of the globe for cartography. In addition he discovered the split in Saturn’s ring which was aptly named after him. He presented a thorough theoretical description of the precision of the axis of rotation of the Moon as well as the rotation period of several planets. Giovanni Cassini is known for his contributions on the description of our solar system, specifically the discovery of four satellites orbiting Saturn. Cassini also discovered the division of the rings of Saturn (not a continuous belt), which are named in his honor: Cassini Division. As an engineer Cassini worked on water management (flow control for rivers; specifically the river Po in Italy, known for its devastating flooding) as well as set out a topographical map of France in 1670, to be completed by his grandson, after the continuation by his son, in 1789. Cassinis name was also used for the (to date) 10 year mission to Saturn, as well as the in situ investigation by the National Aeronautics and Space Administration, powered by the Cassini spacecraft (see Figure C.19).
Figure C.19 Giovanni Domenico Cassini (1625–1712).
[astronomy, general] French physicist, mathematician, and astronomer, son of Giovanni Domenico Cassini (1625–1712). Cassini provided a detailed mathematical description of curvature of various closed loop shapes, primarily oval, and irregular shapes in the general outline of figure eight. These contracted oval shapes are sometimes referred to as cassinoids.
[astronomy, geophysics] A system is defined as residing in a Cassini state when it is in compliance with the following three laws. The Moon revolves the Earth in a 1:1 spin-orbit ratio, meaning that the same side of the moon always faces the Earth. On second observation by giovanni Domenico Cassini (1625–1712) he found that the precession of the moon, describing a cone, is executed in a plane that intersects the elliptic orbit as a circle. The third conclusion from Cassini ’s observations was that the plane carved by the intersect from the normal to the rotational elliptic plane around the Earth with the plane described by the normal to the orbital plane around the Sun will contain the orientation of the rotational axis of the Moon as a function of location. These laws are known as the Cassini’s laws. This applies in the scope of the processes to the mean orientation of a synchronously locked satellite as well.
[astronomy, astrophysics, geophysics] Three sets of planetary motion rules described by Giovanni Domenico Cassini (1625–1712) in 1693, with mathematical geometric derivations of the position and orientation of the Moon with respect to Earth. The same rules have been applied in setting the configuration of geostationary orbits for earth’s satellites. With modifications these laws also appear to apply to the obliqueness of Venus as well. The moon’s axial rotation according to these laws is constrained as follows: (1) The Moon spins at a uniform rate that matches its mean orbital rotation rate; meaning the same side of the Moon always faces the Earth. (2) The normal to the moon’s equatorial plane subtends a fixed angle with the normal to the ecliptic plane as θ = 1.59°. (3) The normal to the moon’s equatorial orbital plane, the normal to general orbital plane of the Moon, and in addition to the normal to the ecliptic lunar plane form three coplanar vectors that are orientated in such a manner that the vector describing the ecliptic lunar plane is confined by the other two planes.
[astronomy, astrophysics, general] The location of the Cassiopeia constellation is found in reference to the North Star (Polaris) (Polaris is fixed in our view of the northern sky), which is part of the ursa minor (little dipper), with ursa major (big dipper) to one side and Cassiopeia of the lower other side (the relative position will change with the seasons as the rotational axis of the earth pivots [precession]); to the right in summer and to the left of Polaris in winter. The shape of Cassiopeia is more or less a flattened “W” (see Figure C.20).
Figure C.20 Outline of the constellation Cassiopeia.
[fluid dynamics] Relatively unknown fluidic behavior engineer who published his model of viscous behavior in 1959, known as the Casson model, or the fluids as Casson fluids.
[biomedical, fluid dynamics, general] Non-Newtonian flow model of colloid suspensions such as blood, dough, and chocolate under low shear rate. The viscosity is defined as ${\text{\eta}}_{\text{visc}}=\left({\text{\sigma}}_{s,0}/\dot{\text{\gamma}}\right)+\sqrt{\left({k}_{C}{\text{\sigma}}_{s,0}/\dot{\text{\gamma}}\right)}+{k}_{C}$
where σ _{ s,0} is the material yield stress, $\dot{\text{\gamma}}$ the shear rate, and k _{ C } the Casson constant or Casson rheological constant. Note that based on the FÅhraeus–Lindqvist effect the determination of the apparent viscosity is a function of the device and methods used to derive the viscosity. Specifically there are four primary device mechanisms in use to determine the viscosity: two concentric rotating cylinders; rotating disk with respect to stationary plane separated by a liquid thickness; rotating cone with respect to stationary plate; and measure of flow rate through a capillary tube (also see viscosity modfx ). It is also known as Casson equation.[general] Computerized axial tomography, also known as CT scan or X-ray tomography. x-ray image reconstruction resulting from multiple sequential or parallel transmission measurements at incremental angles completing a 360° circumferential scan. The computational component is in the calculation of the intersects of lines from various (multiple and incongruent) angles for identification of points in the two-dimensional dissection plane that have equal attenuation, providing the triangulation for the location of the anatomical features for the image reconstruction. The axial component is added by moving the scanning array in the axial direction by discrete stages, or through the use of multiple x-ray sources and detector arrays that are stacked in a scanning belt. Once all the measurements have been acquired from 360° circumferential scans as well as axial increments, a three-dimensional reconstruction is performed by means of a computer program that renders a visualization. The visualization can be selected by choosing slices at azimuthal and zenith angular orientations in order to identify regions with x-ray density that is different from the normal distribution peak or that are sharply distinguished from the neighboring volumes (see Figure C.21).
Figure C.21 CT scanner x-ray machine.
[biomedical, chemical, electronics, general] Negatively charged electrode, usually accompanied by the positively charged anode, as introduced by Michael Faraday (1791–1867). The word “cathode” comes from the Greek word for “the direction in which the Sun sets.” Both the cathode and anode submerged in a solution of acid, salt, or base will divide the constituents of the respective electrolyte(s) based on the sign of the charge. The positive (cation) and negative (anion) charged ions will diffuse respectively to the cathode and anode under the influence of the applied electric field resulting from an external electrical potential source (e.g., battery, chemical reaction), which is required to be stationary in order to induce the ionic migration. When direct current (consisting of electrons) between the electrodes is applied to pure water the electric charge gradient between the cathode and the anode will result in ionization of the water (4H_{2}O ⇄ 2HO^{−} + 2H^{+} + 2H_{2}O ⇄ 2(H_{3}O)^{+} + 2HO^{−} ⇄ 4O^{2−} + 8H^{+} ↔• 4O_{2} + 8H_{2}), which is a poor conductor The formation of the (h_{3}o)^{+} ion is temporary, and is due to the inherent attraction between the polarized water molecule and the hydrogen ion with positive charge (cation). Upon reaching the respective anode and cathode, the respective cation and anion will lose their charge in exchange with the electrodes and form oxygen (o_{2} ) and hydrogen molecules (h_{2} ). The electrolysis of water can be enhanced by the addition of an acid, such as carbonic acid, sulfuric acid, nitric acid, or perchloric acid. The speed of the electrolysis will greatly depend on the strength of the acid (acidity) expressed in ph. Electrode will be at negative electrical potential, with respect to the anode which is at a positive electrical potential. A heated cathode will emit electrons, forming cathode rays. The electron emission will provide a free space current, with current density J, which can be calculated with the use of Richardson’s law, $J=\left(1-\tilde{r}\right)\left(4\text{\pi}e{m}_{e}{k}_{b}^{2}/{b}^{3}\right){T}^{2}{\text{e}}^{-\left({\text{\varphi}}_{\text{elec}}\text{/kT}\right)}$
, also referred to as drift current density or displacement current density; defined as a function of temperature T, using Boltzmann coefficient k _{ b } = 1.3806488 × 10^{−} m kg/s^{2}K; electron charge equivalence, e = 1.60217657 × 10^{−} C; φ_{elec} the work function; electron mass, m _{ e } = 9.10939 × 10^{−31} kg; h = 6.62606957 × 10^{−34} m^{2}kg/s the Plancks constant, and $\tilde{r}$ the mean reflection coefficient for the material surface ( $\tilde{r}\cong 0.5$ for tungsten). The concept of displacement current also applies to the time-dependent Maxwell equations (see Figure C.22).Figure C.22 Cathode ray vacuum tube.
[atomic, nuclear] Low-pressure glow discharge first described in 1675 by the French astronomer Jean Picard (1620–1682). It wasn’t until 1870 that Sir William Crookes (1832–1919) provided a formal description of the cathode glow, and introduced the investigational electrode tube, the Crookes tube. The Crookes tube was the predecessor to the modern neon light signs.
[biomedical] Vacuum tube with a cathode that emits electrons and a hollow anode to provide a projectile electron (electron gun) that can be deflected by electrodes before it impacts a fluorescent screen. CRT was the elementary component in old-fashioned televisions and oscilloscope screens. The monitors predating the flat-panel display, plasma screen, and LED screen are referred to as CRT screens. CRT screens are bulky and heavy due to the large amount of glass and electronics involved. Additionally due to the construction of the CRT mechanism of action these devices are consuming a significant amount of electrical energy, with inherent generation of heat (see Figure C.23).
Figure C.23 CRT computer monitor attached to a camera mounted on an optical microscope.
[atomic, nuclear] Electron beam, emitted from the cathode in a vacuum tube or Crookes tube (after Sir William Crookes [1832–1919]).
[chemical, electronics] Ion that is attracted to the cathode, hence carrying a net positive charge. The process of ion diffusion applies in particular to electrolysis and atmospheric air ionization coronas.
[general] Mathematician, physicist, and engineer from France. Cauchy provided significant details on the description of stress and strain on microscopic scale based on the initial macroscopic definitions by Robert Hooke (1635–1703) more than a century prior in 1676. Another mathematical contribution by Cauchy is the solution method based on the residues of the developed series with respect to a function (see Figure C.24).
Figure C.24 Drawing of Augustin-Louis Cauchy (1789–1857).
[computational, fluid dynamics, general] Mechanism of complex function analysis named after Augustin-Louis Cauchy (1789–1857). The “residue” theorem applies to solving integrals over closed curves in the complex domain. Consider a function (ƒ) that is analytic and holomorphic inside the curve of the domain carved out by the integral loop as well as on the points of the curve of the closed integral path, but is not analytic in the points inside the curve within the complex domain z _{ j } =Xj + iy _{ j }: excluded points z _{1}, z _{2}, …, z _{ n } (i.e., singular points). The function can be developed in a Laurent series as: $f\left(z\right)={\displaystyle {\sum}_{n=-\infty}^{\infty}{a}_{n}{\left(z-{z}_{j}\right)}^{n}}$
where the coefficient of a _{−1} with respect to 1/(z − z _{0}) is the residual of the function f(z) in z _{0}; Res[ƒ, z _{0}] = a _{−1}. For instance the Laurent function for f(z) = e^{ i/z } around the point z _{0} can be written as f(z) = 1 + (2^{1}/1!)(1/z) + 2^{2}(1/2!z ^{2}) + 2^{3}(1/3!z ^{3}) + … with Res[ƒ, z _{0}] = a _{−1} = 2. The Cauchy method of residues is described by the algorithm: ${\int}_{C}f\left(z\right)dz}=2\text{\pi}i{\displaystyle {\sum}_{k=1}^{n}\text{Res}\left[f,{z}_{j}\right]$ , where the residue of the function f at any point z _{ j } is Res[ƒ, z _{ j }]. This is also tied to the Cauchy integral f(a) = 1/2πi∮ ƒ(z)/(z − a)dz (see Figure C.25).Figure C.25 The Cauchy residue method.
[engineering, fluid dynamics] This number identifies regimes in fluid flow where compressibility is a factor of influence, named after a contributor in the field Augustin-Louis Cauchy (1789–1857). This number describes the relative importance of inertial and elastic forces under compressible flow conditions; in fact the ratio of the inertial forces to the compressible forces. The Cauchy number is a function of the fluid density (ρ), as well as the flow velocity (v) and the elastic modulus of the fluid medium (E). The Cauchy number is closely related to the mach number and is often expressed as the Mach number to the second power.
[fluid-dynamics, mechanics] $\text{\epsilon}=\nabla \overrightarrow{v}+{\left(\nabla \overrightarrow{v}\right)}^{T}\sim E$
, where E is the Lagrangian finite strain tensor and $\overrightarrow{v}$ the deformation or flow velocity (solid respectively fluid).[computational, fluid dynamics] Mathematical problem introduced in 1815 by Augustin-Louis Cauchy (1789–1857) and Simeon Denis Poisson (1781–1840) regarding the wave propagation on a (slighdy compressible) liquid at the surface, with finite depth (h). The displacement follows from the local pressure (P) and density (ρ) as P/ρ = (∂φ/∂t) − gz + F(t), under the condition that the Laplace derivative of the velocity potential (φ) equals zero ∇^{2}φ = 0, z the vertical displacement, x and y the propagation directions, g the gravitational acceleration, and F(t) the time-perturbed influence function (e.g., storm). As boundary conditions the displacement pressure will satisfy ξ = 1/g[∂ϕ/∂t]_{ z=0}, as well as ∂ξ = −[∂φ/∂t]_{ z=0}. The solution can be written with the use of a Bessel function of zeroth order ${J}_{0}\left(k\text{\varpi}\right)$
, $\text{\varpi}=r\mathrm{sin}\text{\theta}$ ; the surface rotational displacement, wave with curve of radius r, respectively z = −rcosθ), using the wave number k = 2π/λ, where λ represents the wavelength, provided $\text{\varphi}=gt/2\text{\pi}{\displaystyle {\int}_{-\infty}^{\infty}\left\{k-\left(g{t}^{2}/3!\right){k}^{2}+\left[{\left(g{t}^{2}\right)}^{2}/5!\right]{k}^{3}-\cdots \right\}{\text{e}}^{kz}{J}_{0}\left(k\text{\varpi}\right)dk\approx \left(gt/2\text{\pi}\right)\left\{\left[{P}_{1}\left(\mathrm{cos}\text{\theta}\right)/{r}^{2}\right]-\left(g{t}^{2}/3!\right)\left[2!{P}_{2}\left(\mathrm{cos}\text{\theta}\right)/{r}^{3}\right]+\left[{\left(g{t}^{2}\right)}^{2}/5!\right]\left[3!{P}_{3}\left(\mathrm{cos}\text{\theta}\right)/{r}^{4}\right]\right\}}$ , after developing the pressure in a series, while the displacement satisfies $\text{\xi}=t/2\text{\pi \rho}{\text{\varpi}}^{3}\left\{1-\left[{\left(1\right)}^{2}{\left(3\right)}^{2}/5!\right]\left[\left(g{t}^{2}\right)2/\text{\varpi}\right]+\left({1}^{2}{3}^{2}{5}^{2}/9!\right)\left[{\left(g{t}^{2}\right)}^{4}/\text{\varpi}\right]-\cdots \right\}$ , which for $\left(g{t}^{2}\text{/}2\text{\varpi}\right)\gg 1\text{\hspace{0.17em}}\text{yields}:\text{\xi}=\left(g{t}^{3}\text{/}{2}^{7/2}\text{\pi \rho}{\text{\varpi}}^{4}\right)\mathrm{sin}\left(g{t}^{2}\text{/}4\text{\varpi}\right)$ . Note that the wavefront can be described by $r=t\sqrt{\left(gb\right)}$ .[computational, fluid dynamics] Based on the Cauchy integral f(a) = (1/2πi)∮ f(z)/(z − a) dz, and the fact that holomorphic functions are analytic it follows f ^{ n }(a) = n!/2πi ∮ f(z)/(z − a)^{ n+1} dz. For an arbitrary disk $\left(\mathbb{D}\right)$
within the closure (ℂ) of the integrand it can be shown for $\text{\chi}\in \mathbb{D}\subset \u2102$ , for which $f\left(\text{\chi}\right)=1/2\text{\pi}i{\displaystyle {\int}_{\mathbb{D}}\left[f\left(z\right)\text{/}\left(z-\text{\chi}\right)\right]dz+1/2\text{\pi}i}{\displaystyle \int {\displaystyle {\int}_{\mathbb{D}}\left(\partial f\left(z\right)/\partial {z}^{\prime}\right)\left[dz\wedge d{z}^{\prime}/\left(z-\text{\chi}\right)\right]}}$ , where ∧ is the “logical” “and” for the integration constraints to the complex function. The latter integral provides the tools to solve the Cauchy-Riemann equations with respect to two variables, u(x, y) and v(x, y), as expressed in the thesis by the German mathematician Georg Friedrich Bernhard Riemann (1826–1866) in 1851, based on the work by Jean le Rond d’Alembert (1717–1783) published in 1752, Leonard Euler (1707–1783) published in 1779, and with finishing touches by Augustin-Louis Cauchy (1789–1857) in 1814. The Cauchy-Riemann equations are expressed as = ∂v(x, y)/∂y and ∂u(x, y)/∂y = −∂υ(x, y)/∂x, with respect to the complex number z = x + iy;as ƒ(x + iy) = u(x, y) + iv(x, y), a holomorphic function.[general] Scientist, chemist, physicist, and British nobleman of French origin, one of the wealthiest men of his days. Cavendish derived the universal gravitational constant in 1728 as6.75×10^{−11} Nm^{2}/kg^{2}, compared to current day accepted standard, 6.67259 × 10^{−11}” Nm^{2}/kg^{2} (see Figure C.26).
Figure C.26 Lord Henry Cavendish (1731−1810). (Courtesy of George Wilson.)
[biomedical] Location of actively formed invagination in the cell membrane to support the endocytosis processes. The process results in the formation of vacuole or vesicles used to transport solid or liquid material intended for consumption or processing.
[biomedical, fluid dynamics, general] Sudden decrease in volume (collapse) of expansion (e.g., mechanical deformation or vapor bubble; nucleation) that exerts forces on the surrounding media and materials. Generally the formation of bubble progresses at a slower rate than the collapse, providing a unique mechanism of mechanical interaction. Cavitation may result from interaction of ultrasound pressure wave with soft materials (i.e., initiated by mechanical forces), specifically biological media. Additional occurrences of cavitation can be described resulting from thermal ablation processes, specifically short duration events, such as pulsed laser ablation (i.e., initiated by thermal expansion). The cavitation process is accompanied by shear waves that will obey the wave equation with associated propagation of effects. Depending on the material properties the wave can be critically damped ranging to undamped. Cavitation can provide mechanical effect as well as chemical changes. The collapse of a spherical bubble can be associated with a kinetic energy (KE) that is a function of the rate of change over time (t) of the bubble radius (r = r(t)) expressed as r = dr(t)/dt, with respect to the initial radius R_{0} with associated internal pressure P _{1}, defined using the density ρ = ρ(t) as KE = 2πρr ^{3} ṙ ^{2} = (4/3)πP _{1} (R_{0} ^{3} − r ^{3} ). The true nature of the bubble collapse is more intricate, specifically when involving ionized plasma created during an ablation process (e.g., laser vaporization) or when condensation occurs during the size reduction of the bubble. During condensation the density of the vapor bubble changes and hence other conservation laws need to be included in the theoretical evaluation process. The rate of change in bubble diameter can be described as a wave phenomenon. Assuming the special case of adiabatic expansion/collapse the rate of change is captured by a surface velocity equivalent (i.e., ${{\upsilon}^{\prime}}_{s}=\sqrt{\left({P}_{1}/\text{\rho}\right)}$
; “constant” parameter with the dimensions of velocity) in second-order derivative $\left(\ddot{r}={d}^{2}r/d{t}^{2}\right):r\ddot{r}+\left(3/2\right){\dot{r}}^{2}={{\upsilon}^{\prime}}_{s}^{2}{\left({\text{R}}_{0}/r\right)}^{3{\text{\gamma}}_{a}}$ , where γ_{ a } represents the adiabatic factor (defined as the ratio of the specific heat [ c _{sp} = Q/mΔT, describing the heat (Q) required to change the temperature (T) of a mass ( m ) by 1 K] of the gas in two phases of the rarefaction vs. expansion processes), which ties pressure and density together as $P/{P}_{0}={\left(\text{\rho}/{\text{\rho}}_{0}\right)}^{{\text{\gamma}}_{a}}$ . The rate of heat exchange of the bubble to the surrounding liquid medium is primarily subject to the Nusselt number (Nu) of the system. The force (F) exerted by the cavitation process at any specific point in the collapse is directly proportional to the momentary change in kinetic energy (W = ΔKE, i.e., the work) over the distance traveled by the surface of the bubble captured by incremental delta in radius (Δr), W = FΔr (see Figure C.27).Figure C.27 Cavitation process for bubble generated by laser heating resulting from nanosecond laser pulse.
[energy, fluid dynamics] Ratio of “static pressure” gradient in relation to KE density, where P is the local pressure, P _{ v } the fluid vapor pressure, v _{flow} the flow velocity (average), ρ the fluid density. In addition to pipe flow, especially in a curved vessel, this will also be very useful in determining the impact of shape and angular velocity in propeller action. Even though this may resemble the Euler number the functionality is entirely different.
[computational, electronics, quantum, solid-state] See charge-coupled device.
[electronics, fluid dynamics, optics, quantum, solid-state] Charge-coupled device semiconductor structure from which the top layer has been removed which makes the charge layer light sensitive and can be used in array form to capture images that are limited in resolution by the number of ccd unites in the array or matrix format (see Figure C.28).
Figure C.28 Picture of digital camera using ccd element for registration of light spectrum and radiance.
[general, optics] Correlated color temperature. The color appearance of light emitted by a source, primarily a lamp. The color of source light is related to the emission from a reference source heated to a particular temperature, measured in Kelvin (K). The correlated color temperature classification for a light source, however, does not give information on its specific spectral distribution, more so on the appearance of the color of objects illuminated by the source. Two lamps may visually appear to be the same color, while the respective visual experience of object colors can be significantly different (also see vision) (see Figure C.29).
Figure C.29 Correlated color temperature map: (a) CIE 1931 x, y chromaticity space. (b) Color chart outlining the difference between the CMYK standard (cyan–magenta–yellow–black), for instance, used in dyes with a subtractive character, and the RGB (red–green–blue) standard.
[astronomy/astrophysics, general, mechanics] Any object in galactic space, ranging from planets (e.g., Earth) to galactic dust and stars. The escape velocity for an object from any celestial body with mass M is the minimum speed (v _{ e }), in perpendicular direction, required to overcome the gravitational attraction of the body with radius R and gravitational constant G and can be defined as ${\upsilon}_{e}=\sqrt{\left(2GM/R\right)}$
. Note that the release from higher altitude (e.g., from a plane at cruising altitude) changes the radius (r) factor to the location specifics, which becomes $\sqrt{2}$ times the orbital equilibrium velocity $\left({\upsilon}_{\mathrm{tan}}\right):{\upsilon}_{\mathrm{tan}}=\sqrt{\left(GM/r\right)}$ for stationary orbit, where centripetal (tangential) force balances the gravitationally confined orbital force (see Figure C.30).Figure C.30 A full moon (celestial body) in the eastern sky.
[biomedical, chemical, energy, solid-state] There are several types of cells to be defined: primarily we are familiar with the biological composition of single- and multicell organisms and secondarily the charge pump cell in a battery needs to be considered. The biological cell has a lipid–protein dynamic bilayer forming the cell membrane that encloses the intercellular fluid, which may contain the nucleus with genetic information and physically adjusts to external shear force and strain, reinforcing weak spots as well as providing a mechanism to actively move the cell by means of changing the configuration of the enclosure. Cells can grow and form semipermanent adhesions to other structures and other cells. The ameba is an example of a single-cell organism, whereas the species Homo sapiens has a multitude of specialized cells that form organs, supporting structures, muscles as well as a highly configurable communications network. For a battery the electrical potential that can be achieved is a function of the materials used, the half-cell potential. In biology the half-cell potential is derived from the Nernst potential equation for the specific ions in place at either side of the cell membrane: ε_{ion} =(RT/FZ_{ion})ln([Ion]_{out}/[Ion]_{in}), where R = 8.3144621 J/Kmol is the gas constant, F = 9.64853399 × 10^{4} C/mol is the Faraday constant, z _{ion} the ionic charge, [Ion]_{ i }. represent the concentration of a specific ion, respectively, on the outside or inside of the cell membrane and T the absolute temperature. At the body temperature of 37°C, the equation yields ε_{ion} = 61.5 × ln([Ion]_{out} / [Ion]_{in}), which provides for chlorine with respective intracellular concentration [Cl^{−}]_{in} = 9.0 mM, and extracellular concentration ${\left[{\text{Cl}}^{-}\right]}_{\text{out}}=125.0{\text{mM;\epsilon}}_{{\text{Cl}}^{-}}=-70\text{mV}$
, which can be experimentally verified. The galvanic half-cell potential is ${\text{\epsilon}}_{\text{ion}}=\text{RT}/F\mathrm{ln}\left({a}_{\text{ion}}/\sqrt{\left({p}_{\text{ion}}/{P}^{0}\right)}\right)$ , where a _{ion} = exp[(μ_{ i } − μ_{ i } ^{⊖})/RT] is the “activity” of the ion solution with the chemical potential ${\text{\mu}}_{i}={\left(\partial G/\partial {N}_{i}\right)}_{T,P,{N}_{j\ne i}}$ . (also known as the partial molar energy) where G represents the Gibbs free energy and N _{ i } the particulates for the respective constituents under the operational conditions (concentration [ion], pressure [P], and temperature [T]) and with respect to a chosen standard state μ_{ i } ^{⊖}, representing the partial solution as if it responds as an ideal chemical solution, P _{ion} is the partial pressure of the ionic solution respectively gas, expressed in Pascal, and P ^{0} is the standard pressure 10^{5} Pa. The half-cell potential can also be defined in terms of acidity (ph) of the solution as ε_{ion} = −(ΔG ^{⊖}/nF) − (0.05916/n)log({a _{ A }}^{ a } {a _{ B }}^{ b } /{a _{ c }}^{ c } {a _{ D }}^{ d }) − (0.05916h/n)pH, where the number of released electrons is described by n as in the chemical process: aA + bB + n[e ^{−}] + h[H ^{ + }] ⇄ cC + dD, describing the range of chemical constituents and their respective quantities in the reaction (see Figure C.31).Figure C.31 Biological cell.
[biomedical, electronics] In biological media there are certain cellular configurations that allow the individual cells to respond to electrical influences that are extremely small in magnitude. One specific example is the sensory organ in the head of certain sharks that can detect electric field strengths as small as 10^{−6} N/C. In comparison the background radiation in outer space is ~3×10^{−6} N/C, the electric wiring in the average household produces field strengths in the order of 10^{−2} N/C, and lightning produces approximately 10^{4} N/C. The sensory perception of the shark provides capabilities to detect muscle contractions from several kilometers distance.
[biomedical, nuclear] Cells respond to radiation depending on the type of radiation (a [Helium ion]; β [electron]; γ [EM radiation]; etc.) and dose. Additionally, radiation exposure is cumulative, leading to a slow build-up before catastrophic response is achieved. Damage can be affected on the cell membrane and on the dna, as well as total cell death. Damage may be reversible or irreversible. Although the initial deposition of the energy may be very short (order of 10^{−17}s), the large-scale implications are directly proportional to the energy of the applied radiation and the mechanism of action: particle or electromagnetic radiation. The biological change in specific cells as a result of radiation may occur after a latent period. The duration of the delay in time depends on initial and cumulative dose and may vary, depending on the type (i.e., energy) of the radiation ranging from minutes to years. One specific radiation response may be an altered communication behavior, changes in the chemical responses.
[biomedical, chemical, fluid dynamics, mechanics] Cell to cell interaction (e.g., communication) is mediated by cell junctions that provide a mechanism for protein binding (e.g., ligands) and define the response to deformation. Cell junctions are regions in the cell membrane of a biological medium that are enriched with specific proteins that provide a means of interaction (signal exchange, electrical or chemical, and potentially optical) between two adjacent cells. They also provide a mechanism to sustain shear stress (σ_{ s }), which is of particular importance in the gastrointestinal tract (GI tract) and blood vessels. The shear stress is a function of the viscosity (η) of the fluid in motion, the flow (Q), and the radius (r), σ _{ s } = 4ηQ/πr ^{3}. The resistance to shear stress characterizes the specific cell junctions, in particular for the lumen in question. Three types of cell junctions can be identified: (1) desmosomes, (2) tight junctions, and (3) gap junctions. Desmosomes (zonulae adherens) are located in tissues that are under the influence of shear stress, for instance the skin and GI tract. The desmosomes are proteins that form a strong intercellular bond as well as a strong bond to the basal lamina (extracellular matrix [ECM] layer that is formed by secretion from the epithelial cells). Desmosomes provide a regenerative/reconstructive mechanism to the cell membrane under deformation, in particular with respect to the organization of the cytoskeleton. Tight junctions on the other hand are found in tissue providing a specific exchange function, such as the kidney (nephron cells), the endothelial cells in the blood vessels (nutrients, oxygen, waste exchange) as well as the nutrient resorption by the enterocytes in the GI tract (intestines). Tight junctions have specific functions to prevent the movement of proteins in the cellular membrane, in particular those that serve an apical function (chemical sorting function, for instance found in the Golgi complex [also known as Golgi apparatus]; named after the Italian scientist and physician Camillo Golgi [1843–1926]). Gap junctions are found for instance in the organ of Corti in the cochlea of the ear, supporting the signal transduction in response to deformation by movement of the hair cell. Gap junctions are composed of six connexin proteins (Cx) that form hemichannels, also known as connexons. The connexons will align for proper sharing of cytoplasm between neighboring cells. The sharing mechanism is based on small molecules (<1000Da) and ions providing both electrical and chemical signal transduction through “messengers.” Generally, the gap junction transfer of molecules and ions does not require energy; however, the hearing effort is certainly facilitated by the ATPase activity and recycling of K^{+}ions. The gap junction provides a selection mechanism for which ions may pass by means of polarization of the connexions and the molecular orientation. In addition to the interaction with adjacent cells by means of the cell junction, the cell junctions also support communication with ECM. ECM is one of the key components for multicellular organisms and is composed of a collection of extracellular molecules that is purposely secreted by cells and provides both biochemical and structural support. ECM is composed on any or multiple of the following constituents: collagens, fibronectin, laminin, as well as vimentin and vitronectin. Cells are attached to the ECM by means of iNTEGRiNS (transmembrane receptor molecule acting as a bridge between cells and between cells and the ECM). The integrins provide a chemical response to shear stress (deformation), which is specific for the transmembrane receptor kind. Finally, the cell junction provides interaction with the cellular scaffolding, also known as cytoskeleton, which is an integral part of the cellular structure and support the intracellular transport as well as support cell division. The cellular scaffolding comprise three kinds of filaments: microfilaments, intermediate filaments (IF), and microtubules. The microfilaments form a support mechanism by integrating with the double-helix actin chains in the vicinity of the cellular membrane. The microtubules provide the transportation support. All components of the cellular scaffolding support the shape and in particular the resistance to deformation and tension. The membrane resilience to deformation can be defined by the membrane stiffness (Ei) and the deformation length L as F = 3Ei/L ^{2}. The function of the cytoskeleton in this regard is the restructuring of the cell membrane to compensate for tension by means of actin (F-actin, a component of the cytoskeleton), IFs, and microtubule filaments. Specifically, the IFs provide a membrane “motor function,” providing molecular realignment and thickening of the cell membrane in compensation for the applied deformation. The adjustments are made in steps in the order of 8 nm with local force applied by the cytoskeleton in response to the cell junction efforts in the order of 6pN.
[biomedical] Lipid–protein bilayer that encloses the cellular plasma and in most cases a nucleus containing the biological dna. The membrane is a living structure that can adjust to chemical challenges as well as mechanical influences resulting from both internal and external forces. The cell membrane accommodates chemical and particulate transport through endocytosis next to facilitated gated transport through pores. Mechanically, the cell can modify its cell membrane to become resilient to local stress and strain resulting from external influences on both microscopic and macroscopic scale. The macromolecular structure provides an elastic configuration that supports an active lifestyle. External forces can be found resulting from high-frequency vibrations, as well as pressure gradients resulting from local osmotic pressures as well as gravitational influences. Additional external forces may result from fluid flow resulting in shear stress. Internal forces include the chemical configuration making up actin and myosin to form cytoskeletal cables that orchestrate cellular movements as well as morphological changes. Other external influences include hydrostatic pressure and adhesion from neighboring cell, next to growth. A free (nonenclosed) body of liquid is subject to Laplace law, whereas the cell membrane forms an equilibrium by means of both stretch and modification. The tensile force ( f _{ t }) on the membrane for this situation is expressed as F _{ t } = K _{ a }(ΔA/A _{0}), where ΔA is the increase in surface area for the bilayer with respect to the original area A _{0} and K _{ a } is the area expansion constant (range: 10^{−1}–10^{1} N/m), where the tension 3 × 10^{−3}N/m < F _{ t } < 3 × 10^{2}N/m. With surface area expansion the membrane thickness (d) will change proportionally, Δ a/a _{0} = Δd/d _{0}, where the response to shear stress of the membrane describes it as an elastic solid (see Figure C.32).
Figure C.32 Artist impression of the design of a biological cell membrane.
[biomedical] Regenerated cellulose acetate, used as a filtration mechanism in the early days of dialysis machines (~1930s), following the recurring infection rate when using peritoneal membranes (obtained from the abdominal lining).
[computational] System definitions with an abstract foundation that are used in discrete mathematics problem solving. These concepts are equivalent to the field concept in field equations in general physics. Another analogy may be drawn with respect to the wavelet concept in signal processing, which is both place and time confined. Under this computational approach, the space is divided into a uniform matrix format that contains array parameters which are called the “cells.” Each cell is associated with a state variable defined in digital format. For each cell, time progresses in incremental steps, not continuous, and frequently relies on a “look-up” table as the provider for the definition of the state. The fact that the system can be solved for a finite number of steps in time with respect to a finite segment of the system lends this mechanism ideal for parallel computing, and for that matter for cluster computing, since all system segments are defined to be noninteractive, each with the same local and uniform sets of rules.
[biophysics, chemical, energy] Biological cells communicate with neighboring cells as well as with the autonomic and parasympathetic nerve system to regulate their own metabolic and reproductive activity as well as balance with the organ or tissue they are an integral part of. In addition, the cells regulate their natural chemical and energetic balance by secretion of chemical signals as well as electronic charges which interact with its cellular membrane and the extracellular conditions. The extracellular conditions can involve the secretion of hormones or the opening or closing of ports on the cell’s own or neighboring cell’s membranes (phagocytosis, pinocytosis, active processes as well as the action potential specifically). Some of the signaling processes involve soluble factors, primarily proteins, other are ionic in nature. Some of the signaling processes are identified by their specific mechanism as follows: autocrine, hormonal, paracrine, and synaptic signaling.
[biomedical, chemical] Artificially constructed as well as naturally occurring polymer. Polymer materials that are degradable and biocompatible, made from β-d-glucose (6-carbon sugar) monomers, that is, polysaccharides, are called cellulose. The long molecular configuration provides cellulose with its inherent strength. Cellulose is the main component forming the cellular matrix of plants cell walls. Cotton is a more specific example of naturally occurring material composed of cellulose. This material was used in artificial lung devices developed in the 1950s and 1960s to generate a semipermeable membrane from the transport of oxygen to blood in an extracorporal system. Additional applications are found in drug delivery, sutures, tissue engineering, and bandages and wound dressings. Cellulose can be reconstituted with chemical treatment to break lignin bonds and reformed with the aid of alkali media or bisulfites, followed by cross-linking the cellulose fibers to form paper (see Figure C.33).
Figure C.33 Raw cotton with greater than 90% cellulose content.
[biomedical, chemical] Acetate ester formed from cellulose, which can be reconstituted to form cellophane. Cellulose acetate was first produced in 1865. Cellulose was made to react with acetic anhydride to form cellulose acetate (one of the foundation materials used in the production of photographic emulsions). Several applications are available under commercial names. Other examples of applications of cellulose acetate are in textiles (often in blends with other materials, such as cotton and nylon), cigarette filters, and frames for eye glasses. Cellulose acetate can be spun into strands for weaving, for instance, acetate rayon.
[biomedical, chemical] Chemical result of the treatment of cellulose with sulfuric acid and nitric acid. Chemical component used in the construction of extremely thin microporous membranes, for instance used to encapsulate artificial biologically active components such as sensing chemical element transducer lining with the chemical ligands separated from the transducer. Other applications are in paint (lacquer) and explosives. Cellulose nitrate can be used to produce transparent film sheets and light-sensitive “transparent” sheets and roles used in cameras. With age, chemicals degrade, culminating in the release of acidic by-products such as nitric oxide, makes the cellulose nitrate unstable and highly flammable, it will even burn under water. It is also known as nitrocellulose, guncotton, flash cotton, or flash paper.
[general, thermodynamics] Astronomer from Sweden, generally known for his introduction of the Celsius scale used in temperature measurement. Anders Celsius followed the inspiration of Carlos Renaldini [Rinaldini] (1615–1698) who performed his temperature measurements at least 50 years prior. Another contemporary metrologist was Daniel Gabriel Fahrenheit (1686–1736), competing in the English culture with the Fahrenheit scale (see Figure C.34).
Figure C.34 Painting of Anders Celsius (1701–1744).
[general, thermodynamics] Generally accepted measure for temperature (T) in household use, established by Anders Celsius (1701–1744) as the total range of observable expressions of average molecular ke defined as temperature (T = (2/3k)Ē, where k _{ v } = 1.3806488 × 10^{−23} m^{2}kg/s^{2}K is the Boltzmann constant) in relative format as introduced in 1741. Sometimes one may still find Celsius defined as centigrade. The principle of measuring temperature by means of liquid expansion can be attributed to the Italian scientist Ferdinand II de’ Medici, the grand duke of Tuscany (1610–1670), dating back to approximately 1654. The temperature scale generally uses three points as reference to define the temperature. The Celsius scale uses the boiling point of water at 1 atmosphere pressure (T _{boil} ≡ 100°c); the phase transition point from solid to liquid for H_{2}O recognized as the melting point, also referenced as the freezing point (T _{me}ı, ≡ o°c); and additionally the triplet point for water is expressed with respect to the Kelvin temperature scale as TTriplet ≡ 273.16 K. The Celsius scale is the range of temperatures from melting point to boiling point subdivided in 100 incremental steps. Other temperature scales are the Fahrenheit scale introduced by Gabriel Daniel Fahrenheit (1686≡1736) in 1717 (still used in the United States) as well as the absolute Kelvin scale, next to scales from past exercises; Reaumur (defined by the French scientist René-Antoine Ferchault de Reaumur [1683–1757]) and Rankine (defined by the Scottish scientist William John Macquorn Rankine [1820–1872]). The thermometer used to express the Celsius scale uses either alcohol or mercury in a closed tube, relying on linear thermal expansion (Δℓ = α (T _{2} − T _{1} ), where α is the linear expansion coefficient and ℓ the length of the medium) of the medium to indicate a magnitude when lining up with a calibrated scale according to the Celsius definitions. The first thermometer invented is attributed to Galileo Galilei (1564–1642) dated circa 1595, using gas expansion to raise or lower the hydrostatic pressure in a tube; hence raising or lowering the liquid level of the open container medium connected to the gas-filled tube. Other thermometer mechanisms from early stages of thermodynamics work are based on gas or liquid expansion principles. Later mechanisms of action used for the determination of temperature use Planck’s law and rely on the black-body radiation captured by optical spectroscopic techniques. Absolute temperature scales are expressed in Kelvin or Rankin, both referencing the point of lowest temperature with no molecular motion as the zero point. A useful conversion between degree Fahrenheit (T _{ F }) and degree Celsius (T _{ C }) is T _{ C } = (5/9)(T _{ F } − 32).
[biomedical] Egyptian scientist and medic. Author of an encyclopedia of medicine called the “De Medicina.”
[biomedical, mechanics] The virtual point in the volume of a body where for convenience the forces are apparently acting upon. A body in equilibrium requires that the sum of the forces through the center of gravity align with the normal force. In case the normal force and sum of acting forces do not line up, the system forms a torque that will result in rotation. The center of gravity may be defined for a specific subsection of a total system, for instance the foot of a human, in reference to the entire human body.
[general, mechanics, nuclear] The point inside the outline of a body of a system where all mass can be considered to be concentrated. For instance, for an air-filled rubber ball all the mass is in the rubber shell whereas the center of mass is in the center of the ball. The location of the perceived single mass in a reference frame of choice as summarized over all the masses (Σ_{ i } m _{ i } = M) (each respective mass [m _{ i }] constituent identified by i) as a function of each respective location (r _{ i }) contributed from a system of particles (regardless of size and structure; including atoms and molecules) or concurrently the location of the combined effect of all the masses of the constituents of a device with various components and materials. The definition of the center of mass is formulated as r_{CM} = Σ_{ i } r _{ i } m _{ i } ∕ Σ_{ i } m _{ i }. The center-of-mass will directly influence the determination of the moment of inertia for an object. The center of mass will also be the point where all forces (F _{ i }) are considered to be acting on the object providing the acceleration to the center of mass $\left(\overrightarrow{{a}_{\text{cm}}}\right)$
in Newton’s second law, $\sum \overrightarrow{F}=m\overrightarrow{{a}_{\text{cm}}}$ . The location of the center of mass and dimensions of a body directly determine the moment of inertia for that body, specifically if the body is nonuniform and has various geometric extensions of certain composition and materials that hold mass. The location (R) of the center of mass in a coordinate system is defined by the components of an object, each with respective mass (m _{ i }) and respective distance to an origin (r _{ i }) in a coordinate system, defined by the total mass (M = Σm _{ i }) as R = Σ_{ i } m _{ i } r _{ i } / M. The relative position (r*) of each of the components (i) can now be defined for a specific subsection (k) as r* _{ k } = r _{ k } − R; similarly the velocity is defined by $\overrightarrow{{\upsilon}_{k}^{*}}=\overrightarrow{{\upsilon}_{k}}-\overrightarrow{V}$ , where V is the velocity vector for the system. Under relativistic conditions (approaching the speed of light [c], which applies to nuclear conditions), the velocity needs to be corrected by means of the Lorentz transformation, which translates in the momentum (p = mv) formulation as follows: $\overrightarrow{{p}_{k}^{*}}=\overrightarrow{{p}_{k}}-\left[\left({\text{\gamma}}_{\text{cm}}{e}_{k}/c\right)-{\text{\gamma}}_{\text{cm}}^{2}/\left({\text{\gamma}}_{\text{cm}}+1\right)\left(\overrightarrow{\text{\beta}}\cdot \overrightarrow{{p}_{k}}\right)\right]\overrightarrow{\text{\beta}}$ , where the quantum energy is ${e}_{k}={m}_{k}{c}^{2}/\sqrt{\left(1-{\left\{\overrightarrow{{\upsilon}_{k}}/c\right\}}^{2}\right)}$ and “inertial energy” $\overrightarrow{\text{\beta}}={\displaystyle {\sum}_{i}\overrightarrow{{p}_{k}}c/{e}_{i}{\text{and\gamma}}_{\text{cm}}={\displaystyle {\sum}_{i}{e}_{i}/{E}^{*}}}$ . In this the quantum energy is defined as ${E}^{*}=\sqrt{\left[{\left({\displaystyle {\sum}_{i}{e}_{i}}\right)}^{2}-{\left({\displaystyle {\sum}_{i}\overrightarrow{{p}_{i}}}\right)}^{2}{c}^{2}\right]}$ . In the Lorentz transformation the momentum components that are orthogonal to the parameter $\overrightarrow{\text{\beta}}$ are conserved, while the parallel components are modified. This last description can be applied under various conditions, including Compton scattering (see Figure C.35).Figure C.35 A high jumper is manipulating her center of mass to enhance the high jump level when performing a pole vault jump during the different vaulting phases.
[computational, fluid dynamics] Computational technique used to isolate extremes by using the half-intervals (Δh/2) in the first derivatives of a function f(f′(x _{ i }) = [ƒ(x _{ i } + (Δh/2)) − f(x _{ i } − (Δh/2))/Δh] + o(Δh)) when derived over incremental step size Δh, the error is expressed by O({Δh}^{2} ). The slope connecting these two points and respective accuracy can be expressed in (and is directly dependent on) the increment step size. Increasing this into a Taylor series the derivative has a second component: f(x _{ i }) = −ƒ(x _{ i } + (2Δh/2)) + 8ƒ (x _{ i } + (Δh/2)) [−8ƒ (x _{ i } − (Δh/2)) + f(x _{ i } − (2Δh/2))/12(Δh/2)] + O({Δh}^{2}) the second-order difference now becomes f″(x _{ i }) = [f(x _{ i } + (Δh/2)) + f(x _{ i }) − ƒ(x _{ i } − (Δh/2))/ {(Δh/2)}^{2}] + O(Δh) and ƒ″(x _{ i }) = [− ƒ (x _{ i } + (2Δh/2)) +168 ƒ (x _{ i } + (Δh/2)) − 30 ƒ(x _{ i }) − 16ƒ(x _{ i } − (Δh/2)) + f(x _{ i } − (2Δh/2))/12(Δh/2)] + O({Δh}^{2}), which uses the centered differences around x _{ i }. This solution method is frequently used in computational fluid dynamics, primarily since the numerical solution needs to be solved in a finite element configuration due to the complexity of the local boundary conditions.
[general, mechanics] Any object with mass (m) moving in a curved trajectory (e.g., circular, elliptic motion) with certain tangential velocity (v) will be forced to follow the curved path with radius of curvature (r) under the influence of a centripetal force. The centripetal force (F _{ c }) is directed toward the center of the curvature with magnitude ${f}_{c}=m{a}_{c}=m{\upsilon}^{2}/r$
; this force may result from friction (tires on the pavement), normal force (barrel racing), or tension (e.g., rope) (see Figure C.36).Figure C.36 Merry-go-round with center-seeking force.
[thermodynamics] See Celsius.
[general] Metric system. Fractional unit of DiSTANCE/length, 1/100 of the SI unit meter.
[general, mechanics] Circular motion obtained by balancing forces, determining the magnitude of the centripetal force maintaining the object in revolution, F _{ C } = mv ^{2}/R, where m is the mass of the projectile, v the velocity of motion, and R designates the radius of curvature of the circular motion. Force is required to keep a moving mass travel in a circular path and should be directed toward the axis of the circular path.
[astrophysics, energy, mechanics] Named after the prototype Delta Cepheid. Indication of the mechanical properties of stars, specifically the oscillatory behavior.
[atomic, mechanics, nuclear, quantum] High-energy particle accelerator located in Switzerland, at the French border, near the city of Geneva. The particle accelerator is formed in a large circular loop with radius R. An applied voltage alternates with a single period determined by the condition T = 2πm/qB. The particle accelerator uses a magnetic field (B) to generate a force (F = qvB = m(v ^{2}/R)) on a charged particle with charge q and mass m to induce acceleration resulting in a maximum velocity v _{max} = qBR/m, with KE upon exit from the cyclotron (1/2)mv ^{2} = q ^{2} B ^{2} R ^{2}/2m (see Figure C.37).
Figure C.37 CERN (“Conseil Européen pour la Recherche Nucléaire,” or European Council for Nuclear Research) facilities and operations in Meyrin, Switzerland: (a) outline of the 27 km diameter facilities of the European Organization for Nuclear Studies with beam guide (Large Hadron Collider: LHC) as insert. (Courtesy of CERN, Geneva, Switzerland.) (b) Compact Muon Solenoid (CMS) inner tracker barrel consisting of three layers of silicon modules placed at the center of the CMS (LHC) experiment, guiding 14 TeV proton–proton collisions, the silicon that is used will be able to withstand the powerful magnetic field and high doses of radiation without damage. (Courtesy of Maximilien Brice, CERN, Geneva, Switzerland.) (c) Calorimeter used measure the energy of particles that are produced during collision of protons, close to the axis of the beam, chilled inside a cryostat to provide optimal operational conditions for the detector. This is part of the LHC used to verify the Higgs boson and provide an insight into the origin of dark matter. (Courtesy of Claudia Marcelloni, CERN, Geneva, Switzerland.) (d) Simulation of particle trajectories. (Courtesy of CERN, Geneva, Switzerland.) (e) The World Wide Web was conceived at CERN by the scientist Sir Timothy John “Tim” Berners-Lee (1955–) from Great Britain in 1989, the use of the Internet made the transport of large amounts of data easy and convenient. (Courtesy of Rory Cellan-Jones, BBC, London, UK.)
[atomic, general, nuclear] Physicist from Great Britain. In 1914 Chadwick described the release of electrons with different energies, introducing the concept of recoil energy to the atomic and nuclear interaction from projectile particle interaction. Chadwick worked with Rutherford on the definition of the nuclear composition and in 1932 described the release of the neutron (n) resulting from the bombardment of beryllium (Be) with alpha particles (α), ${}_{2}{}^{4}\text{\alpha}+{}_{4}{}^{9}\text{B}\text{e}\to {}_{6}{}^{12}\text{C}+{}_{0}{}^{1}n$
, also producing carbon (see Figure C.38).Figure C.38 James Chadwick (1891–1974).
[chemical, general] Any chemical or nuclear process in which some of the products of the process are instrumental in the continuation or magnification of the process.
[astronomy/astrophysics, biomedical, energy, general, optics] Indian mathematician who theoretically described the radiative transfer of energy within stellar atmospheres. The radiative transfer theory was toward the end of the twentieth century successfully adapted for biomedical purposes in light tissue interaction—equation of radiative transfer (see Figure C.39).
Figure C.39 Subrahmanyan Chandrasekhar (1910–1995).
[astronomy/astrophysics, energy, quantum] The gravitational mass of a star where gravity will overcome the Fermi energy and collapses, M ~ 1.44M _{⊙}, where M _{⊙} represents the solar mass. Stellar mass less than the Chandrasekhar mass will not possess enough energy to produce neutrons, thus preventing the formation of a neutron star by means of the constraints to the electron degeneracy. At a mass less than the Chandrasekhar mass the star will only be able to produce a white dwarf. This also defines the theoretical upper limit for the mass of a stable white dwarf. The electron density (N _{ e }) for the star defines the Fermi energy of that star, E _{ F } = (5/3)(1/N _{ e })C(N _{ e } ^{5/3}/R), where R defines the equilibrium radius for the star and C is a constant for the star (based on its history and size).
[atomic, nuclear] See X-ray, characteristics.
[electronics, general] Excess or shortage of electrons in an atomic or molecular system that produces either negative or positive charge. On a nuclear level the excess protons can provide a positive charge. The concept of two different charges was officially introduced by Benjamin franklin (i706/i70 5 ? – 1790) in 1747; however, the concept of charge was known and has been described as far back as ancient Greek philosophers and old Chinese documentation dating back well before Christ on the Christian/western calendar. It is also referred to as electric charge.
[computational, relativistic, thermodynamics] Under a Lorentz transformation all particles are transformed into their respective antiparticles. The operator is discontinuous and applies only to relativistic–quantum–mechanical situations. The charge conjugation follows the pattern outlined for space inversion and time reversal.
[atomic, solid-state, thermodynamics] Periodic charge density fluctuations in a low-dimensional metal lattice structure. Because of an interaction between electron density in free flow and phonon propagation an electron density wave pattern is generated with a periodic charge density modulation that has a rhythmic intermittent lattice distortion superimposed, causing a charge density wave pattern. Each perturbation is associated with the Fermi wave vector. The phonon spectral pattern that results is referred to as the Kohn anomaly. The periodic phase transitions induced by the electron charge density fluctuations generate a wave pattern with a wavelength λ_{charge} = π/k _{ F }, where k _{ F } is the Fermi wave vector The wavelength may be commensurate with the lattice constant, however not so when the lattice has only partially filled electron bands. When the lattice density perturbations are disorganized, the particle gap occurring at the Fermi level will create an insulator
[general] Total charge that is distributed evenly on a “two-dimensional” object per unit area.
[general] Total charge that is distributed evenly on a “one-dimensional” object per unit length.
[computational, electronics, quantum, solid-state] Capacitive semiconductor material structure that can be used to temporarily store electric charge. The storage time can be controlled by external circuitry and can be used to form a delay line (time delay) and concurrently acts as a “bucket memory,” temporarily storing the electronic information and transferring it over to the next ccd in the circuit. The stored information is primarily binary, but there are also analog applications.
[general] Scientist and physicist from France. Charles’ work was in the behavior of ideal gasses with pre–ideal gas law definitions. Cotemporary of Joseph Louis Gay-Lussac (1778–1850) (see Figure C.40).
Figure C.40 Jacques Alexandre César Charles (1746–1823). (Courtesy of the United States Library of Congress, Washington, DC.)
[atomic, nuclear] Gas law introduced by Jacques Alexandre César Charles (1746–1823) with respect to the volume (V) and temperature (T) of an ideal gas expressed as V/T = constant for constant pressure and number of moles. It is also known as the Gay-Lussac law.
[general] Classification of elementary particles, specifically quarks. In reference, an electron can be identified by spin-up or spin-down. In the construction of rudimentary particles, mesons consist of a quark and an antiquark, whereas a baryon will be composed of three quarks. With the broad variety of baryons and mesons the type of quark defines the final product. Next to the fact that various quarks have fractional charge the charm provides another identification. The charm can be “up (u)” with charge u :+(2/3)e (rest energy 360 MeV), electron charge magnitude: |e| = 1.60217657 × 10^{−19} C, “down (d)” with charge d :−(1/3)e (rest energy 360 MeV), “charmed (c)” with charge c :+(2/3)e (rest energy 1500MeV), “strange (s)” with charge s : −(1/3)e (rest energy 540MeV), “top (t)” with charge t :+(2/3)e (rest energy 173,000MeV), and “bottom (b) with charge b :+(2/3)e (rest energy 5000 MeV). The respective antiquaries: ū, $\overline{d},\overline{c},\overline{s},\overline{t},\overline{b},$
, have opposing charge to the “regular” quark and identical rest energy. The quark charm principle was introduced by Murray Gell-Mann (1929–), for which he received the Nobel Prize in Physics, and George Zweig (1937–) in 1963 (see quark) (see Figure C.41).Figure C.41 Concept of “charm” pertaining to elementary particles, quarks in particular.
[chemical, thermodynamics] The principles of the changes to the chemical equilibrium introduced by the French chemist Henry Louis Le ChÂtelier (1850–1936) and independently by the German physicist and inventor Karl Ferdinand Braun (1850–1918). A system defined by the number of moles of the constituents of the medium, the pressure, and volume and temperature when subjected to change will affect the other parameters as well as the chemical balance of the constituents. In this situation an exothermic reaction will be forced to reverse its reaction when the system temperature is artificially increased, hence reducing the reaction constant. Alternatively, a temperature increase for an endothermic reaction will be encouraged to proceed in the direction that requires energy, thus increasing the equilibrium reaction constant. Similarly changes in pressure or volume will force the chemical reaction in the direction that complies with the changing boundary conditions. This principle is also known as Le Châtelier principle, or as le ChÂtelier–braun principle. Also referred to as Châtelier-braun inequalities, or Le Châtelier theorem.
[computational, fluid dynamics] Mathematician from Russia. Chebyshev described several stochastic principles and introduced the basic concepts of number theory providing basic mathematical foundations, as well as probability theory fundamentals.
[computational] In a probability distribution mostly all values of a series of data are near the average value. Introduced by Pafnuty Chebyshev (1821–1894).
[chemical] Pure substance composed of two or more elements combined in a fixed and definite proportion by weight.
[chemical, general, solid-state] Chemical reaction that delivers electrical energy with electrical current in the form of free electrons. The electrochemical property is a direct result of the half-cell phenomenon. This principle applies in particular to batteries. Alkaline batteries are producing nonreversible chemical reactions (disposable), whereas lithium-ion (i.e., lithium) batteries (used in mobilephones and laptop computers) are rechargeable and the chemical reaction is reversed to the point where the electromotive force (V _{emf}) will be maintained for a long duration. The alkaline battery is for instance based on the chemical reaction between zinc (Zn) and manganese dioxide (MnO_{2}), whereas the electrodes are potassium hydroxide (i.e., the alkaline). In the lithium-ion battery, lithium ions actually migrate between the cathode and the anode, hence producing a current externally; during the recharging process the ions are forced back by the applied external electric field. Other battery materials include lead-ACID, used in automobiles and hospital equipments. The charge carrying capability of a battery and the chemical reaction is expressed in ampere-hours, or charge multiplied by time. Another chemical energy application is in fuel cells, relying on oxidation of an electrolyte into free electrons, for example, hydrogen–oxygen and alcohol and fossil fuel-based systems. The first battery (voltaic pile) was conceived by the Italian physicist Alessandro Volta (1745–1827) in 1800 (see Figure C.42).
Figure C.42 (a) Chemical energy expressed by voltaic pile and (b) “dry cell.”
[biomedical] The relative difference in concentration over a distance within specific constituents of a mixture (gas, liquid, or solid-state: n- and p-structures). One specific application is in the use of reverse osmosis in water purification (also see chemical potential) (see Figure C.43).
Figure C.43 (a) Chemical gradient in reverse osmosis water filtration, (b) Chemical gradient for nicotine patch used by individuals who are in the process of smoking cessation.
[biomedical, thermodynamics] The partial derivative change in free energy (F) per change in atomic and molecular (N) content, respectively, of the constituent μ_{ i } = (∂F/∂N) _{ T,V } = G(T, P, N)/N under constant temperature (T) and constant volume (V), incorporating the definition of the Gibbs free energy (G). Two systems in the same volume under identical conditions with the same ith constituent and in equilibrium will have the same chemical potential. There are four different types of chemical potential that can be discriminated: (1) thermodynamic chemical potential, (2) chemical potential, (3) electronic chemical potential, and (4) in relativistic concepts. The thermodynamic concept is used to describe the state in a system under certain conditions. For instance water will evaporate when the water temperature is above the boiling point, thus migrating from liquid to gas state with an associated lower chemical potential in the gas/vAPOR state in comparison with the liquid state at that specific temperature. The rise in temperature will initiate the reordering from the higher to the lower potential. Similar change of state or equilibrium situations can be depicted for chemical reactions such as the oxidation of butane as described by the chemical reaction $2{\text{C}}_{4}{\text{H}}_{10}+13{\text{O}}_{2}\stackrel{\text{flame}}{\to}8{\text{CO}}_{2}+10{\text{H}}_{2}\text{O}$
with respective chemical potentials and the release of energy described by $E=2{\text{\mu}}_{{\text{gas,C}}_{4}{\text{H}}_{10}}+{\text{C}}_{4}{\text{H}}_{10}+13{\text{\mu}}_{{\text{gas,O}}_{2}}{\text{O}}_{2}-8{\text{\mu}}_{{\text{gas,CO}}_{2}}{\text{CO}}_{2}+10{\text{\mu}}_{{\text{gas,H}}_{2}\text{O}}$ at the combustion temperature. The change in internal energy per change in unit state for each of the constituents i is written as μ_{ i } (S, V, n) = (∂U/∂n _{ i })_{ S,V,n }, for i = 1, 2, …, r, where U is the internal energy, V the volume of the mixture, S the entropy of respective state, n the number of states, and r the total number of constituents. Chemical potential of solvent with respect to constituent i is expressed as μ_{ i } = μ_{ ii }(T, p) + RT ln y _{ i }, where μ_{ ii }(T, p) = μ_{ i }(T, p, y _{1}, y _{2}, … y _{ r }) or μ _{ ii }(T, p _{ ii }) = h _{ ii }( T, p _{ ii }) − Ts _{ ii }( T, p _{ ii }) is the chemical potential of the pure solvent in the mixture at temperature T and pressure p, and y _{ i } is the fractional component of each respective ingredient, with lim_{ i }, y _{ i } → 1 yielding the solvent factor for constituent i and R = N _{ A } k 8.3145 J/molK is the universal gas constant, N _{ A } = 6.022 × 10^{23}molecules/mol the Avogadro number and k = 1.38066 × 10 J/K molecule the Boltzmann constant. In this configuration the following variable are used: h _{ ii }(T, p _{ ii }) the specific enthalpy of system ii and s _{ ii }(T, p _{ ii }) the respective specific entropy with P _{ ii } the partial pressure of constituent i. Under chemical equilibrium at a ground state p _{0} the chemical potential of a genuine constituent will equal the Gibbs free energy of reaction for that particular constituent, μ_{ ii }( T, p _{0}) = g _{ ii }(T, P _{0}). The latter can describe the conversion of chemical energy into electrical energy for a battery, for instance. The use in true chemical potential applies to biomedical physics and relates to the chemical gradient. The chemical potential describes the difference in chemical concentration across a cellular membrane creating an electrical potential gradient according to the respective Nernst potential for the constituents at either side of the membrane. The electronic chemical potential falls under theoretical chemistry as applied to density functional or energy functional theory. The electronic chemical potential is the functional partial derivative of the electrochemical density functional with respect to the system state defined as the electron density, which is expressed as ${\text{\mu}}_{i}\left(r\right)={\left[\partial E\left(\text{\rho}\right)/\partial \text{\rho}\left(r\right)\right]}_{\text{\rho}={\text{\rho}}_{\text{ref}}}={V}_{\text{ext}}\left(r\right)+{\left[\partial F\left(\text{\rho}\right)/\partial \text{\rho}\left(r\right)\right]}_{\text{\rho}={\text{\rho}}_{\text{ref}}}$ , where ρ is the density functional ( e (ρ) = ∫ρ(r)V(r)d ^{3} r + F(p), where F(ρ) is the universal functional which identifies the KE of the electrons in the chemical compound and V _{ext} (ρ) is the combined influence of nuclear electrostatic potential and the electric influences of electric and magnetic fields external to the atom or molecule resulting from surrounding chemicals and outside influences, also referred to as the external potential). Since the electronic chemical potential is based on the electron density, this potential is equivalent to the electron negativity of the atom, as a matter of fact the sum of the electron affinity (EA) and the ionization potential (IP) for the atom. This commodity is also referred to as the Mulliken potential, ${\text{\mu}}_{\text{Mulliken}}\left(r\right)-{\text{\chi}}_{\text{Mulliken}}\left(r\right)=-\left(\text{IP+EA}\right)/2={\left[\partial E\left(N\right)/\partial N\right]}_{N={N}_{0}}$ . Last but not least, in relativistic physics the term chemical potential relates the states of fundamental particles analogous to the thermodynamic potential but with the following inherent and unique characteristics relativistically there will be no enthalpy of state for fermions and bosons, but each elementary particle contributes to the total internal energy of the system into which it is introduced or from which it escapes. The potential describes the tendency of elementary particles to migrate out of energetic regions with higher chemical potential. The “relativistic” chemical potential is associated with the wave mechanical description of the elementary particles by the Boltzmann equation in quantum physics and possesses a higher potential, which relates to a higher particle density. The elementary particle can be described as a gas of fermions and bosons. When just considering the fermions, the electrical potential is ${\text{\mu}}_{F}=k,T\mathrm{ln}\left(z\right)\text{=}kT\mathrm{ln}\left({\text{e}}^{{\u03f5}_{F}/kT}-1\right)$ , where is the fugacity, є _{ F } is the Fermi energy, or μ_{ F } = (∂E(N)/∂N)_{ s } = (∂E _{orbital} (N)/∂N)_{ s } + (∂E _{electrinic} (N)/∂N)_{ S }, where both terms represent the change in energy of the system if one particle is added under constant entropy (S). For an ideal gas the chemical potential is linked to the pressure (P) as [∂μ_{ i } (N)/∂P]_{ T } = V = RT/P, or equivalently [∂(μ_{ i }/RT)/∂ln P]_{ T } = 1 (also see Fermi energy ).[biomedical, chemical, solid-state] Light produced as the result of a chemical reaction. The most well-known chemiluminescence reaction is oxidation–reduction, specifically produced during a fire. A more intricate oxidation–reduction reaction is the chemical energy transfer that results in an excited singlet state, which has a limited lifetime and degrades with the emission of light. A strictly chemical reaction describing just such formation of a singlet state is in the reduction reaction of an amino-based derivative with a base and oxygen-based compound that can release the oxygen for oxidation, producing nitrogen and (high-energy) blue light. Other available mechanisms that produce light under a variety of energy transfer principles are bioluminescence (e.g., firefly), electroluminescence (e.g., lightning), radioluminescence (e.g., scintillation), and thermoluminescence (every object with a temperature above absolute zero kelvin emits light with a wavelength range directly inversely proportional to the absolute temperature; gloving heating coil on electric stovetop or, indirectly, the incandescent lightbulb) (see Figure C.44).
Figure C.44 Chemiluminescence example producing light in a “glow stick,” for instance, used during deep-sea diving. Also used as decorative jewelry.
[fluid dynamics] Engineer from France. In 1769 Chézy performed experiments on the flow resistance in open channels such as the Seine River near Paris and the Courpalet Canal. This information provided the heuristic Chézy formulas. The Chézy quantity (i.e., coefficient), C _{chezy}, varies from about 30m^{1/2}/s for small rough channels to 90m^{1/2}/s for large smooth channels (see Figure C.45).
Figure C.45 Antoine de Chézy (1718–1798).
[fluid dynamics] Heuristic expression for flow velocity in an open canal. The flow velocity in an open channel is defined as $v={C}_{\text{chezy}}\sqrt{\left(m{\text{\theta}}_{\text{incl}}\right)}$
, where m is the mean hydraulic depth, θ_{incl} the inclination angle of the riverbanks, and C _{chezy} the Chézy’s flow velocity coefficient. The Chézy’s flow velocity coefficient can be approximated by the formula derived by the Swiss engineers Emile-Oscar Ganguillet (1818–1894) and Wilhelm Rudolf Kutter (1818–1888) (Ganguillet–Kutter equation, 1869): ${C}_{\text{chezy}}=\left[23+\left(1/n\right)+\left(0.00155/{\text{\theta}}_{\text{incl}}\right)\right]/\left[1+\left[23+\left(0.00155/{\text{\theta}}_{\text{incl}}\right)\right]\left(n/\sqrt{m}\right)\right]$ , where n defines the conditions of the surface of the wall of the flow and is found listed in tables for specific materials (e.g., polished wood: n = 0.010 to 0.013; river with rocks imbedded in the shores and bottom as well as grass and growth: n = 0.035 to 0.05).[fluid dynamics, thermodynamics] See Colburn j-factor, heat transfer.
[fluid dynamics, mechanics, thermodynamics] See Colburn j-factor, mass transfer.
[electronics, solid-state] Silicon semiconductor crystal substrate designed to perform select electronic functions using n-type and p-type materials, also known as integrated circuit (see Figure C.46).
Figure C.46 Chip.
[biomedical, chemical, optics] Definition of perceived color space, also defined under cie standards, based on the organization that has standardized the concept of color “Commission International de Illumination” (see Figure C.47).
Figure C.47 Chromaticity color chart.
[electronics, general, solid-state] Analytical device to assist in the analysis of the composition of media in a process called chromatography. Also used as gas–LIQUID Chromatograph, or liquid–gas Chromatograph, gas Chromatograph, and gel permeation chromatography (see Figure C.48).
Figure C.48 Gas Chromatograph equipment for analytical processing based on spectral attenuation profile of chemical constituents.
[electronics, general, solid-state] Analytical process designed to resolve the composing constituents of a mixture. Chromatography is applied to chemical analysis. The applications of chromatography range from analysis of petrochemical, environmental, pharmaceuticals, cosmetics (“fragrance”), food- (e.g., safety, flavor) and water quality, and in therapeutic diagnostics as well as for analysis of biological specimen submitted for instance during urine analysis or drawn blood, next to forensics. Chemical chromatography uses the process of diffusion when subjected to a bed of resin particles, with different diffusion coefficients for different solute molecule sizes. The resin is generally arranged in a column, analyzing the mobile phase of the respective components with high degree of resolution. The “steady-state” medium, affecting the separation process, is referred to as the stationary phase of the mixture. The separation process is arranged in a column. In gas chromatography the mobile unit is in gas form. Gas chromatography is more popular for volatile components. The analysis relies on the optical spectral attenuation from transmitted light, providing specific representative absorption peaks at representative wavelengths (actually in chromatography one relies on the chromatography “wave numbers,” k′ = 1/λ; note that the regular wave number is defined as k = 2π/λ). Different chromatography techniques are available for specific applications. Chromatography can define molecular chains and atomic ingredients. Different mechanisms of action involved in the chromatographic analysis are, for instance, adsorption chromatography, affinity chromatography, ION-exchange chromatography, gel chromatography, and partition chromatography, each with its own mechanism of molecular separation. Specifically, the mechanisms described influence the retardation process associated with the respective diffusion processes. For instance gel chromatography uses Polyacrylamide and other types of gels to act as sieves. In affinity chromatography the use of a chemical matrix (for instance, a biomolecular matrix used to identify antigens or antibodies) provides a binding process used for separation. Specific analyses are available for the identification, for instance, of alkaloids, amino acids, nucleic acids, proteins, steroids, and vitamins.
[biomedical, general, optics] Dye constituent that provides the essence of color of a molecular composite medium observed or measured with optical devices. The chromophore is either a separate molecule or a component of a larger molecule and gains color when irradiated by a broad band light source, ideally white light. The chromophore will absorb selected ranges of the source bandwidth, while the remaining spectral band(s) are re-emitted by means of shallow scattering processes, which yields the visible color spectrum distribution (see Figure C.49).
Figure C.49 (a) The orange color on the hull of the supply boat for oil rigs is the result of the choice in chromophores in the paint used, absorbing all but the “orange” color band of the incident white light. Whereas the “blue” color of the water is the result of Raleigh scatter of the incident white light. (b) Absorption lines for the specific chromophores of the chemical compound paraben. (c) color of object based on backscattered/back-reflected portion of the incident white light; remaining part of spectrum is absorbed by the chromophores inclosed in the (surface) of the object. A black object inherently absorbs all incident light, a white object reflects all incident light. The full spectrum is perceived as white.
[astronomy/astrophysics, geophysics] Solar layer above the photosphere, with a temperature greater than 4200 K, and a thickness for our Sun is approximately 2000 km, containing primarily helium and hydrogen. The chromosphere is best investigated during a full total eclipse, exposing just the chromosphere (see Figure C.50).
Figure C.50 Layers of the Sun, including the chromosphere.
[general, optics] Commission Internationale de l’Eclairage; The International Commission on Illumination; technical, scientific organization implementing standards and information exchange related to light, luminescence, color and spectrophotometry, vision and imaging as well as photobiology. CIE was founded in 1913 and is a nonprofit organization that acts independently providing advice on standardization. Although operating on a voluntary basis, CIE is recognized by ISO (International Organization for Standardization) as an international standardization institute. The committee is seated in Vienna, Austria.
[biomedical, general, optics] The definition of color perception by the International Commission on Illumination (cie) initially released in 1931. The CIE 1931 color space provides a mathematically definition of color spaces associated with the virtual XYZ color space as introduced. In the color space, Y means brightness, Z is proportional to blue stimulation, and X is an interpreted representation of the red sensitivity curve of the cones of the human eye. The XYZ color space is also referred to as the tristimulus values. XYZ can be confused with red–green–blue (RGB) cone responses even if X and Z are roughly equivalent to red and blue, respectively. However, in the CIE XYZ color space, these values are not equal or similar to the S, M, and L responses of the human eye, but can be considered derived values (also see vision ).
[general, optics] Graphical representation of the hues and radiance of color in a three-dimensional space, defined in “brightness” (L), hue and chrome (a: red-green; b: yellow-blue), expressed in the cie L* a* b color space, yielding the three axes. This scientific analysis overcomes subjectivity. For instance, when analyzing the color of teeth by a dentist for reconstructive dental work the ambient light, or examination light color temperature, will influence the observations, as will the personal history for the observer (good night rest, etc.; color blindness). The CIE color analysis uses spectrophotometric instrumentation for numerical determination. The color representation in Euclidean space is defined based on the respective measurements and plotted according to the “E-value” as $E=\sqrt{\left({L}^{2}+{b}^{2}+{c}^{2}\right)}$
. In case only hue and saturation is displayed (two-dimensional graph), the space is defined as $\text{Cab}=\sqrt{\left({a}^{2}+{b}^{2}\right)}$ (see Figure C.51).Figure C.51 CIE color charts and related tools for spectral identification and standardization.
[fluid dynamics] The average flow velocity (i.e., wind velocity) on a path looping around the object in a flow pattern (e.g., wing), where flow against the path direction has a negative value and flow directions perpendicular to the path $\left(\overrightarrow{s}\right)$
are not considered. Circulation is defined as the steady-state closed loop integral of the vorticity within the enclosed path. Where, the vorticity is the degree of “rotation” experienced in flow velocity $\left(\overrightarrow{v}\right)$ as a function of location $\left(\overrightarrow{r}\right)$ and time (t), which is the “curl” of the velocity at a given place. This will not consider initiation and termination processes. This yields for the circulation ${\oint}_{C}\overrightarrow{\text{\varpi}}}\left(\overrightarrow{r},t\right)d\stackrel{\rightharpoonup}{s}={\displaystyle {\oint}_{c}\nabla}\times \overrightarrow{v}\left(\overrightarrow{r},t\right)d\overrightarrow{s$ . A flow at rest will have circulation zero. The wake of the flow in, for instance, the airstream around a wing has zero circulation, which also describes the vortex at the tip of the wake, assuming the loop integral is encompassing a large enough volume of space. The wake and wing-tip vortex have no viscous forces (no boundary layers) and hence the circulation is zero.[fluid dynamics] The average fluid flow velocity (i.e., wind velocity) on a path looping around the perturbation (i.e., wing), and can be represented as the closed loop integral of the vorticity $\left(\overrightarrow{\text{\varpi}}\left(\overrightarrow{r},t\right)\right)$
within the enclosed path. ${\text{\Gamma}}_{\text{circ}}={\displaystyle {\oint}_{C}\overrightarrow{\varpi}}\left(\overrightarrow{r},t\right)d\stackrel{\rightharpoonup}{s}={\displaystyle {\oint}_{c}\nabla}\times \overrightarrow{v}\left(\overrightarrow{r},t\right)d\overrightarrow{s}$ . Where the vorticity is the degree of “rotation” experienced in flow velocity $\left(\overrightarrow{v}\right)$ as a function of location $\left(\overrightarrow{r}\right)$ and time (t), which is the “curl” of the velocity at a given place. The circulation at the boundary of the phenomena will be finite, the outer (i.e., horizontal) edges of the wings create a vortex that is at the edge of the wake.[fluid dynamics] Arbitrarily closed loop over the flow around an object, ∮_{ s }[v _{ x }(dx/ds) + v _{ y }(dy/ds) + v _{ z }(dz/ds)]ds, in a Cartesian system (x, y, z) with flow velocity $\overrightarrow{v}=\left({v}_{x},{v}_{y},{v}_{z}\right)$
over a loop S with path steps s tangential to the loop.[biomedical, fluid dynamics, general] Blood flow loop in a biological system; heart, arteries, arterioles, capillaries, venules, veins, and back to hearts. The circulatory system has an oscillatory component (induced by the pumping rhythm of the heart) on the arterial side that dampens the amplitude (both velocity and pressure) in the growing impedance with reduction in flow lumen associated with increasing number of branching vessels. The circulatory system is defined by conservation of mass. In addition to the pumping mechanism of the heart, the veins have a flow mechanism that is supported by encapsulation from skeletal muscles. The skeletal muscle function is important, especially when considering that a large number of people will faint when standing perfectly still for extended periods of time. An easy exercise to maintain circulation in the veins of the leg is to periodically flex and release the leg muscles (see Figure C.52).
Figure C.52 Blood circulation diagram. Venous blood in blue and arterial (oxygen rich blood) blood in red.
[thermodynamics] Physicist and engineer from France. Clapeyron made several recommendations for thermodynamics and defined many conditions as a pioneer in the new field of thermodynamics. Clapeyron defined the two-phase mixture, for instance, steam and boiling water (also see Clausius–Clapeyron relation ) (see Figure C.53).
Figure C.53 Benoî t Paul Émile Clapeyron (1799–1864).
[general, mechanics, thermodynamics] German physicist and scientist. Clausius’ father was a contemporary of James Prescott Joule (1818–1889) and Lord Kelvin (a.k.a. William Thomson: 1824–1907), while he himself was a contemporary of Nicolas LÉonard Sadi Carnot (1796–1832). The work of Carnot inspired Clausius to formulate his own interpretation of heat transfer, different from that expressed by Lord Kelvin in the second law of thermodynamics as: There is no single isolated process that results in the transfer of heat from a body at low temperature to a body at higher temperature. Meaning that there are multiple processes at a stage to accomplish one goal, in the refrigeration this equates to work performed with losses due to the work itself (generating heat of its own), while transferring heat against a gradient. In 1865 Clausius introduced the concept of entropy (see Figure C.54).
Figure C.54 Rudolf Julius Emanuel Clausius (baptized name: Rudolf Gottlieb; 1822–1888).
[thermodynamics] dP/dτ_{ T } = L/τ_{ T } (ρ_{ V } ^{−1} −ρ_{ l } ^{−1}) = L/τ_{ T }Δv _{ a }, where P is the vapor pressure, τ_{ T } the temperature, ρ_{ V } the density of the vapor phase, ρ_{ L } the density of the liquid phase, l the latent heat of vaporization (L ≡τ_{ T } (S _{ g } – S _{ℓ} ) = dQ, where S _{ i } the entropy of the gas and liquid phases, respectively, and dQ the heat added to the system), and v _{ a } the volume occupied by one atom or molecule of the constituent. Note the derivative is not simply as in the equation of state for the gas, but assumes the gas and liquid to coexist. Generally we can assume that the gas phase of an atomic gas (v _{ag}) occupies a greater volume than in the liquid phase (v _{aℓ} ) and Δv _{ a } = v _{ ag } −v _{aℓ} ≅ v _{ ag } = V _{ g } /N _{ g }, with V _{ g } the gas volume of the constituent and N _{ g } the number of molecules or atoms in the gas state, respectively.
[energy, fluid dynamics, general, geophysics] Field of physics dealing with physical phenomena in the lower part of earth′s atmosphere directly related to the weather and providing warnings for people in the path of inclement weather (see Figure C.55).
Figure C.55 Climatological tools: (a) cold and warm front migration in three dimensions Climatological tools: (b) drawing of isobars on a section of the global map. (Courtesy of University of Illinois, Department of Atmospheric Sciences, IL.) and (c) mobile meteorological station. (Courtesy of CBS KCNC-TV Denver, CO.)
[electromagnetism] Expression used in frequency modulation synthesis, where M is the modulator frequency and C the carrier frequency. Frequency modulation synthesis is a tool used in spectral analysis.
[astrophysics] Dark “cloud” observed in the band of the Milky Way galaxy, dating back to millennia, documented by the Inca′s and early European observers (documented in 1499 by Spanish explorer Vicente Yáñez Pinzón [1462–1514]), next to Australian Aborigines approximately 40,000 years ago (wall drawings). Recent discoveries show that the interstellar “dust” cloud of particles is so dense that it blocks virtually all background light (blocks better than 90%) at an azimuth in the “southern” portion of the Milky Way. The Coalsack Nebula is located between 610 and 790 light-years distance, in the constellation Crux (“The Southern Cross”) and spans approximately 50 light-years at its widest expansion. The Coalsack Nebula is also featured in the original science fiction television series Star Trek, the “Immunity Syndrome” episode (1968). The configuration of the Coalsack Nebula can be derived from the equations on galactic light scattering introduced by Karl Schwarzschild (1873–1916), based on cumulative information acquired over the years, and most recently by observations made by the MPG/ESO 2.2-m telescope at European Southern Observatory’s La Silla Observatory in Chile, which is one of the driest areas in the world as well as extremely remote, located 150 km northeast of La Serena on the periphery of the Atacama Desert in Chile. The dust spread-out in the nebula provides significant attenuation for transmitted light from remote stars. The dark spot has been known and described for a considerable time. The aboriginal population of Australia described it as the head of an emu. The Incas in South America circulated the story that it was the god Ataguchu who kicked a hole in the band of stars (now known as the Milky Way) in a fit of anger (see Figure C.56).
Figure C.56 “Coalsack” in the constellation Crux, depicted by the dark “hole.” The Crux constellation is up and to the right, in the shape of a cross. (Courtesy of Dr. Poshak Gandhi.)
[fluid dynamics, mechanics] Coefficient defining the influence of the retarding effects resulting from friction and viscosity with respect to a body moving through a fluid. The coefficient of drag (D _{flow}) can be found in tables for fluids and surface conditions and is correlated to the drag force (F _{drag}) as F _{drag} = D _{flow}ρA(v ^{2} /2), with v the velocity of the object in the fluid (e.g., water, air), ρ the fluid density, and A the effective cross-sectional area of the object in motion.
[fluid dynamics, mechanics] Surface shear stress expressed as dimensionless number defined by the stress over the kinetic energy density, where ρ the density of the fluid, v velocity, and σ_{ s } the stress. Also defined as the ratio of shear stress (σ_{ s }) with respect to normal stress (σn), C _{f} = σ_{ s } /σ_{ n }.
[mechanics] The ratio of the friction force (F _{ f }) to the normal force (F _{ n } = mg cos(θ), where θ is the angle with the normal to the surface) for an object in motion. An object being dragged over a surface will experience kinetic friction, such as a sled sliding down a snowy hill (see Figure C.57).
Figure C.57 Sliding down a ski slope with limited kinetic friction.
[mechanics] The ratio of the friction force (F _{ f }) to the normal force (F _{ n } = mg cos(θ), where θ is the angle with the normal to the surface) for an object in motion. The friction force needs to be overcome to maintain uniform rolling motion at uniform velocity (see Figure C.58).
Figure C.58 Deformation of an automobile tire resulting in rolling friction. Rear axle with tire cut open illustrating room for deformation. (Courtesy Daimler AG, Stuttgart, Germany.)
[mechanics] The ratio of the friction force (F _{ f }) to the normal force (F _{ n } = mg cos(θ), where θ is the angle with the normal to the surface) for an object at rest. This would apply to an automobile tire on the road under normal steady-state velocity and acceleration without slip. Also a box resting on a slope will experience static friction (see Figure C.59).
Figure C.59 Person standing in fixed location on Lombard Street incline in San Francisco due to static friction.
[mechanics] See coefficient of friction, kinetic.
[general, mechanics] Relation between the resistive force (F _{ K }) and normal force (f _{ n } ) for a body in uniform motion while experiencing a force with a component parallel to the free surface the body rests on, F _{ K } =μ_{ K } F _{ N }.
[mechanics] See coefficient of friction, rolling.
[general] Friction coefficient for the dissipative force resulting from deformations observed, for instance, for a tire on the road surface or a waltz rolling out asphalt (see coefficient of friction, rolling ).
[mechanics] See coefficient of friction, static.
[general, mechanics] Relation between the resistive force (F _{ s }) and normal force (f _{ n } ) for a body at rest while experiencing a force with a component parallel to the free surface the body rests on. As long as the parallel component of the force does not exceed the frictional force (F _{ f } = μ_{ s } F _{ N }) the body will remain at rest, F _{ s } ≤ μ_{ s } F _{ N }.
[general, solid-state, thermodynamics] Binding force between molecules of a substance. Contrast to adhesion, which applies to macroscopic entities.
[fluid dynamics, thermodynamics] Dimensionless number illustrating the ratio of heat transfer to crossflow Reynolds number, where s describes the conditions of flow on the shell or wall, h _{0} the film heat-transfer coefficient, G _{ m } = W _{ s } /S _{ m } the mass velocity, specifically pertaining to the free flow area bridging adjacent tubes, with W _{ s } the mass flow rate at the wall and S _{ m } the minimum free flow through either crossflow areas, c _{ p } the specific heat under constant pressure,c _{ p }η the specific heat under constant flow at wall friction, κ the thermal conductivity, η the viscosity of the fluid , η_{ w }the viscosity at the wall, St the Stanton number, and Pr the Prandtl number. Sometimes also referred to as Chilton–Colburn j-factor for heat transfer.
[fluid dynamics, mechanics, thermodynamics] j _{ m } = (κ_{ m } /v)( η/ρD _{dif}) = St_{ m }Sc^{2/3}, dimensionless number representing the ratio of friction forces to diffusion forces, where κ_{ m } = mole/A × t × [a] is the mass transfer coefficient, with A the area, t time, [a] the concentration of constituent “a,” v the velocity of mass transport (either flow or diffusion), D _{dif} diffusion coefficient, ρ the density, St_{ m } the Stanton mass transfer number, and Sc the Schmidt number. Sometimes also referred to as Chilton–Colburn j-factor for mass transfer. In case there is transfer of momentum, the Colburn mass transfer j-factor will be equal to the Colburn heat transfer j-factor, which is only the case when there is no form drag. The conditions of no form drag apply under certain specific circumstances to flat plates and inside straight conduits.
[astrophysics, relativistic] Generate ripples in time referenced as gravitational space-time perturbations (see time perturbation, colliding black holes; gravitational wave; and Einstein equations ).
[biomedical, chemical, thermodynamics] The osmotic pressure of a solution as if the particle solution would be a gas with the same volume and temperature as the solution. The osmotic pressure can be expressed by the ideal gas law, Π_{osm} = nRT/V = [C]RT, where R = 8.135 J/molK is the gas constant, T the local temperature in Kelvin, n is the number of moles of solution, and [C] the concentration (also see Starling’s law and Van’t Hoff law).
[computational, energy, general, nuclear, quantum, relativistic, solid-state, thermodynamics] Also referenced as color force. This label is associated with the Four Forces. Designation in the strong nuclear force that acts on a property defined as “color,” which has three states: r, g, b (also referenced as: red, green, and blue). This in comparison with the electromagnetic forces that act on charges (positive and negative) and the gravitational force which acts on mass. Basic constituents red, green, and blue can form all other colors visible to the human eye. Depending on the mechanism the colors can be additive (e.g., light, where all three form white light) or canceling or subtractive (e.g., paint; a mixture of all three colors yields black).
[astronomy/astrophysics, mechanics] Celestial object consisting of frozen medium and solids, leaving a trail of gas and charged particles, the comet’s tail. The tail emanates from the head, or coma of the comet. The principal content of the comet is supposedly found in the nucleus of the coma. Note that the tail of charged particles has a different angle to the comet’s trajectory than the vapor cloud tail; forming two tails. This is different from an asteroid, which has no tail and consists of solids only. One of the more noted comets is Halley’s comet, last seen in 1986. Halley’s comet (initially Comet 1982i; renamed Comet 1986III) moves on its orbit around the Sun, traveling to the edges or our solar system, every 75–76 years, depending on our own position with respect to the observation in our orbit around the Sun. Another notable comet is Hale–Bopp (astronomy nomenclature: Comet C/1995 Ol, “discovered” in 1995), which has been described dating back to millennia and has a period of 2537 years, and Hyakutake. So far a total of 10 comets have been identified in our solar system. The direction of the gas/vapor tail is indicative of the solar wind. Comets are considered to be essential constituents of the formation of our solar system; hence are bound to carry information about the history of the creation of the solar system (see Figure C.60).
Figure C.60 A comet.
[general, fluid dynamics] The fluid surface of open vessel that are connected by free-flowing passages will be at equal level under equilibrium, independent of the shape and size of the respective vessels (see Figure C.61).
Figure C.61 Communicating vessels.
[biomedical, general, mechanics] (C _{compl}) indication of elastic nature of a material or composition (e.g., amalgamation of multiple components such as multilayer or mash/webbing and “solid” filler). The phenomenon is in particular applicable for an distensible tube, in which case the tube expands with increasing applied pressure (P), making the compliance a direct function of the change in volume (V) as a result of the change in pressure: C _{compl} = ΔV/ΔP.
[thermodynamics] Parameter indicating the deviation from the ideal gas law, and ideal gas conditions. The compressibility factor, Z _{com} = PV/nRT, will equal 1 for an ideal gas (also see Van der Waals equation of state).
[fluid dynamics] The rate of change in volume of a dissolved gas under compression of the solvent fluid: B _{ g } = γP/∞, with P the externally applied pressure (in Pascal), γ = c _{ p } /c _{ v } the ratio of the specific heats of the gas, and ∞ the volume fraction of the undissolved gasses.
[acoustics, atomic, biomedical, fluid dynamics, geophysics] Transfer wave in liquids, solids, and gasses. For compression waves in fluids see both acoustics and sound.
[acoustics, atomic, biomedical, fluid dynamics, geophysics] Any solid, liquid, or gas can be compressed by an external force, resulting in relaxation based on the bulk modulus, which culminates in a (damped-) oscillation in the form of a longitudinal elastic compression wave. This compression wave can be at the atomic level. In fluids the medium responds differently than in solids and the wave is called an acoustic wave. In general the compression oscillation mode is also the direction of propagation. The oscillatory medium is identified by alternating rarefactions and condensations (also see Lamb wave ). The speed of propagation (v) in sea water is a direct function of depth, salinity, and temperature and can be defined in first-order approximation as $v=\sqrt{B/\text{\rho}}$
, where B is the bulk modulus and ρ the local density. The propagation velocity at the water surface at certain wavelength and temperature is approximately 1.4 × 10^{3}m/s, while at a depth of 5 km this becomes 1.5 × 10^{3}m/s while an increase of 1°C results in an increase of 3.7m/s and an increase in salinity by 1% increases the speed of wave propagation by 1.2 m/s. In comparison the speed of propagation in solids is defined by $v=\sqrt{Y/\text{\rho}}$ , where Y is the Young’s modulus and ρ the local density. For earthquake compression, wave propagation velocity is 1.3 × 10^{4}m/s, approximately 10× greater. Compression waves are also used in ultrasonic imaging, relying on the differences in speed of propagation or modulus of tissue constituents in organs (see Figure C.62).Figure C.62 Example of atmospheric compression wave. The expansion (lowering the local pressure) in a linear direction forms condensation (cooling during expansion), expressed by parallel rows of clouds.
[atomic, biomedical, nuclear] Scientist from the United States who provided empirical proof of the momentum as well as energy phenomena associated with electromagnetic radiation next to that of particles, published in 1922. Based on the energy observations and the prevailing conservation laws the energy loss of a colliding electrons generates a photon with the energy balance at hand as described by the Compton effect. Arthur Compton received the Nobel Prize in Physics in 1927 for his description of the atomic energy explained by the Compton effect (see Figure C.63).
Figure C.63 Arthur Holly Compton (1892–1962). (Courtesy of Noble Foundation, Stockholm, Sweden.)
[atomic, biomedical, condensed matter, energy, nuclear] Description of the energy loss of a photon involved in a collision with free electrons. The conservation of momentum forms the basis of the determination of the wavelength of the re-emitted photons as follows: $\overrightarrow{{p}_{i,\text{photon}}}=\overrightarrow{{p}_{\text{elec}}}+\overrightarrow{{p}_{s,\text{photon}}}$
, where Pi,photon = h/λ is the momentum of the incident photon (h = 6.6260755 × 10^{−34} Js the Planck’s constant, λ the wavelength of the incident electromagnetic radiation with energy Pi,photon = hv, v the frequency of the radiation), the momentum of the scattered photon Ps,photon with momentum of the electron as P _{elec} = m _{ e } c with rest energy: E _{elec} = m _{ e } c ^{2}, however the electron needs to be considered in relativistic terms which yields E _{elec} ^{2} = p _{ e } ^{2} c ^{2}+ m _{ e } ^{2} c ^{4}, based on the conservation of energy: E _{ i },photon + m _{ e } c ^{2} = E _{ s },photon + E _{elec}. The increase in wavelength from the incident photon with wavelength λ_{ i } to the emitted photon with wavelength λ_{ s } is due to the collision loss, which can be written as Δλ = λ_{ i } − λ_{ s } = h/m _{ e } c (l − cos θ), where θ represents the angle of scattering with respect to the incident direction and Δλ represents the Compton wavelength (see Figure C.64).Figure C.64 Compton effect. The angular deflection of a beam of alpha particles nearing an atomic nucleus.
[atomic, biomedical, condensed matter, energy, nuclear] See Compton effect.
[atomic, biomedical, condensed matter, energy, nuclear] The increase in wavelength from the incident photon with wavelength λ_{ i } to the emitted photon with wavelength λ_{ s } is due to the collision loss, which can be written as Δλ = λ_{ i } − λ_{ s } = h/m _{ e } c(1 − cos θ), where θ represents the angle of scattering with respect to the incident direction. In molecular physics the interaction between two protons with the release of a pion (“π”) (i.e., π-meson), with mass m _{π}, is represented by the potential equa-tion: $V=\overline{\overline{{\text{\tau}}_{\text{a}}}}\cdot \overline{\overline{{\text{\tau}}_{\text{b}}}}{g}_{\text{\pi}}^{2}\left({m}_{\text{\pi}}/2M\right)\left[\left(1/3\right)\left({\text{e}}^{-{\text{\mu}}_{C}r}/r\right)\left(\overline{\overline{{\text{\sigma}}_{a}}}\cdot \overline{\overline{{\text{\sigma}}_{b}}}\right)+\left[\left(1/3\right)+\left(1/{\text{\mu}}^{2}{}_{c}{r}^{2}\right)\right]\left({e}^{-{\text{\mu}}_{c}r}/r\right){S}_{\text{ab}}\right]$
, where l/μ_{ c } = ℏ/m _{π} c = 1.4 fm is the pion Compton wavelength $\sqrt{\mathcal{G}{\text{\pi}}^{2}/hc}$ = is the pion-nucleon coupling constant, ℏ = h/2π, where h = 6.6260 × 10^{−16} Js is Planck’s constant), $\overline{\overline{{\text{\sigma}}_{\text{a}}}}$ and $\overline{\overline{{\text{\sigma}}_{\text{b}}}}$ are the Pauli spin matrices for the respective nucleons a and b, $\overline{\overline{{\text{\tau}}_{\text{a}}}}$ and $\overline{\overline{{\text{\tau}}_{\text{b}}}}$ are the respective isospin matrix in 2 × 2 format for nucleon a and b, r the nucleonic interspacing distance, c the speed of light, g_{π} the pion energy, and ${S}_{\text{ab}}=3\left(\overline{\overline{{\text{\sigma}}_{a}}}\cdot \overrightarrow{r}\right)\left(\overline{\overline{{\text{\sigma}}_{b}}}\cdot \overrightarrow{r}\right)-\left(\overline{\overline{{\text{\sigma}}_{a}}}\cdot \overline{\overline{{\text{\sigma}}_{b}}}\right)$ the tensor operator; the intrinsic spin can also be characterized as $\overline{{S}^{\left(a\right)}}=\overline{\overline{{\text{\sigma}}_{a}}}h/2$ .[biomedical, computational, fluid dynamics, thermodynamics] Fluid dynamics problems solved by advanced and extensive mathematical analysis. Early on (prior to computers) numerical solutions were attempted by hand dating back to the eighteenth century, referred to as theoretical fluid dynamics, in contrast to experimental fluid dynamics. The intricacy of the theoretical approach extended to complex and extensive problem statements with lengthy periods (e.g., months) spent on working out the solutions. More recent examples are the work by Lewis Fry Richardson (1881–1953) in 1910 on Laplace equations for heat transfer and Richard Courant (1888–1972), Kurt Otto friedrichs (1901–1982), and Hans Lewy (1904–1988) in 1928 for their work on hyperbolic partial differential equations. The culmination of these efforts came to flourish with the more widespread availability of computers in the 1960s and 1970s shown by the 1973 work of W. Roger Briley (twentieth century) and h. McDonald (twentieth century), and the work of Richard M. Beam (twentieth century) and R.F. Warming (twentieth century) in 1976 and 1978 solving Navier–Stokes and Euler algorithms (see Figure C.65).
Figure C.65 A computational analysis of fluid flow in a tube.
[thermodynamics] The ratio of molecular condensation on a surface to the total number of molecules in contact with the surface, where ΔH _{vap} is the latent heat of vaporization, g gravitational acceleration, L the characteristic length, ΔT temperature gradient, κ the thermal conductivity (Kappa), η viscosity, and ρ the density.
[electromagnetism, general] Old terminology for capacitor, a device that can store electric charge.
[atomic, electronics, general] Under the influence of an external force (e.g., electric or kinetic), electrons can be moved to a higher energy orbit, removed from the valence band (with low binding energy) to an energy configuration that allows the electron to move away from the host atom’s nuclear binding force as a free electron. The energy configuration is referenced as the conduction band. Under room temperature (~300 K) the kinetic energy of electrons is approximately KE = 0.026 eV ≈ 4.1 × 10^{−21} J. In comparison the gap energy (energy gap between valance band and conduction band) for a semiconductor such as germanium or silicon is approximately 1.1 eV, whereas in common conductors, such as iron and copper for instance, the conduction band overlaps the valence band, allowing electrons to move freely between neighboring copper atoms. When the thermal energy can bring the valence electron in the conduction band the phenomenon of electrical conduction is enabled and an electric current can be established.
[atomic, general] Materials made of elements with specific electron configuration. An atom has the electrons arranged according to the Bohr atomic model with electrons in specific allowed energy levels or orbit shells. In comparison with either insulator or semiconductor the electron configuration is more energetic than in these two. In an insulator the conduction band containing free electrons is unpopulated and separated by a forbidden gap from the valence band, whereas in conductor configuration the valence band is overlapping the conduction band, hence populating the conduction mechanism of action with free electrons.
[biomedical, chemical, optics] Anatomical feature in the eye responsible for the electrochemical conversion of electromagnetic radiation in the perception of three elementary colors that in combination with relative intensity will generate virtually infinite number of color combinations. The various color pattern definitions are, for instance, defined by the cie system and described in greater detail under chromaticity (see Figure C.66).
Figure C.66 Cones (color vision) and rods (radiance vision) in the retina of the eye.
[atomic, general, thermodynamics] The following conservation principles/laws can be distinguished: conservation of angular momentum, conservation of atomic nuclei, conservation of baryons, conservation of leptons, conservation of charge, conservation of current, conservation of electromagnetic energy, conservation of energy, conservation of linear momentum, conservation of mass, conservation of mass–energy, conservation of mechanical energy, and conservation of momentum. Each conservation principle will be outlined at the respective location.
[fluid dynamics, general, nuclear] The angular momentum is the product of the angular velocity (ω) and the moment of inertia (I _{inertia}) of the object (L = I _{inertk}ω), when no external forces are involved the total angular momentum of a system will be conserved. When a rotating system disintegrates (without exchange of energy), the sum of the angular momentum as vectors will combine to provide the same angular momentum as for the initial structure. Conservation of angular momentum also applies to nuclear and atomic transitions, setting boundary conditions and selection rules for transitions, in direct combination with conservation of energy (see Figure C.67).
Figure C.67 Conservation of energy (conversion of potential energy to kinetic energy) and conservation of angular momentum illustrated by ball rolling down incline, which will continue its rolling path when a level plane is reached.
[atomic, fluid dynamics, general, nuclear] Charge cannot be destroyed or altered. Combining a particle with positive charge and a particle with negative charge as part of the same system will have as a system the net charge for the two particles, as will the combined particle.
[energy, general, optics] Based on the Maxwell equations the continuity in electromagnetic radiation is defined by $\left(\partial {u}_{e}/\partial t\right)+\nabla \cdot \overrightarrow{S}+\overrightarrow{J}\cdot \overrightarrow{E}=0$
, where $\overrightarrow{E}$ is the electric field, ${u}_{e}=1/8\text{\pi}\left({\left|\overrightarrow{E}\right|}^{2}+{\left|\overrightarrow{B}\right|}^{2}\right)$ the energy density per unit volume V, t is time, $\overrightarrow{J}$ is the current density, $\overrightarrow{S}=\sqrt{{\text{\epsilon}}_{0}{\text{\mu}}_{0}}/4\text{\pi}\left(\overrightarrow{E}\times \overrightarrow{B}\right)$ the Poynting vector, $c=\sqrt{{\text{\epsilon}}_{0}{\text{\mu}}_{0}}$ the speed of light, $\overrightarrow{B}$ is the magnetic field, $\overrightarrow{n}$ : the normal to the surface: A, of the enclosed space, and $\overrightarrow{J}\cdot \overrightarrow{E}$ represents the work per unit time per unit volume performed as a function of the electromagnetic field interaction.[general] The principle that energy can neither be created nor destroyed, and therefore the total amount of energy in the universe is constant. This law of classical physics is modified for certain nuclear reactions (see conservation of mass – energy ).
[general, mechanics] Specifically applying to lossless collisions (no external net forces, specifically no friction, no permanent deformation), the momentum $\overrightarrow{p}$
as a vector will be conserved when transferred to a different set of objects, or adding object to the motion: $\overrightarrow{p}={\displaystyle {\sum}_{n}^{\text{\Omega}}{m}_{i}{\overrightarrow{v}}_{i}}$ , for a system with constituents with mass m _{ i }, each traveling with respective velocity v _{ i }; where $\text{\Delta}\overrightarrow{p}=0$ (see Figure C.68).Figure C.68 During the game of pool (billiards) the principle of conservation of momentum is the driving principle however; there are friction losses involved during the rolling action of the billiard balls.
[thermodynamics] In principle, mass (m) cannot be destroyed. The exception will be nuclear reactions where mass can be converted into energy based on Albert Einstein’s (1879–1955) energy principle: E = mc ^{2}, where c =2.99792458 × 10^{8} m/s is the speed of light. In flow the conservation principle applies to gasses and liquids, where the mass is captured by the density (ρ) multiplied by the volume (V), m = ρV. In chemical reactions the conservation of mass is represented by the reaction equation; no atoms are lost in the forming or dissociation of molecules and residue atoms. The concept of flow is a primary example of the conservation of mass principle (see Figure C.69).
Figure C.69 Conservation of mass illustrated.
[general, mechanics] The principle that both mass and energy combined are conserved based on the principle that energy and mass are interchangeable in accordance with the equation: E = mc ^{2}, where E is the energy, m is the mass, and c is the velocity of light.
[fluid dynamics, general, nuclear] The general conservations laws: conservation of mass, conservation of momentum, and conservation of energy, as well as conservation of angular momentum, next to conservation of charge.
[fluid dynamics] For instance a Knudsen number of Kn ≤ 0.1 sets the boundary conditions where the fluid flow can be treated as a continuous medium, with the macroscopic parameters such as pressure, temperature, volume, velocity, and density. More confined is the regime 0 < Kn ≤ 0.1, describing diffusive slip-flow in the continuum.
[fluid dynamics, mechanics, meteorology] Atmospheric nondispersive wave feature, resembling a chimney effect, primarily centered close to, or on the equator that can extend for thousands of kilometers. cckw consists of a wall of rising air, which tends to tilt to the west with increasing altitude (primarily resulting from the earth’s rotation). The rising air is accompanied by air masses that flow toward the earth’s surface, generating a circulation which generates thunderstorms when reaching the air at lower altitude. These rain storms are reinforcing the effect combined with divergence in air flow at higher altitude leading to cyclonic spin. Especially when two of these systems reach each other, for example, a westward rolling pattern across the Atlantic Ocean clashing with an eastward migrating CCKW can provide the mechanism for the generation of tropical cyclones. CCKW is also referred to as the active convective phase associated with the Madden–Julian oscillation (named after the scientists and meteorologists from the United States: Roland A. Madden [1938–] and Paul Rowland Julian [1929–]; introduced in 1994). The El Niño—Southern Oscillation is a phenomenon that is related, only under a standing pattern. These waves generally travel with a phase velocity of 10–17 m/s, which is a function of the geographic location. The time frame associated with Kelvin waves is exemplified by the fact that is takes approximately 45 days to 2 months for the CCKW to traverse the Pacific Ocean from west to east. However, the anomalies associated with the migration pattern (e.g., tropical storms) may arise as fast as weeks, over a distance in the order of several hundred kilometers (see Figure C.70).
Figure C.70 (a) Schematic cross section through a convectively coupled Kelvin wave (CCKW). (b) Real-life CCKW phenomenon as observed on land in Dubai. (c) CCKW diagram at 40° and 70° latitude outlined by the “Frequency Zonal Wave number; frequency spectrum.” (Courtesy of Michael Ventrice.) (d) OLR, outgoing longwave radiation data. (Courtesy of Paul Roundy.)
[condensed matter, electronics, solid-state] Physicist from the United States. Leon Copper in collaboration with John Bardeen (1908–1991) and John Robert Schrieffer (1931–) developed a theoretical model for superconductivity, referred to as the BCS theory of superconductivity. The Nobel Prize in Physics was awarded to all three men in 1972 for their contributions.
[condensed matter, electronics, solid-state] Pair of free electrons (conducting electrons) in a crystalline solid that behave as they are linked together by means of a long-range interaction. The Cooper pair provides a credible explanation of certain aspects associated with the phenomenon of superconductivity. The first observation of superconductivity was in 1911 by the Dutch physicist Heike Kamerlingh Onnes (1853–1926). The Cooper pair electrons will migrate through the lattice structure totally free of being impeded by the crystalline structure itself, nor any impurities, providing the conditions for zero resistance.
[astronomy, astrophysics, general] (alias of Niklas Koppernigk) German astrophysicist and medicine student. His astrophysics work contributed (although delayed) to the adjustment of the calendar (Gregorian calendar 1581). Copernicus defended the heliocentric planetary system (Sun as the center) with detailed scientific observations and theoretical proof in contrast to the accepted geocentric system (Earth as the center) postulated by Claudius Ptolemaeus (also Ptolemy) (c. 90–168 AD). The Copernican heliocentric model also included the proof of a revolving Earth. Copernicus, however, still assumed the world to be a spherical object, which was challenged by William Gilbert (1540–1603) in 1600, favoring an ellipsoidal model (see Figure C.71).
Figure C.71 Nicolaus Copernicus (1473–1543). (Courtesy of E. Scriven.)
[fluid dynamics, general, mechanics] Physicist from France. In 1835 Coriolis recognized that the rotational motion affects the direction of the path of an object as well as the flow of liquids. Additionally, Coriolis introduced the displacement distance $\left(\overrightarrow{s}\right)$
resulting from an applied force $\left(\overrightarrow{F}\right)$ as work, $W=\overrightarrow{F}\cdot \overrightarrow{s}$ , in 1829 (see Figure C.72).Figure C.72 Gaspard-Gustave de Coriolis (1792–1843).
[computational, fluid dynamics, mechanics, thermodynamics] The principle that the direction of the path of an object as well as the flow of liquids is affected by rotational motion, introducing a motion-dependent acceleration and resulting redirection, while no apparent real external force is present. The acceleration of moving object under influence of a rotating reference frame was described by Gaspard-gustave de Coriolis (1792–1843) in 1835. The phenomenon is however still also referred to as Coriolis force. The Coriolis effect will for instance result in a higher water level on the east side of a river running south to north on the northern hemisphere and on the western riverbank for a similar river on the southern hemisphere. The river itself on the northern hemisphere will also tend to starboard. The same will apply to a sail boat, but these effects are so small that they will be negligible, and may never be recognized due to other external forces, such as wind force. Alternatively, because of Coriolis effect the air flow on the northern hemisphere will be forced to move in counterclockwise direction, which is clearly visible when observing hurricanes (“Atlantic Ocean”) and typhoons (cyclonic action in the northwest Pacific basin: western North Pacific ocean; between the 180° longitude and the 100° east longitude) as observed from a weather satellite position (see Figure C.73).
Figure C.73 The influence of the earth′s rotation on the ocean currents under the Coriolis effect.
[computational, fluid dynamics, mechanics, thermodynamics] Force exerted on an object with mass m by its movement with velocity v with respect to a rotating system with angular velocity ω expressed as $F={m}^{*}-2\overrightarrow{\text{\omega}}\times \overrightarrow{v}$
, specifically identified by the acceleration aspect, $\overrightarrow{a}=-2\overrightarrow{\text{\omega}}\times \overrightarrow{v}$ . The fictional force is primarily perpendicular to the motion of the object. This results, for instance, in having the water level on one side of a flowing river to be higher than the opposite side with respect to sea level due to the earth’s rotation.[computational, fluid dynamics, mechanics, thermodynamics] The vertical component of the angular velocity (ω), also referred to as the planetary vorticity, defined as ν=2ωsin θ, where θ is the reciprocal angle with respect to the normal to the earth’s surface, that is, the latitude on the globe (see Figure C.74).
Figure C.74 The Coriolis frequency concept.
[electromagnetism, general] Electric flux of excess charges from a surface under the influence of a potential difference V between two locations separated by a distance d. The potential difference may result from a variety of factors, man-made or natural. The potential difference thus generates an electric field E that is partially influenced by the radius of curvature (r _{ c }) of the object with the excess charge (also see electric field in conductor as function of radius of curvature of the surface contour). When the radius is much smaller than the separation distance between the opposite charged points the conditions for a corona discharged arc are greater with exceeding ratio. The electric field resulting from the excess electron ionizes the gas(es) that fill the space between the charged points. The electric field and the discharge of charges creates a plasma in the gas between the locations with opposite charge. One specific example is the glowing discharge in a neon light. Another example is lighting, which creates a plasma of the oxygen (o_{2} ) in atmospheric air, forming ozone (o_{3} ). Coronas are also used in copying machines to charge nonconducting surfaces to hold ink for transfer of an image. Free electrons are drawn into the electric field in the conductor, with a field distribution that depends on the radius of curvature, smaller radius higher field due to the higher surface charge density. The electrons (e) with electron charge are accelerated (a) by the electric field due to the electric force, $F=eE=ma$
. The accelerated electrons collide with the resident neutral molecules at a high frequency of ν_{en} ~ 10^{12} Hz. At this point the energy of the electrons is still limited by the inelastic collisions and remains below the photoelectric effect energy. Only a limited number of electrons will escape from the surface of the conductor, contributing to the discharge arc. In standard air pressure with relative humidity 60%, a corona will form for a rounded surface with radius 200 μm under 5 kV electrical potential when placed at a distance of 10^{−2} m with a conductive plate. This discharge voltage increases to 10 kV when the diameter is 2 mm (also see arc, lightning, spark , and St. Elmo’s fire ) (see Figure C.75).Figure C.75 Corona discharge.
[biomedical] Dense bone of the human skeleton, making up approximately 80% of the bone structure. The cortical bone is strong and can support large sheer force. The remaining bone structure is cancellous bone. The main function of the cortical bone is to support and transfer force (e.g., femur, humerus, tibia, more generally [but not limited to] the bones in the arms and legs). Cortical bone forms the protective hard shell of all bone materials. The core material of skeletal bone still often consists of cancellous osseous tissue bones. It is also referred to as compact bone (see Figure C.76).
Figure C.76 Cortical (compact) bone layer of skeletal bone structure.
[general] Set of laws applying to planetary and satellite motion and gravitational interaction on galactic scale derived from the work by Tycho Brahe (1546–1601) and his successor Johannes Kepler (1571–1630). The general concept of cosmic force is captured by the Kepler’s three laws of planetary motion, next to the description of satellite orbits (applying to comets and asteroids), and additionally, the description of the gravitational field, including the hypothetical gravitational particle the “graviton.”
[astronomy/astrophysics, atomic] Radiation consisting of both electromagnetic energy as well as particles emerging from outer space as well as from the Sun. Cosmic rays consist of gamma rays, protons, alpha particles, neutrinos, and electrons next to a minor contribution from isotopes of heavy nuclei. The interaction of cosmic rays with atoms in the upper atmosphere of Earth generate excitation and decay effects next to scattering, which all result in (cascade of; depending on the incident energy) secondary radiation. The stream of particles and electromagnetic radiation reaching Earth from the Sun, the stars in our milky way as well as emission from other galaxies. The particles range in energy from 10^{6} eV to in excess of 10^{22}eV and are composed of protons (~86%), helium nuclei (alpha particles; 12.7%), heavy nuclei (1.3%) as well as electrons (~1%) and a trace of electromagnetic radiation (depending on the interpretation). At the lower end of the scale, gamma rays released in the production of π^{0}eV mesons have an energy of approximately 10^{5} eV, higher energies are in electrons and positrons, increasing to alpha particles (He^{2+}). Additionally, neutrinos and a mixture of nuclei are also detected using methods including bubble–chamber At the highest range the energetic content is dominated by protons at increasing velocity. The particle flux (“j”) for particle in excess of a specific threshold energy (E) is expressed as j(> E) = K _{cosmic} E ^{−δ} K _{cosmic} and where K _{cosmic} and δ are positive constants in the energy regime described by the power law E ≥ 10 GeV/ nucleon.
[astrophysics, computational, nuclear, quantum, theoretical] In the relativistic quantum theoretical description of symmetry breakdown there are hypothetical defects or discontinuities in linear dimension that are referred to as cosmic strings. The theoretical concept is bound by energy in excess of ~ TeV in very short dimensional physics. The cosmic string is part of string theory, in this case relating energy configurations of oscillating open string networks that extend to infinity as well as vibrating closed loops. The general concept of string theory is captured in Schriefer unified theory.
[astronomy/astrophysics, general] Astronaut under the Union of Soviet Socialist Republics (USSR; now Russian Federation, “Russia”) space flight program (see Figure C.77).
Figure C.77 Russian cosmonaut Yuri Gagarin.
[fluid dynamics] Laminar fluid flow between plates with a gradual, and frequently linear, gradient in flow velocity. Couette flow obeys the simplified Navier-Stokes equation, d ^{2} u/ dy ^{2} = 0, where u represent the flow velocity parallel to the planes in the “X-direction” and y is the plate separation distance: the plates can move with respect to each other, the plates can be curved for the case of concentric cylinders, and the flow can describe the fluid motion between stationary plates. The flow velocity as a function of distance between two plates at separation h for a fluid with viscosity η with respect to a pressure (P) gradient is in the direction of flow x can be described under two conditions: (1) moving plate or (2) stationary plates. The moving (sliding) plates solution for relative velocity u _{0} yields u(y) = u _{0}(y/h) + (1/2η)(dP/dx)(y ^{ 2 } − hy).. The laminar Couette flow, with average flow velocity u _{avg} = −(h ^{2}/8η)(dP/dx) between stationary plates is described with respect to the center plane at h/2 in the form u = 3/2u _{avg} [l − (4y ^{2}/h ^{2})], which has similarity to Poiseuille flow and will develop into Poiseuille flow for larger flow velocity. Additional combination solutions are available, with a special case of plates moving in opposite direction. Couette flow generally describes shear stress-dependent flow, such as found in the connection between the piston rod and the crankshaft for an automobile engine, however only below a critical Reynolds number. The flow velocity between two rotating concentric cylinders, with r _{1} the inner cylinder radius, r _{2} the outer cylinder radius, and ω the relative angular velocity, as a function of radius (r) is u _{θ}(r) = (ωR _{1} ^{2}/r)[(R _{2} ^{2} −r ^{2})/(R _{2} ^{2} −R _{1} ^{2})]. In Poiseuille flow, the flow velocity has a quadratic dependence to the location on the radius of the tube under an applied pressure gradient along the length of the tube. Similarly, in Couette flow the flow between two stationary plates has a quadratic dependence to the midpoint plane between the two plates. In comparison, the Poiseuille flow magnitude in a tube will have a dependency to the tube radius to the fourth power where Couette flow will only yield a maximum of quadratic dependence on plate separation. This type of flow is primarily found under low flow velocity, or alternatively low translational velocity of two plates with respect to each other, separated by a viscous fluid. Couette flow is not stratified and has constant vorticity. Under conditions of spanwise rotation, a plane turbulent Couette flow can develop where the velocity is spin in forward and backward flow with respect to the central line between the two moving object, again with only gradual gradient in flow velocity as a function of separation distance, and zero flow velocity on the central dividing plane (see Figure C.78).
Figure C.78 Couette flow: (a) comparison between Couette and Poisseuille flow and (b) example of locations for potential Couette flow.
[energy, general] French scientist whose publication of electric attraction in 1785 (Histoire et Mêmoires de l’Académie Royal des Sciences) “Coulomb’s Law” opened the doors for the Bohr atomic model as well as (see Figure C.79).
Figure C.79 Charles-Augustin de Coulomb (1736–1806).
[chemical, electronics] Electric charge unit, defined indirectly from the Lorentz force between two parallel wires conducting a current of 1 ampere, where 1A = 1C/s defines the flow of an electric charge of 1 coulomb across the cross-sectional area of the wire per second.
[general] Torsion balance used by Charles-Augustin de coulomb (1736–1806) to derive the electrostatic force between electric charges. a gold leaf-covered ball attached to a rod is suspended from a silver wire, counterbalanced by a loop with a paper disk. The suspended ball will be charged by a rod that has an electric charge applied, for instance, a glass rod that has been rubbed by silk. The suspended rod is in the same horizontal plane with a ball of identical material and size as the suspended ball is fixed in three-dimensional space by a nonconducting geometric device. When the two balls are in contact, and if the balls are touched by a charged rod, both will be loaded with the same electrostatic charge (both in sign and magnitude) and will repel. The balls will move away from each other to the point where the torque and electrostatic force are balanced, based on Newton’s third law, and the charge can be derived. Based on Coulomb’s law the electrostatic force will be equal to the force applied to the arm of the suspended rod, expressed as torque.
[atomic, condensed matter, energy] V ^{Coulomb} = e ^{2} /r, where e = −1.6 × 10^{−19}C is the electron charge, however, this also applies to protons as a positive charge, and r the separation between the protons.
[chemical, electronics, mechanics] The force of attraction or repulsion (F _{ e }) exerted between two electrostatic charges, Q _{1} and Q _{2}, respectively, with a distance, s , separated by a medium of dielectric value, ε, is given by the equation F _{ e } = (l/4πε)(Q _{1} Q _{2}/s ^{2}). Introduced by Charles-Augustine de Coulomb (1736–1806).
[computational, thermodynamics] Charge–space–time theorem. Invariance of the Lagrangian theory under standard “proper” Lorentz transformation, specifically pertaining to quantum field theory. Additionally the Lagrangian theory is invariant to time reversal (in either direction) (T), charge conjugation (C), and space inversion (P). In charge conjugation, all particles are transformed into their respective antiparticles. The independence to the space-time continuum requires the following condition to maintain invariance, Λ_{ζx }Λ_{ζg } = δ_{ xg }, yielding a Kronecker delta function for the matrix multiplication.
[general] Remnants of a supernova that presumably exploded in 1054 AD, based on documented observations by Chinese astronomers (keeping in mind the rudimentary tools available at the time and the distance). The Crab Nebula is at approximately 2000 parsecs from Earth (1 parsec = 3.26 light-years =3.1 × 10^{16}m). According to the documentation, the explosion was visible for two years, three weeks of this was also during the daytime. At the center of the nebula is a pulsating neutron star, spinning in similar fashion to an old-fashioned lighthouse beam, with steady pulsating frequency of 30 Hz. The estimated size of this pulsating neutron star is merely 25 km, but has the mass of our Sun (see Figure C.80).
Figure C.80 Crab Nebula, part of the constellation Taurus. Remnant of a supernova that supposedly exploded in 1054 AD. The Crab Nebula has a strong pulsar neutron star in its core. (Courtesy of NASA/STScI, Space Telescope Science Institute, Baltimore, MD.)
[general, mechanics] Anelastic deformation of a solid medium. Anelastic creep is defined by a nonlinear elastic behavior described as a function of stress (σ_{stress} = f/A, the force f acting parallel to the area A) and strain (ϵ_{strain} = ΔL/L _{0}; L the length): J _{ R }σ + τJ _{ n }(∂σ/∂t) = ϵ + τ(∂ϵ/∂t), where j _{ r }, j _{ n }, and τ are material constants and τ the relaxation time with respect to deformation. The material can be defined by a complex compliance, j* = ϵ_{strain}/σ_{stress} = J _{1} + iJ _{2} where the real part of the compliance (J _{1}) is in phase with the applied stress. For a cyclically (angular frequency ω) applied stress the compliance is related to the constants as J _{1} (ω) = J _{ n } + [(J _{ R } − J _{ n })/(l + ω^{2}τ^{2})] and j _{2}(ω) = (J _{ R } − J _{ n } )ωτ/(l + ω^{2}τ^{2}) (known as the Debye equations). The relaxation process under elastic deformation adheres to $\text{\tau}={\text{\tau}}_{0}{\text{e}}^{{E}_{A}/{k}_{b}T}$
, as a function of the activation energy required for the process and the temperature T (Boltzmann coefficient: k _{ b } = 1.3806488 × 10^{−23} m^{2}kg/s^{2} k). Applying specific boundary conditions this will provide three specific types of creep: anelastic, secondary, and tertiary creeps. For instance, anelastic creep can be assumed under constant stress, which provides ϵ_{strain};(t)/σ_{stresss,0} = J _{ n } +(j _{ r } − J _{ n })[l − e^{−(t/ τ)}]. This process also applies to phonon propagation and “dislocated” lattice vibrations (vibrational damage). In biomedical context, this can relate to hearing losses resulting from excessively loud music for extensive periods of time (see Figure C.81).Figure C.81 The creep phenomenon.
[biophysics, general] Molecular biologist, neuroscientist, and biophysicist from England, codiscoverer of the double helix structure of dna with James Dewey Watson (1928–), published in 1953. He dedicated his work to unraveling the mystery of the genetic code, and published the dna–rna–protein correlation as a one-way flow of genetic information (see Figure C.82).
Figure C.82 Francis Harry Compton Crick (1916–2004).
Critical angle (θ_{c})
[general] Angle of incidence at an interface between two media of different index of refraction at which total reflection occurs. The critical angle is based on the refracted angle of 90° under Snell’s law. The critical angle is of particular importance in fiber-optic transmission (see Figure C.83).
Figure C.83 Critical angle for refraction/reflection.
[general, thermodynamics] The boiling point of liquids is directly correlated to the pressure. An increase in pressure will result in a proportional increase in boiling temperature. The difference in density between vapor and fluid phase diminishes with increasing pressure and temperature until the critical point is reached and the density of the liquid and vapor phases become equal. This phenomenon is a second-order phase transition. Examples of media operating at the critical point are superconductors, ferro-magnets experiencing spontaneous magnetization, ferroelectrics exhibiting polarization, and binary fluids, which will separate out the two phases of the constituents (see critical temperature [t _{ c }] and critical pressure [Pc]) (see Figure C.84).
Figure C.84 Dependence of the conductivity of a medium with respect to the critical temperature.
[nuclear] The minimum amount of a fissionable material that will support a chain reaction.
[general, thermodynamics] Temperature below which a material relinquishes its resistance and becomes superconductive (see Figure C.85).
Figure C.85 Critical point in a phase diagram for a substance that contracts when melting, for instance, water. In contrast, carbon dioxide is a substance that will expand upon melting.
[atomic, electronics, nuclear] Physicist from Great Britain who introduced the investigational electrode tube, the Crookes tube in 1870 (see Figure C.86).
Figure C.86 Sir William Crookes (1832–1919). (Courtesy of Leslie Ward, Vanity Fair, 1903.)
[atomic, electronics, nuclear] Vacuum CRT introduced by Sir William Crookes (1832–1919), predecessor to the modern neon light signs. The Crookes tube was based on the earlier observations in a vacuum barometer by the French physicist Jean Picard (1620–1682) (see Figure C.87).
Figure C.87 Crookes tube and mechanism of operation.
[atomic, general, mechanics, nuclear] The area subtended by an atom or molecule for the probability of a reaction, that is, the reaction probability measured in units of area.
[biomedical, energy, general] Freeze-drying, also see lyophilization . Preservation mechanism for biological media used to slow down the chemical processes as well as facilitate the removal of water by means of deepfreeze quick cold storage.
[atomic, biomedical, electronics, general, nuclear] Mechanism of producing extremely low temperature to observe the changes in physical properties of a material. The most known applications in cryogenics are in superconductivity. Most cryogenic processes take place at temperatures below 123K ~−150°c. In biomedical applications the temperature requirements are not that extreme, for instance, the preservation of sperm for in vitro fertilization. In biological applications, generally, the use of frozen carbon dioxide (also known as “dry-ice”) provide the mechanism for quick reduction of temperature by submersion. The melting point of the solid co_{2} is ~−79°C. Attempts of cryogenics on large objects is primarily limited by the heat diffusion and heat capacity of the object in question. Freezing entire human bodies, for instance, will require perfusion with liquid co_{2} , otherwise the core will remain too warm for too long a period and there will be risk for cracking of the solid outer shell due to the fact that most materials either expand or reduce in size with decreasing temperature. At lower temperatures, the molecular mobility will reduce (see temperature ) resulting in a reduction of the probability for collision of migrating free electrons under the influence of an applied external electric field, that is, superconductivity.
[biomedical, general, optics] Adaptive optics instrument in the human eye that can be adjusted for focal length by contraction and relaxation of the muscle in the eye attached to the lens. When the muscles are relaxed the lens is most rounded with the image of the “near point” focused on the retina at approximately 24 mm from the lens. On contraction the lens flattens out, increasing the focal length, as defined by the lens equation, to the point of focusing “infinity” on the retina. The near point is at approximately 25 cm distance from the eye for the average adult, whereas children have a shorter near point (see accommodation ) (see Figure C.88).
Figure C.88 Crystalline lens of the human eye forming an image on the retina for signal acquisition and processing by the brain.
[computational, electromagnetism, general, theoretical] Nonlinearity in electric amplifier. Amplifier with a gain performance profile that can mathematically be described by a polynomial up to the third order (i.e., cubic) without significant loss in accuracy. The polynomial terms can incorporate the higher harmonics and desensitization of interference (i.e., band-block filter or “jammer”) (also see Van der pol equation ).
[atomic, general, nuclear] Scientist and physicist, who left her homeland of Poland to start her doctoral studies at the French Sorbonne. Because of the exposure to radiation Marie Curie eventually died of cancer (see Figure C.89).
Figure C.89 (a) Manya (Marie) Sk∤odowska Curie (1867-1934) at the 1911 Solvay conference: “Conseil Solvay,” organized by the industrialist Ernest Solvay by invitation only. Ernest Gaston Joseph Solvay (1838–1922) chemist from Belgium, shown in (b). The conference was held in Brussels in the latter part of 1911. The subject of the conference was a very popular topic of the day: “Radiation and the Quanta.” The conference became open to the general scientific audience in 1912, upon peer review.
[atomic, general, nuclear] Ascientist from France responsible for the discovery of the piezoelectric activity of crystalline structures under deformation in 1880. Some of the crystalline structures under investigation were quartz, tourmaline, and Rochelle salt. Brother of Pierre Curie (1859–1906) (see Figure C.90).
Figure C.90 Paul-Jacques Curie (1856–1941).
[atomic, general, nuclear] Scientist from France mostly known for his work on radioactivity with his wife Marie Curie (1867–1934). Exemplary contributions of Pierre Curie are the discovery of radium and polonium, next to his work on his work on crystals and magnetism, specifically the formal description of piezoelectric behavior. The husband–wife research couple shared a Nobel Prize in Physics with Antoine Henri Becquerel (1852–1908) in 1903 for their work on radiation (see Figure C.91).
Figure C.91 Pierre Curie (1859–1906).
[atomic, nuclear] Unit of radioactive disintegrations, 1 Cu = 3.70 × 10^{10}dismtegrations/s. The number of disintegrations closely resembles the radium emittance of alpha particles per second from 1 g; however, the Curie is independent of the particle disintegration and particular particles emitted. The value of 1Cu indicates a very powerful radioisotope: 7.4 × 10^{4} [(β − particle/s)] = 2μCu.
[atomic, general, nuclear] Behavior of paramagnetic devices/materials described by Pierre Curie (1859– 1906). The Curie law relates the magnetic dipole moment (m _{ b } ) to the applied magnetic field B as m _{ B } = C _{ c } (B/T), where C _{ c } is the material constant and T the absolute temperature (in Kelvin). The inverse proportionality with respect to temperature ties in with thermal agitation disrupting alignment.
[atomic, general, nuclear] The temperature at which the magnetic structures (also called domains) in a permanent magnet are disrupted by the kinetic motion and the magnet relinquishes its magnetic identity. This phenomenon was discovered by Pierre Curie (1859–1906) in 1894. The Curie temperature is material specific, for instance, for magnetite it is 575°C and for hematide 675°C, respectively.
[atomic, nuclear] Radioactive isotope in the actinide series. The element is named after Curie husband and wife research team: Marie M(anya) SŁodowska Curie (1867–1934) and Pierre Curie (1859–1906).
[computational] The mathematical vector operator describing “rotation” of a vector or function $\left(\overrightarrow{\mathbb{V}}\right)$
within an area (A) at a location $\left(\overrightarrow{r}\right)$ ; defining the rotation of the vector in infinitesimal steps, hence describing the projection of the vector upon all possible lines passing through the location in the three-dimensional space. The curl is expressed as $\nabla \times \overrightarrow{\mathbb{V}}\cdot \overrightarrow{n}\underset{A\to 0}{\mathrm{lim}}\left(1/\left|A\right|{\displaystyle {\oint}_{C}\overrightarrow{\mathbb{V}}\cdot d\overrightarrow{r}}\right)$ , observed as the closed integral over a loop (C), with direction defined by unit direction vector $\overrightarrow{n}$ which is the axis of vector rotation. It is also referred as cross-product. A vector field with curl = 0 is considered “irrotational.”[computational, fluid dynamics] a fundamental component of Helmholtz decomposition in vector calculus. In three-dimensional space, the vector field composed of sufficiently smooth, rapidly decaying vectors can be decomposed into the sum of two “orthogonal” components, one consisting of an irrotational (curl-free) vector field and the second segment composed of rotational (divergence-free) or solenoidal vector field $\left(\overrightarrow{V}\right)$
. The formulation of this series is defined as a function of location $\left(\overrightarrow{r}\right)$ within a volume in space (V) as $\u2102=\left(1/4\text{\pi}\right){\displaystyle {\int}_{V}^{\text{\Omega}}{\nabla}^{\prime}\cdot \overrightarrow{V}\left(\overrightarrow{{r}^{\prime}}\right)/\left|\overrightarrow{r}-\overrightarrow{{r}^{\prime}}\right|}d{V}^{\prime}-\left(1/4\text{\pi}\right){\displaystyle {\int}_{S}^{\text{\Omega}}\overrightarrow{V}\cdot d{S}^{\prime}/\left|\overrightarrow{r}-\overrightarrow{{r}^{\prime}}\right|}$ , the second term will have limit zero when the phenomenon comprises all of free space with the vector field rapidly decreasing.[electromagnetism, general] Electron flow; more specifically the flow of “holes,” since the current direction is in the opposite direction of the displacement of electrons. The current flow was based on the assumption that positive particle where involved, before the analysis of the atomic structure was performed or understood. The flow of electrons relies on a gradient in applied electrical potential (voltage) with an inherent electric field gradient.
[fluid dynamics, geophysics, meteorology] Low-pressure system, generating a fluid volume rotating in the same direction as the Earth. The pressure gradients associated with the cyclonic action generates winds that flow counterclockwise on the northern hemisphere and clockwise on the southern hemisphere. a meteorological cyclone is generally associated with thunderstorms and heavy rainfall (see Figure C.92).
Figure C.92 Image from satellite showing cyclone off the Florida coast.
[atomic, nuclear] Particle accelerator. Charged particles are released from the center of a circular accelerator and gain velocity with increasing radius (spiral path) as a result of an applied magnetic field. The cyclotron is used to investigate the structure of atomic nuclei and create new elements. The cyclotron was invented by Ernest Orlando Lawrence (1901–1958) in the 1920s, and was not feasible for practical use until a large enough magnetic field could be generated in the 1930s. Cyclotrons range in size from less than a meter to several meters. The largest cyclotron is the RIKEN in Japan, with a diameter of 19 m, 8 m high, and can operate with a maximum magnetic field strength of 3.8 T. The RIKEN cyclotron can reach 345 MeV of acceleration energy per atomic mass unit. The cyclotron designed by Ernest Lawrence was built in 1939 has a diameter of 1.52 m. A block-wave periodic magnetic field is applied that matches the resonance conditions to induce acceleration, based on the orbital period of the charge. The cyclotron frequency (angular velocity ω_{cyclotron}; frequency ν_{cyclotron} = ω_{cyclotron}/2π) is a function of the applied magnetic field (B) and the magnitude of the charge (q) on the mass (m) as ω_{cyclotron} = qB/m (see Figure C.93).
Figure C.93 Cyclotron: (a) mechanism of action for particle acceleration, (b) 1.52 m loop at Argonne National Lab, and (c) David Lind at 26 MeV cyclotron beam guide during the 1962 construction. (Courtesy of University of Colorado, Boulder, CO.)