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A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
An example assuming a parabolic dispersion relation for the density of states and the Maxwell–Boltzmann statistics, which is often used to describe inorganic semiconductor materials, one can compute (see density of states): =, where is the total density of available energy states, which gives the simplified relation: =.
Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...
Dispersive mass flux is analogous to diffusion, and it can also be described using Fick's first law: J = − E d c d x , {\displaystyle J=-E{\frac {dc}{dx}},} where c is mass concentration of the species being dispersed, E is the dispersion coefficient, and x is the position in the direction of the concentration gradient.
Given that a system obeys detailed balance, the theorem is a proof that thermodynamic fluctuations in a physical variable predict the response quantified by the admittance or impedance (in their general sense, not only in electromagnetic terms) of the same physical variable (like voltage, temperature difference, etc.), and vice versa.
The Sellmeier equation is an empirical relationship between refractive index and wavelength for a particular transparent medium. The equation is used to determine the dispersion of light in the medium. It was first proposed in 1872 by Wolfgang Sellmeier and was a development of the work of Augustin Cauchy on Cauchy's equation for modelling ...
In optics, group-velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium affects the duration of an optical pulse traveling through it. Formally, GVD is defined as the derivative of the inverse of group velocity of light in a material with respect to angular frequency , [ 1 ] [ 2 ]