Equation that describes density changes of a material that is diffusing in a medium
The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's laws of diffusion). In mathematics, it is related to Markov processes, such as random walks, and applied in many other fields, such as materials science, information theory, and biophysics. The diffusion equation is a special case of the convection–diffusion equation when bulk velocity is zero. It is equivalent to the heat equation under some circumstances.
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The diffusionequation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian...
Laplacian and of the heat equation in modeling any physical phenomena which are homogeneous and isotropic, of which heat diffusion is a principal example...
Anomalous diffusion – Diffusion process with a non-linear relationship to time Convection-diffusionequation – Combination of the diffusion and convection...
current together are described by the drift–diffusionequation. It is necessary to consider the part of diffusion current when describing many semiconductor...
molecular diffusion, and its mathematical aspect is captured by the diffusionequation. In turbulent flows, on top of mixing by molecular diffusion, eddies...
Diffusion-weighted magnetic resonance imaging (DWI or DW-MRI) is the use of specific MRI sequences as well as software that generates images from the...
numerical solutions to differential equations. It is one of the schemes used to solve the integrated convection–diffusionequation and to calculate the transported...
Continuity equations underlie more specific transport equations such as the convection–diffusionequation, Boltzmann transport equation, and Navier–Stokes...
wave equation, the diffusionequation, and the Schrödinger equation for a free particle. In optics, the Helmholtz equation is the wave equation for the...
transfer equation (RTE). However, the RTE is difficult to solve without introducing approximations. A common approximation summarized here is the diffusion approximation...
first part consists in the formulation of a diffusionequation for Brownian particles, in which the diffusion coefficient is related to the mean squared...
derivatives Anomalous diffusion processes in complex media can be well characterized by using fractional-order diffusionequation models. The time derivative...
magnetization of the material and μ0 is the vacuum permeability. The diffusionequation therefore is ∇ 2 H = μ 0 σ ( ∂ M ∂ t + ∂ H ∂ t ) . {\displaystyle...
cases can be described by a generalization of the usual diffusionequation where the diffusion coefficient, instead of being a constant scalar, is a function...
also convection–diffusionequation. The equation is a nonlinear integro-differential equation, and the unknown function in the equation is a probability...
magnetic diffusionequation and is due primarily to induction and diffusion of magnetic fields through the material. The magnetic diffusionequation is a...
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