Laplacian and of the heat equation in modeling any physical phenomena which are homogeneous and isotropic, of which heat diffusion is a principal example...

for the diffusion coefficient, D. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation. Fick's first...

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...

Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of...

In machine learning, diffusion models, also known as diffusion probabilistic models or score-based generative models, are a class of latent variable generative...

Stable Diffusion is a deep learning, text-to-image model released in 2022 based on diffusion techniques. The generative artificial intelligence technology...

Klein–Kramers equation. The case with zero diffusion is the continuity equation. The Fokker–Planck equation is obtained from the master equation through Kramers–Moyal...

interpreted as a diffusion coefficient and ∇ ⋅ ( ⋅ ) {\displaystyle \nabla \cdot (\cdot )} is the divergence operator. Despite being a nonlinear equation, the porous...

Continuum mechanics Convection–diffusion equation Derivation of the Navier–Stokes equations Einstein–Stokes equation Euler equations Hagen–Poiseuille flow from...

Rotational diffusion is the rotational movement which acts upon any object such as particles, molecules, atoms when present in a fluid, by random changes...

In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow...

current together are described by the drift–diffusion equation. It is necessary to consider the part of diffusion current when describing many semiconductor...

the diffusion coefficient). It has been found that equations describing normal diffusion are not capable of characterizing some complex diffusion processes...

diffusivity or diffusion coefficient is usually written as the proportionality constant between the molar flux due to molecular diffusion and the negative...

to the electrode. That is, the current is said to be "diffusion controlled". The Cottrell equation describes the case for an electrode that is planar but...

Continuity equations underlie more specific transport equations such as the convection–diffusion equation, Boltzmann transport equation, and Navier–Stokes...

differential equations describing physical phenomena. Poisson's equation describes electric and gravitational potentials; the diffusion equation describes...

first part consists in the formulation of a diffusion equation for Brownian particles, in which the diffusion coefficient is related to the mean squared...

was Fourier's proposal of his heat equation for conductive diffusion of heat. This partial differential equation is now a common part of mathematical...

False diffusion is a type of error observed when the upwind scheme is used to approximate the convection term in convection–diffusion equations. The more...

Diffusion maps is a dimensionality reduction or feature extraction algorithm introduced by Coifman and Lafon which computes a family of embeddings of...

mole). The potential across the cell membrane that exactly opposes net diffusion of a particular ion through the membrane is called the Nernst potential...

context of a diffusion process, for the backward Kolmogorov equations see Kolmogorov backward equations (diffusion). The forward Kolmogorov equation is also...

(and similar diffusion processes) in a way compatible with special relativity. In special (and general) relativity, the usual heat equation for non-relativistic...

general form of the equation in the classical case is D = μ k B T , {\displaystyle D=\mu \,k_{\text{B}}T,} where D is the diffusion coefficient; μ is the...

also convection–diffusion equation. The equation is a nonlinear integro-differential equation, and the unknown function in the equation is a probability...

similarly to how the Schrödinger equation gives the time evolution of the quantum wave function or the diffusion equation gives the time evolution of chemical...

In applied mathematics, Arnold diffusion is the phenomenon of instability of nearly-integrable Hamiltonian systems. The phenomenon is named after Vladimir...

Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical...

long economic cycles and on diffusion of innovations. Arnulf Grübler's book (1990) gives a detailed account of the diffusion of infrastructures including...