diffusion equation


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diffusion equation

[də′fyü·zhən i′kwā·zhən]
(physics)
An equation for diffusion which states that the rate of change of the density of the diffusing substance, at a fixed point in space, equals the sum of the diffusion coefficient times the Laplacian of the density, the amount of the quantity generated per unit volume per unit time, and the negative of the quantity absorbed per unit volume per unit time.
More generally, any equation which states that the rate of change of some quantity, at a fixed point in space, equals a positive constant times the Laplacian of that quantity.
References in periodicals archive ?
Combining fractional differential operator with anisotropic diffusion equation, a denoising algorithm based on adaptive fractional order anisotropic diffusion is put forward.
Assuming diffusion only in the longitudinal direction, the solution to the one-dimensional diffusion equation, Equation 13, can be extended to rectangular-shaped wood blocks (Kumaran 1999):
The light transport of photons through a biological tissue is established during diffusion equation.
Recent analytical solutions of the advection diffusion equation with dry deposition at the ground have utilized height-dependent wind speed and eddy diffusivities (Horst and Slinn [4], Koch [11], Chrysikopoulos et al.
There is already some important progress for the fractional diffusion equation or advection-diffusion equations.
In this work a multi-grid method is developed for the solution of 2D convection diffusion equation based on fourth order compact scheme.
Luchko, Initial boundary value problems for the one dimensional time-fractional diffusion equation, Frac.
Analytical-Numerical Solution of a Parabolic Diffusion Equation Under Uncertainty Conditions Using DTM with Monte Carlo Simulations
for the convection and diffusion equation are shown in Table 1 (Mora Acosta 2001).
In this case heating relies on the diffusion equation, which involves the drying rate in the energy balance (Karim and Hawlader, 2005; Mariani et al.
The diffusion equation, Fick's second law with a constant diffusion coefficient during the wet or dry portion of the cycle, is nondimensionalized.
Tuan (2011) proved that by taking suitable initial distributions only finitely many measurements on the boundary were required to recover uniquely the diffusion coefficient of one dimensional fractional diffusion equation.

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