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 ?
On the basis of the solution to the diffusion Equation (Eq 5), it is possible to estimate whether, and over which cross section this minimum concentration prevails for different gas holding times (bottom right-hand diagram in [ILLUSTRATION FOR FIGURE 3 OMITTED]).
That is, we solved the heat diffusion equation in one dimension by the method of finite differences, and using the temperature arrays thus obtained, the ratio of excimer to monomer fluorescence [I.
The diffusion equation for the dissolved blowing agent in LDPE melt is:
The diffusion equation is made dimensionless by considering a characteristic time, [Tau], characteristic length, L, and a dimensionless concentration, [C.
The dissolution rate data of the polymer were correlated with a transient diffusion equation based on a pseudo-homogenous model.
But fear not: by making some simplifying assumptions, the radiative transfer equation can yield the diffusion equation, an approximation that can be tested against reference figures.
However, the desorption rate is closely predicted using the diffusivity obtained from a curve fit of the absorption data and the appropriate diffusion equation, indicating that the phenol is not bound within the polymer.
Equation 7 is the standard diffusion equation and various solutions are known (Carslaw and Jaeger 1959; Crank 1979).
It is usually acknowledged that the time enters into the diffusion equation thanks to the continuity condition that leads to the second Fick law.
For the case of spherical symmetry with the formation of species from chemical reactions the diffusion equation may be written as
We investigate two numerical examples of the reaction diffusion equation with polynomial nonlinearity and non-polynomial nonlinearity to show comparison of accuracy for our perturbation method with other well-known nonlinear Galerkin methods such as Foias-Manley-Temam and Euler-Galerkin methods.

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