Sentence examples for by the diffusion equation from inspiring English sources

Light propagation in the diffusive medium is described by the diffusion equation [ 20]: where c is the light velocity, D (r → ) is the diffusion coefficient, μ a (r → ) is the absorption coefficient, δ (r →, t ) is the Dirac distribution and G s (r →, t ) is the photon density resulting from the Dirac source excitation (Green's function).

The diffusive flow of the volatiles dissolved within the melt into the gas bubble is governed by the diffusion equation: (7 where c is the concentration of volatiles in the melt, D is the diffusive coefficient of the volatiles in the melt, D/Dt is the total derivative, and r is the radial coordinate.

Again, this is an idealized situation for pressure evolution controlled by the diffusion equation.

Inside the channel the movement of the gas was described by the equation; outside by the diffusion equation.

The spatial form and temporal evolution of the geomagnetic field B is then given by the diffusion equation: nabla^{2}textbf{B} - musigmapartial_{t}textbf{B} = 0, (1).

Even a step-wise increase of pressure at the injection point will become a smooth time history by the diffusion equation at close distances.

The model was tested by solving the diffusion equation numerically on example structures that differed in architecture.

The jump rates can be computed by discretizing the diffusion equation on that unstructured mesh.

The conditions for the model having a solution have been determined by solving the diffusion equation in the gas phase around the particle.

Problems containing regions with a small mean free path can frequently be accurately simulated much more quickly by employing the diffusion equation as an approximation.

The concentration profiles of reacting species at the electrode solution interface under a periodic square wave perturbing potential are calculated by solving the diffusion equation for the case of a fast reversible metal metal ion reaction.