In this work, the problem of Rayleigh wave propagation is considered in the context of the theory of thermoelastic diffusion. The formulation is applied to a homogeneous isotropic thermoelastic half space with mass diffusion at the stress free, isothermal, isoconcentrated boundary. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obt...

– The porous media equation has been proposed as a phenomenological “nonextensive” generalization of classical diffusion. Here, we show that a very similar equation can be derived, in a systematic manner, for a classical fluid by assuming nonlinear response, i.e. that the diffusive flux depends on gradients of a power of the concentration. The present equation distinguishes from the porous medi...

We investigate the experimental limits of validity of the Stokes–Einstein equation. There is an important difference between diffusion and self-diffusion. The experimental evidences show, that in the case of selfdiffusion the product Dg/T is constant and the Stokes–Einstein equation is still valid. On the other hand, comparison of existing experimental data, on viscosity g and diffusion coeffic...

We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain ...

We consider the simultaneous diffusion and homogenization limit of the linear Boltzmann equation in a periodic medium in the regime where the mean free path is much smaller than the lattice constant. The resulting equation is a diffusion equation, with an averaged diffusion matrix that is formally obtained by first performing the diffusion limit and then the homogenization one. The rigorous pro...

in this study, the effect of grain size on nitrogen diffusion into ck45 has been investigated. in order to obtain different grain sizes, samples were annealed and normalized at various temperatures and durations.the grain size was determined with clemex vision software. then, the specimens were exposed to dc plasma nitriding treatment and again analyzed by optical microscope ,scanning electron ...

a simple mathematical model of steady state  oxygen distribution subject to diffusive transport and non- linear uptake in a retinal cylinder has been developed. the approximate analytical solution to a reaction- diffusion equation are obtained by using series expansions. the computational results for the scaled variables are presented through graphs. the effect of the important parameters (1) d...

The paleoclassical model of radial electron heat transport in resistive, current-carrying toroidal plasmas is based on a key hypothesis — that electron guiding centers move and diffuse with radially localized annuli of poloidal magnetic flux. This hypothesis is shown to result from transforming the drift-kinetic-equation to poloidal flux coordinates in situations where this flux is governed by ...

The paleoclassical model of radial electron heat transport in resistive, current-carrying toroidal plasmas is based on a key hypothesis—that electron guiding centers move and diffuse with radially localized annuli of poloidal magnetic flux. This hypothesis is shown to result from transforming the drift-kinetic-equation to poloidal flux coordinates in situations where this flux is governed by a ...

We propose a method which utilizes the radiative transfer equation in optical tomography. In this approach, the radiative transfer equation is used as light propagation model in those regions in which the assumptions of the diffusion theory are not valid and the diffusion approximation is used elsewhere. Both the radiative transfer equation and the diffusion approximation are numerically solved...