in this paper, we propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

We derive a coarse-grained equation of motion of a number density by applying the projection operator method to a non-relativistic model. The derived equation is an integrodifferential equation and contains the memory effect. The equation is consistent with causality and the sum rule associated with the number conservation in the low momentum limit, in contrast to usual acausal diffusion equati...

The Li⁺ diffusion coefficients in Li⁺-adsorbed graphene systems were determined by combining first-principle calculations based on density functional theory with Kinetic Monte Carlo simulations. The calculated results indicate that the interactions between Li ions have a very important influence on lithium diffusion. Based on energy barriers directly obtained from first-principle calculations f...

chloride ion ingress in concrete is the main reason of concrete corrosion. in real world both uncertainty and stochasticity are main attributes of almost all measurements including testing and modeling of chloride content profile in concrete. regarding these facts new models should be able to represent at least some of the uncertainties in the predictions. in this paper after inspiration from c...

The Ginzburg-Landau equation is essential for understanding the dynamics of patterns in a wide variety of physical contexts. It governs the evolution of small amplitude instabilities near criticality. It is well known that the (cubic) Ginzburg-Landau equation has various unstable solitary pulse solutions. However, such localized patterns have been observed in systems in which there are two comp...

Fractional Langevin equation to describe anomalous diffusion. Abstract A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle, with the power exponent being noninteger. More general equation containing fractional ...

In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach considered here uses the properties of the linear equation satisfied by the error process. This methodology seems to apply to a large class of processes and we pre...

A fast diffusion equation is investigated with symmetry point of view. The set of exact non-Lie solutions constructed by M.L. Gandarias [Phys. Lett. A, 2001,V.286, 153-160] are supplemented with the similar ones. The non-classical symmetries of the corresponding potential equation are completely classified with respect to the Lie symmetry group of this equation. As a result, we obtain new wide ...

Since its inception by Kimura in 1955 [M. Kimura, Proc. Natl. Acad. Sci. U.S.A. 41, 144 (1955)], the diffusion equation has become a standard technique of population genetics. The diffusion equation is however only an approximation, valid in the limit of large populations and small selection. Moreover, useful quantities such as the fixation probabilities are not easily extracted from it and nee...

The present paper is aimed to study an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel based on three-dimensional generalized theories of thermoelastic diffusion. After applying the displacement potential functions in the basic governing equations of generalized thermoelastic diffusion, it is noticed that a purely transverse mo...