Torque fluctuations due to magnetorotational turbulence in proto-planetary disks may greatly influence the migration patterns and survival probabilities of nascent planets. Provided that the turbulence is a stationary stochastic process with finite amplitude and correlation time, the resulting diffusive migration can be described with a FokkerPlanck equation, which we reduce to an advection-dif...

This paper studies how patterns derived from a system of reaction-diffusion equations may vary significantly depending on boundary and initial conditions, as well as in the spatial dependence of the coefficients involved. From an extensive numerical study of the BVAM model, we demonstrate that the geometric pattern of a reaction diffusion system is not uniquely determined by the value of the pa...

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

We apply the weighted-residual approach recently introduced in [7] to derive dis-continuous Galerkin formulations for advection-diffusion-reaction problems. We devise the basic ingredients to ensure stability and optimal error estimates in suitable norms, and propose two new methods. 1. Introduction. In recent years Discontinuous Galerkin methods have become increasingly popular, and they have ...

We consider the space fractional advection-dispersion equation, which is obtained from the classical advection-diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulas for the discretisation of the fractional derivative, to numerically solve the equation on a f...

In this paper, we propose to improve the stabilized POD-ROM introduced in [48] deal with numerical simulation of advection-dominated advection-diffusion-reaction equations. particular, a three-stage stabilizing strategy that will be very useful when considering low diffusion coefficients, i.e. strongly regime. This approach mainly consists three ingredients: (1) addition “streamline diffusion” ...

The perifusion apparatus is an experimental tool used to model information transfer in endocrine systems. The major drawback of the penfusion system derives from the dispersion, diffusion and mixing of the hormone within the apparatus which distort the original released hormone concentration profile. In this paper we develop a mathematical model of the perifusion system that accounts for a numb...