Particle-tracking simulation of fractional diffusion-reaction processes

Particle tracking for time-fractional diffusion.

A particle tracking code is developed to solve a general time-fractional diffusion equation (FDE), yielding a Lagrangian framework that can track particle dynamics. Extensive simulations demonstrate the efficiency and flexibility of this simple Langevin approach. Many real problems require a vector FDE with variable parameters and multiscaling spreading rates. For these problems, particle track...

Particle Simulation of Fractional Diffusion Equations

This work explores different particle-based approaches to the simulation of one-dimensional fractional sub-diffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on a direct differentiation of the particle representation; it follows the Riesz definition of the fraction...

Particle Tracking and the Diffusion - Reaction

Particle tracking and the diffusion-reaction equation

[1] Particle tracking algorithms are very useful methods to model conservative transport in surface and subsurface hydrological systems. Recently, a novel ad hoc particle-based method was proposed to account for multicomponent reactive transport by Benson and Meerschaert (2008). This one-dimensional particle method has been shown to match theoretical predictions, but, to date, there has been no...

Stochastic Simulation of Coupled Reaction–Diffusion Processes

actants is used to compute the time evolution of reactant concentrations. The stochastic algorithm is rigorous in the The stochastic time evolution method has been used previously to study non-linear chemical reaction processes in well-stirred hosense that it provides an exact solution to the correspondmogeneous systems. We present the first treatment of diffusion, in ing master equation for ch...