Continuous-time random-walk approach to normal and anomalous reaction-diffusion processes

Abstract

We study the dynamics of a radioactive species flowing through a porous material, within the Continuous-Time Random Walk (CTRW) approach to the modelling of stochastic transport processes. Emphasis is given to the case where radioactive decay is coupled to anomalous diffusion in locally heterogeneous media, such as porous sediments or fractured rocks. In this framework, we derive the distribution of the number of jumps each particle can perform before a decay event. On the basis of the obtained results, we compute the moments of the cumulative particle distribution, which can be then used to quantify the overall displacement and spread of the contaminant species.

6 pages, 4 figures

References in corpus (8)

• Physical Pictures of Transport in Heterogeneous Media: Advection-Dispersion, Random Walk and Fractional Derivative Formulations
• On reaction-subdiffusion equations
• Mesoscopic description of reactions under anomalous diffusion: A case study
• Disorder-Induced Anomalous Kinetics in the $A+A\to \varnothing$ Reaction
• Normal and Anomalous Transport across an Interface: Monte Carlo and Analytical Approach
• The Effect of Static Disorder and Reactant Segregation on the $A+B\to \varnothing$ Reaction
• The Monte Carlo and fractional kinetics approaches to the underground anomalous subdiffusion of contaminants
• First passage times and distances along critical curves

Cited by in corpus (8)

• Non-Markovian Random Walks and Non-Linear Reactions: Subdiffusion and Propagating Fronts
• Spatio-temporal anomalous diffusion in heterogeneous media by NMR
• A continuous time random walk model of transport in variably saturated heterogeneous porous media
• Evanescent continuous time random walks
• Cattaneo--type subdiffusion--reaction equation
• Effects of mortality on stochastic search processes with resetting
• A nonlinear random walk approach to concentration-dependent contaminant transport in porous media
• Demographic fluctuations in a population of anomalously diffusing individuals