Heterogeneous continuous time random walks

Abstract

We introduce a heterogeneous continuous time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatio-temporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.

11 pages, 5 figures

References in corpus (15)

• Reaction-diffusion processes and metapopulation models in heterogeneous networks
• Scaling theory of transport in complex networks
• Random walks and search in time-varying networks
• Anomalous, non-Gaussian tracer diffusion in heterogeneously crowded environments
• Exact solution for mean first-passage time on a pseudofractal scale-free web
• Mortality, Redundancy, and Diversity in Stochastic Search
• The escape problem for mortal walkers
• Splitting of the universality class of anomalous transport in crowded media
• Localization Transition of Biased Random Walks on Random Networks
• Partially Reflected Brownian Motion: A Stochastic Approach to Transport Phenomena
• The two-particle problem in comb-like structures
• Solvable continuous time random walk model of the motion of tracer particles through porous media
• A nonlinear random walk approach to concentration-dependent contaminant transport in porous media
• Evaluating transport in irregular pore networks
• Random Walks on Complex Networks

Cited by in corpus (13)

• Diffusion-limited reactions in dynamic heterogeneous media
• Emergent memory and kinetic hysteresis in strongly driven networks
• Preface: New trends in first-passage methods and applications in the life sciences and engineering
• Joint distribution of multiple boundary local times and related first-passage time problems with multiple targets
• Inference from gated first-passage times
• Universal cover-time distribution of heterogeneous random walks
• Diffusive Exit Rates Through Pores in Membrane-Enclosed Structures
• Classes of random walks on temporal networks with competing timescales
• Temperature Equilibration Due to Charge State Fluctuations in Dense Plasmas
• Structural and temporal heterogeneities on networks
• Multi-target search in bounded and heterogeneous environments: a lattice random walk perspective
• First-passage on disordered intervals
• Diffusive search and trajectories on spatial networks: a propagator approach