Related papers: Accelerating random walks by disorder
We introduce a formalism of fractional diffusion on networks based on a fractional Laplacian matrix that can be constructed directly from the eigenvalues and eigenvectors of the Laplacian matrix. This fractional approach allows random walks…
Stochastic resetting is a protocol of starting anew, which can be used to facilitate the escape kinetics. We demonstrate that restarting can accelerate the escape kinetics from a finite interval restricted by two absorbing boundaries also…
Levy walks define a fundamental concept in random walk theory which allows one to model diffusive spreading that is faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a…
Transport of the Brownian particles driven by L\'evy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination…
Standard Reaction-Diffusion (RD) systems are characterized by infinite velocities and no persistence in the movement of individuals, two conditions that are violated when considering living organisms. Here we consider a discrete particle…
We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…
Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the…
We study a random walk on a point process given by an ordered array of points $(\omega_k, \, k \in \mathbb{Z})$ on the real line. The distances $\omega_{k+1} - \omega_k$ are i.i.d. random variables in the domain of attraction of a…
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…
We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact…
This paper concerns the propagation of particles through a quenched random medium. In the one- and two-dimensional models considered, the local dynamics is given by expanding circle maps and hyperbolic toral automorphisms, respectively. The…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
We investigate the dynamics of a particle moving randomly along a disordered hetero-polymer subjected to rapid conformational changes which induce superdiffusive motion in chemical coordinates. We study the antagonistic interplay between…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
The time that waves spend inside 1D random media with the possibility of performing L\'evy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered…
The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronise populations of interacting species, stabilise them, and diversify gene pools [1-3].…
The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination…
After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models',…
The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…