Expanding media are typical in many different fields, e.g. Biology and Cosmology. In general, a medium expansion (contraction) brings about dramatic changes the behavior of diffusive transport properties. Here, we focus on such effects when diffusion process is described by Continuous Time Random Walk (CTRW) model. For case where jump length waiting time probability density functions (pdfs) long-tailed, derive general bifractional equation which reduces to normal appropriate limit. We then...

We investigate how confinement may drastically change both the probability density of first-encounter time and related survival in case two diffusing particles. To obtain analytical insights into this problem, we focus on one-dimensional settings: a half-line an interval. first consider with equal particle diffusivities, for which exact results can be obtained associated over full domain. also evaluate moments when they exist. then turn to diffusivities are not equal, long-time behavior...

We consider a separable continuous-time random walk model for describing normal as well anomalous diffusion of particles subjected to an external force when these diffuse in uniformly expanding (or contracting) medium. A general equation that relates the probability distribution function (pdf) finding particle at given position and time single-step jump length waiting pdfs is provided. The takes form generalized Fokker-Planck pdf has finite variance. This becomes fractional case heavy-tailed...

A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted infinite square well, and expressing wave functions as finite superpositions of eigenfunctions well. eigenvalue equation then yields energy levels within acceptable accuracy. has been successfully used deal based on well-known Kronig-Penney (KP) model. Besides original model, these are a dimerized KP...

Reaction-diffusion equations are widely used as the governing evolution for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion to model transport with reactions on a one-dimensional domain that is evolving. The equations, which have been derived from generalized continuous time random walks, can incorporate complexities such subdiffusive inhomogeneous stretching shrinking. A method constructing analytic expressions short moments of position...

The kinetics of encounter-controlled processes in growing domains is markedly different from that a static domain. Here we consider the specific example diffusion-limited coalescence and annihilation reactions one-dimensional space. In case, such are among few systems amenable to exact solution, which can be obtained by means well-known method intervals. case uniformly domain, show double transformation time space allows one extend this compute main quantities characterizing spatial temporal...

The statistics of the first-encounter time diffusing particles changes drastically when they are placed under confinement. In present work, we make use Monte Carlo simulations to study behavior a two-particle system in two- and three-dimensional domains with reflecting boundaries. Based on outcome simulations, give comprehensive overview survival probability S(t) associated density H(t) over broad range spanning several decades. addition, provide numerical estimates empirical formulas for...

We study normal diffusive and subdiffusive processes in a harmonic potential (Ornstein-Uhlenbeck process) on uniformly growing or contracting domain. Our starting point is recently derived fractional Fokker-Planck equation, which covers both the case of Brownian diffusion continuous-time random walk (CTRW). find high sensitivity properties to details domain growth rate, gives rise variety regimes with extremely different behaviors. At origin this rich phenomenology fact that walkers still...

Abstract We consider the emerging dynamics of a separable continuous time random walk (CTRW) in case when walker is biased by velocity field uniformly growing domain. Concrete examples for such domains include biological cells or lipid vesicles, biofilms and tissues, but also macroscopic systems as expanding aquifers during rainy periods, Universe. The CTRW this study can be subdiffusive, normal diffusive superdiffusive, including particular Lévy flight. first absent. In subdiffusive case,...