Related papers: Model of subdiffusion--absorption process in a mem…
In this paper we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided in two phases: water and biofilm. The biofilm is assumed to consist of four components: water, extracellular polymeric…
Subdiffusion equation and molecule survival equation, both with Caputo fractional time derivatives with respect to another functions $g_1$ and $g_2$, respectively, are used to describe diffusion of a molecule that can disappear at any time…
Absorption of two-state coined quantum walks on a finite line with two sinks located at $N$ and $-N$ is investigated. Elaborating on the results of Konno et al., J. Phys. A: Math. Gen. 36 241 (2003), we derive closed formulas for the…
Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
The adsorption phenomenon of neutral particles from the limiting surfaces of the sample in the Langmuir approximation is investigated. The diffusion equation regulating the redistribution of particles in the bulk is assumed to be of…
We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…
We consider the motion of an underdamped Brownian particle in a tilted periodic potential in a wide temperature range. Based on the previous data [1] and the new simulation results we show that the underdamped motion of particles in…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
This paper studies the mechanisms of dispersion in the laminar flow through the pore space of a $3$-dimensional porous medium. We focus on pre-asymptotic transport prior to the asymptotic hydrodynamic dispersion regime, in which solute…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Fluid flow through bimodal porous media, characterized by a distinct separation in pore size distribution, is critical in various scientific and engineering applications, including groundwater management, oil and gas production, and carbon…
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…
We have random number of independent diffusion processes with absorption on boundaries in some region at initial time $t=0$. The initial numbers and positions of processes in region is defined by Poisson random measure. It is required to…
The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense. For a general distribution of…
Continuous time random walks and Langevin equations are two classes of stochastic models for describing the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
We report a Lattice-Boltzmann scheme that accounts for adsorption and desorption in the calculation of mesoscale dynamical properties of tracers in media of arbitrary complexity. Lattice Boltzmann simulations made it possible to solve…
In this paper we propose and validate a multiscale model for the description of particle diffusion in presence of trapping boundaries. We start from a drift-diffusion equation in which the drift term describes the effect of bubble traps,…
We study the one-dimensional motion of a Brownian particle inside a confinement described by two reactive boundaries which can partially reflect or absorb the particle. Understanding the effects of such boundaries is important in physics,…