Related papers: On diffusion in narrow random channels
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We study molecular diffusion in linear nanopores with different types of roughness in the so-called Knudsen regime. Knudsen diffusion represents the limiting case of molecular diffusion in pores, where mutual encounters of the molecules…
We analyze the diffusive transport of Brownian particles in narrow channels with periodically varying cross-section. The geometrical confinements lead to entropic barriers, the particle has to overcome in order to proceed in transport…
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…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
We investigate the dependence of the displacements of a molecular motor embedded inside a glassy material on its folding characteristic time. We observe two different time regimes. For slow foldings (regime I) the diffusion evolves very…
We introduce a novel linear transport equation that models the evolution of a one-particle distribution subject to free transport and two distinct scattering mechanisms: one affecting the particle's speed and the other its direction. These…
We investigate the consensus problem in a network where nodes communicate via diffusion-based molecular communication (DbMC). In DbMC, messages are conveyed via the variation in the concentration of molecules in the medium. Every node…
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…
We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics…
Continuous diffusion models are commonly acknowledged to display a deterministic probability flow, whereas discrete diffusion models do not. In this paper, we aim to establish the fundamental theory for the probability flow of discrete…
Diffusion models have recently brought a powerful revolution in image generation. Despite showing impressive generative capabilities, most of these models rely on the current sample to denoise the next one, possibly resulting in denoising…
We developed analytical and numerical methods to study a transport of non-interacting particles in large networks consisting of M d-dimensional containers C_1,...,C_M with radii R_i linked together by tubes of length l_{ij} and radii a_{ij}…
Most motion deblurring algorithms rely on spatial-domain convolution models, which struggle with the complex, non-linear blur arising from camera shake and object motion. In contrast, we propose a novel single-image deblurring approach that…
The rise of digital and mobile communications has recently made the world more connected and networked, resulting in an unprecedented volume of data flowing between sources, data centers, or processes. While these data may be processed in a…
In this work we are concerned with the inverse problem of the estimation of modeling parameters for a reactive bimolecular transport based on experimental data that is non-uniformly distributed along the interval where the process takes…
Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic…
We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…
We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the…
We consider random flights of point particles inside $n$-dimensional channels of the form $\mathbb{R}^{k} \times \mathbb{B}^{n-k}$, where $\mathbb{B}^{n-k}$ is a ball of radius $r$ in dimension $n-k$. The particle velocities immediately…