Related papers: Chemical diffusion master equation: formulations o…
We consider a Markovian jumping process which is defined in terms of the jump-size distribution and the waiting-time distribution with a position-dependent frequency, in the diffusion limit. We assume the power-law form for the frequency.…
The self-diffusion process of a hard sphere fluid confined by two parallel plates separated by a distance on the order of the particle diameter is studied. The starting point is a closed kinetic equation for the distribution function that…
The recent advancements in mathematical modeling of biochemical systems have generated increased interest in sensitivity analysis methodologies. There are two primary approaches for analyzing these mathematical models: the stochastic…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…
Molecular conformation generation, a critical aspect of computational chemistry, involves producing the three-dimensional conformer geometry for a given molecule. Generating molecular conformation via diffusion requires learning to reverse…
In synaptic molecular communication (MC), the activation of postsynaptic receptors by neurotransmitters (NTs) is governed by a stochastic reaction-diffusion process. This randomness of synaptic MC contributes to the randomness of the…
In this work we are concerned with generating solutions of a class of Convection-Diffusion-Reaction equation from the solutions of another CDR equation through the Darboux transformations. The method is elucidated by cases with certain…
Diffusion phenomena in a multiple component lattice Boltzmann Equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is…
We consider absorbing chemical reactions in a fluid flow modeled by the coupled advection-reaction-diffusion equations. In these systems, the interplay between chemical diffusion and fluid transportation causes the enhanced dissipation…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
In inhomogeneous environments, the correct expression of the diffusive flux is often not given by the Fick's law $\Gamma = - D \nabla n $. The most general hydrodynamic equation modelling diffusion is indeed the Fokker-Planck Equation…
This article presents a new approach to the dynamics of a particle system, divided into two distinct microstates spreading out in a homogeneous medium. The particles belonging to the main microstate spread according to classical Fick's law…
Chemical and biological networks can describe a wide variety of processes, from gene regulatory networks to biochemical oscillations. Modeled by chemical master equations, these processes are inherently stochastic, as fluctuations dominate…
A mesoscopic multi-particle collision model for fluid dynamics is generalized to incorporate the chemical reactions among species that may diffuse at different rates. This generalization provides a means to simulate reaction-diffusion…
Usually Fokker-Planck type partial differential equations (PDEs) are well-posed if the initial condition is specified. In this paper, alternatively, we consider the inverse problem which consists in prescribing final data: in particular we…
The generalized master equation with two times, introduced in earlier, applies to the problem of diffusion in an time-dependent (in general inhomogeneous) external field. We consider the case of the quasi Fokker-Planck approximation, when…
Diffusion processes have been applied with great success to model the dynamics of large populations throughout science, in particular biology. One advantage is that they bridge two different scales: the microscopic and the macroscopic one.…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…
Diffusive molecular communication (DMC) is one of the most promising approaches for realizing nano-scale communications in biological environments for healthcare applications. In this paper, a DMC system in biological cylindrical…