相关论文: Diffusion-Controlled Quasi-Stationary Mass Transfe…

The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications…

We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as…

This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…

A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…

We consider the classical problem of particle diffusion in $d$-dimensional radially-symmetric systems with absorbing boundaries. A key quantity to characterise such diffusive transport is the evolution of the proportion of particles…

The problem of a spatially discontinuous diffusion coefficient ($D(\boldsymbol x)$) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow…

General dynamical transport of classical particles in disordered quasi-1D samples is viewed in the framework of scattering approach. Simple equation for the transfer-matrix is obtained within this unified picture. In the case of diffusive…

We study a random process with reinforcement, which evolves following the dynamics of a given diffusion process in a bounded domain and is resampled according to its occupation measure when it reaches the boundary. We show that its…

We establish the convergences (with respect to the simulation time $t$; the number of particles $N$; the timestep $\gamma$) of a Moran/Fleming-Viot type particle scheme toward the quasi-stationary distribution of a diffusion on the…

We develop a quasi-chemical theory for the study of packing thermodynamics in dense liquids. The situation of hard-core interactions is addressed by considering the binding of solvent molecules to a precisely defined `cavity' in order to…

A model for diffusion-controlled spherical particle growth is presented and solved numerically, showing how, on cooling at sufficient rate from a given fraction solid, growth velocity first increases, and then decreases rapidly when solute…

We study spherical, charged and self--similar distributions of matter in the diffusion approximation. We propose a simple, dynamic but physically meaningful solution. For such a solution we obtain a model in which the distribution becomes…

In this paper, we develop a model to describe the generalized wave-particle instability in a quasi-neutral plasma. We analyze the quasi-linear diffusion equation for particles by expressing an arbitrary unstable and resonant wave mode as a…

In this paper we present a mathematical study of particle diffusion inside and outside a spherical biological cell that has been exposed on one side to a propagating planar diffusive front. The media inside and outside the spherical cell…

The paper addresses the study of a class of evolutionary quasi-variational inequalities of the parabolic type arising in the formation and growth models of granular and cohensionless materials. Such models and their mathematical…

In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be…

In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…

A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…

In this paper, we study quasi-stationary distributions (QSDs) for one-dimensional diffusions killed at 0, when 0 is a regular boundary and $+\infty$ is a natural boundary. More precisely, we not only give a necessary and sufficient…

For a large class of processes with an absorbing state, statistical properties of the surviving sample attain time-independent values in the quasi-stationary (QS) regime. We propose a practical simulation method for studying…