Related papers: Heat diffusion with frozen boundary
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor.…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
Diffusive scaling of position moments and a central limit theorem are obtained for the mean position of a quantum particle hopping on a cubic lattice and subject to a random potential consisting of a large static part and a small part that…
Particles moving along curved trajectories will diffuse if the curvature fluctuates sufficiently in either magnitude or orientation. We consider particles moving at a constant speed with either a fixed or with a Gaussian distributed…
We study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and when two particles meet, they annihilate. We focus on spatial…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
The following model is studied analytically and numerically: point particles with masses $m,\mu,m, \dots$ ($m\geq\mu$) are distributed over the positive half-axis. Their dynamics is initiated by giving a positive velocity to the particle…
Though classical random walks have been studied for many years, research concerning their quantum analogues, quantum random walks, has only come about recently. Numerous simulations of both types of walks have been run and analyzed, and are…
We study a Markovian model for the random fragmentation of an object. At each time, the state consists of a collection of blocks. Each block waits an exponential amount of time with parameter given by its size to some power $\alpha$,…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
We consider random Schr\"odinger equations on $\bZ^d$ for $d\ge 3$ with identically distributed random potential. Denote by $\lambda$ the coupling constant and $\psi_t$ the solution with initial data $\psi_0$. The space and time variables…
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…
Evolution of a multiplicity distribution can be described with the help of master equation. We first look at 3rd and 4th factorial moments of multiplicity distributions and derive their equilibrium values. From them central moments and…
We discuss a class of diffusion-type partial differential equations on a bounded interval and discuss the possibility of replacing the boundary conditions by certain linear conditions on the moments of order 0 (the total mass) and of…
Melting is often understood in purely equilibrium terms, where crystalline order disappears once the free energy of the solid equals that of the liquid. Yet at the microscopic level, the initiating events for melting can often be traced to…
We consider a diffusion in a Gaussian random environment that is white in time and study the large-scale behavior of the quenched density with respect to the Lebesgue measure. We show that under diffusive rescaling, the fluctuations of the…
We investigate the ballistic spreading behavior of the one-dimensional discrete time quantum walks whose time evolution is driven by any balanced quantum coin. We obtain closed-form expressions for the long-time variance of position of…
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 concept of random walk, in which particles or waves undergo multiple collisions with the microscopic constituents of a surrounding medium, is central to understanding diffusive transport across many research areas. However, this…