Related papers: Escape and Finite-Size Scaling in Diffusion-Contro…
A method for classifying $n$-species reaction-diffusion models, admitting shock solutions is presented. The most general one-dimensional two-species reaction-diffusion model with nearest neighbor interactions admitting uniform product…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
We consider a system of charged particles moving on the real line driven by electrostatic interactions. Since we consider charges of both signs, collisions might occur in finite time. Upon collision, some of the colliding particles are…
I characterize the extreme location and extreme first passage time of a system of $N$ particles independently diffusing in a space-time random environment. I show these extreme statistics are governed by the Kardar-Parisi-Zhang (KPZ)…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We…
Nucleation on top of two-dimensional islands with step edge barriers is investigated using scaling arguments. The nucleation rate is expressed in terms of three basic time scales: The time interval between deposition events, the residence…
We consider exclusion processes with two types of particles which compete strongly with each other. In particular, we focus on the case where one species does not diffuse at all and killing rates of two species are given by monomials with…
We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…
Scaling laws in astrophysical systems that involve the energy, the geometry, and the spatio-temporal evolution, provide the theoretical framework for physical models of energy dissipation processes. A leading model is the standard…
Extinction times in resampling processes are fundamental yet often intractable, as previous formulas scale as $2^M$ with the number of states $M$ present in the initial probability distribution. We solve this by treating multinomial updates…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…
Given the right set of circumstances, ultracold quantum gases are able to change character and condense into a liquid state of quantum droplets. The size distribution of the droplets is determined dynamically in the condensation process. A…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
We consider an interacting particle system where equal-sized populations of two types of particles move by random walk steps on a graph, the two types may have different speeds, and meetings of opposite-type particles result in…
The problem of the lattice diffusion of two particles coupled by a contact repulsive interaction is solved by finding analytical expressions of the two-body probability characteristic function. The interaction induces anomalous drift with a…
Coalescing ballistic annihilation is an interacting particle system intended to model features of certain chemical reactions. Particles are placed with independent and identically distributed spacings on the real line and begin moving with…
I present a systematic analysis of formation of the universal annihilation catastrophe which develops in an open system, where species $A$ and $B$ diffuse from the bulk of restricted medium and die on its surface (desorb) by the reaction $A…
A system of particles hopping on a line, singly or as merged pairs, and annihilating in groups of three on encounters, is solved exactly for certain symmetrical initial conditions. The functional form of the density is nearly identical to…
In the ballistic annihilation process, particles on the real line have independent speeds symmetrically distributed in $\{-1,0,+1\}$ and are annihilated by collisions. It is widely believed that there is a phase transition at $p=p_{\mathrm…