Related papers: Survival Probability in a Random Velocity Field
The kinetics of single-species annihilation, $A+A\to 0$, is investigated in which each particle has a fixed velocity which may be either $\pm v$ with equal probability, and a finite diffusivity. In one dimension, the interplay between…
The asymptotic survival probability of a spherical target in the presence of a single subdiffusive trap or surrounded by a sea of subdiffusive traps in a continuous Euclidean medium is calculated. In one and two dimensions the survival…
In a recent paper the mean square displacement (MSD), <R^2(T)>, of a particle carried by a turbulent liquid over time T has been shown to be proportional to T^6/5, meaning that the motion of the particle is slightly super-diffusive. In some…
Three approaches are considered to solve the equation which describes the time-dependent diffusive shock acceleration of test particles at the non-relativistic shocks. At first, the solution of Drury (1983) for the particle distribution…
We consider time-dependent relaxation of observables in quantum systems of chaotic and regular type. We show that the spread of the wave function in the Hilbert space is determined by the survival probability which is known to have…
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival…
Diffusion in a one dimensional random force field leads to interesting localisation effects, which we study using the equivalence with a directed walk model with traps. We show that although the average dispersion of positions $\bar{< x^2 >…
Consider an advancing `front' $ R(t) \in \mathbb{Z}_{\geq 0} $ and particles performing independent continuous time random walks on $ (R(t),\infty)\cap\mathbb{Z} $. Starting at $R(0)=0$, whenever a particle attempts to jump into $R(t)$ the…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy and…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite…
We derive the asymptotic behaviour of the one point probability density for the inhomogeneous shock slopes in the turbulent regime, when a Gaussian fluctuating flux at origin derives the system. We also calculate the time dependence of the…
The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and ; (ii) by the solution of the diffusion…
Transition probabilities for a class of two level systems described by explicitly time dependent Hamiltonians are considered. Provided only that the approach to the infinite time limit is non-trivial falling at least as fast as 1/t for…
The survival probability and the first-passage-time statistics are important quantities in different fields. The Wiener process is the simplest stochastic processwith continuous variables, and important results can be explicitly found from…
We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated to the probability that the process remains below a…
We consider a particle moving in a one dimensional potential which has a symmetric deterministic part and a quenched random part. We study analytically the probability distributions of the local time (spent by the particle around its mean…