相关论文: Microscopic Deterministic Dynamics and Persistence…
We numerically solve microscopic deterministic equations of motion for the 2D $\phi^4$ theory with random initial states. Phase ordering dynamics is investigated. Dynamic scaling is found and it is dominated by a fixed point corresponding…
Taking the two-dimensional $\phi^4$ theory as an example, we numerically solve the deterministic equations of motion with random initial states. Short-time behavior of the solutions is systematically investigated. Assuming that the…
We study the persistence probability for some discrete-time, time-reversible processes. In particular, we deduce the persistence exponent in a number of examples: first, we deal with random walks in random sceneries (RWRS) in any dimension…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
Phase ordering dynamics of the (2+1)- and (3+1)-dimensional $\phi^4$ theory with Hamiltonian equations of motion is investigated numerically. Dynamic scaling is confirmed. The dynamic exponent $z$ is different from that of the Ising model…
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
We examine persistence in one dimensional Ising model under zero temperature Glauber dynamics for random initial states with unequal fraction of up and down spins. We find the persistence exponent varies continuously with the fraction of up…
We have investigated the random walk problem in a finite system and studied the crossover induced in the the persistence probability scales by the system size.Analytical and numerical work show that the scaling function is an exponentially…
Motivated by certain problems of statistical physics we consider a stationary stochastic process in which deterministic evolution is interrupted at random times by upward jumps of a fixed size. If the evolution consists of linear decay, the…
This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
Understanding under what conditions populations, whether they be plants, animals, or viral particles, persist is an issue of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations…
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.…
The scaling behaviour of the persistence probability in the critical dynamics is investigated with both the heat-bath and the Metropolis algorithm for the two-dimensional Ising model and Potts model. Special attention is drawn to the…
This thesis consists of two separate parts: in each we study the stability under small perturbations of certain probability models in different contexts. In the first, we study small random perturbations of a deterministic dynamical system…
We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as…
We present an exact derivation of the survival probability of a randomly accelerated particle subject to partial absorption at the origin. We determine the persistence exponent and the amplitude associated to the decay of the survival…
A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are…
We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the…