Related papers: Persistence in systems with conserved order parame…
We study a system of particles which jump on the sites of the interval $[1,L]$ of $\mathbb Z$. The density at the boundaries is kept fixed to simulate the action of mass reservoirs. The evolution depends on two parameters $\lambda'\ge 0$…
We characterize steady-state static and dynamic properties in a broad class of mass transport processes on a periodic hypercubic lattice of volume $L^d$, where both mass and {\it center-of-mass} (CoM) remain conserved and detailed balance…
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter $\delta$, we review their formulation defined on a bounded domain subject to various conditions that correspond to…
The dynamical evolution of a recently introduced one dimensional model in \cite{biswas-sen} (henceforth referred to as model I), has been made stochastic by introducing a parameter $\beta$ such that $\beta =0$ corresponds to the Ising model…
The $s=1$ spinor Bose condensate at zero temperature supports ferromagnetic and polar phases that combine magnetic and superfluid ordering. We investigate the formation of magnetic domains at finite temperature and magnetic field in two…
Diluted Ising antiferromagnets in a homogenous magnetic field have a disordered phase for sufficiently large values of the field and for low temperatures. Here, the system is in a domain state with a broad size-distribution of fractal…
The spatial distribution of unvisited/persistent sites in $d=1$ $A+A\to\emptyset$ model is studied numerically. Over length scales smaller than a cut-off $\xi(t)\sim t^{z}$, the set of unvisited sites is found to be a fractal. The fractal…
This paper is a study of some of the critical properties of a simple model for flux. The model is motivated by gauge theory and is equivalent to the Ising model in three dimensions. The phase with condensed flux is studied. This is the…
We study the zero-temperature persistence phenomenon in the random bond $\pm J$ Ising model on a square lattice via extensive numerical simulations. We find strong evidence for ` blocking\rq regardless of the amount disorder present in the…
We consider the d-dimensional diffusion equation for a field phi(x,t) with random initial condition, and observe that, when appropriately scaled, phi(0,t) is Gaussian and Markovian in the limit d->0. This leads via the Majumdar-Sire…
We study a model of assisted diffusion of hard-core particles on a line. The model shows strongly ergodicity breaking : configuration space breaks up into an exponentially large number of disconnected sectors. We determine this…
Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\alpha}$ interactions with $\alpha>D$. The bound contains two terms: One…
Normal dynamics in a quasi-one-dimensional channel of length L (\to\infty) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W…
We repeat the numerical experiments for diffusion limited aggregation (DLA) and show that there is a potentially infinite set of conserved quantities for the long time asymptotics. We connect these observations with the exact integrability…
The theory of elastic magnets is formulated under possible diffusion and heat flow governed by Fick's and Fourier's laws in the deformed (Eulerian) configuration, respectively. The concepts of nonlocal nonsimple materials and viscous…
We introduce coarse-grained hydrodynamic equations of motion for diffusion-annihilation system with a power-law long-range interaction. By taking into account fluctuations of the conserved order parameter - charge density - we derive an…
We study conserved one-dimensional models of particle diffusion, attachment and detachment from clusters, where the detachment rates decrease with increasing cluster size as gamma(m) ~ m^{-k}, k>0. Heuristic scaling arguments based on…
We study the coherent propagation and incoherent diffusion of in-plane elastic waves in a two dimensional continuum populated by many, randomly placed and oriented, edge dislocations. Because of the Peierls-Nabarro force the dislocations…
The persistence exponents associated with the T=0 quenching dynamics of the two dimensional XY model and a two dimensional uniaxial spin nematic model have been evaluated using a numerical simulation. The site persistence or the probability…
We consider macroscopic descriptions of particles where repulsion is modelled by non-linear power-law diffusion and attraction by a homogeneous singular kernel leading to variants of the Keller-Segel model of chemotaxis. We analyse the…