Related papers: Activity, diffusion, and correlations in a two-dim…
We characterize the dynamic non-equilibrium steady state behavior of active particles using density fluctuations in the system. We analyze the effective local density around a particle in the steady state and numerically calculate its mean,…
When sand flows out of a funnel onto a surface, a three dimensional pile that is stabilized by friction grows taller as it spreads. Here we investigate an idealized two dimensional analogue: spreading of a pile of monodisperse oil droplets…
We perform numerical simulations to examine particle diffusion at steady shear in a model granular material in two dimensions at the jamming density and zero temperature. We confirm findings by others that the diffusion constant depends on…
A quantitatively reliable theoretical description of the dynamics of fluctuations in non-equilibrium is indispensable in the experimental search for the QCD critical point by means of ultra-relativistic heavy-ion collisions. In this work we…
A recently proposed generalised continuum theory of curved dislocations describes the spatial and temporal evolution of statistically stored and geometrically necessary dislocation densities as well as the curvature. The dynamics follow…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
We address the equilibrium and out-of-equilibrium behavior of the particle density in many-body systems undergoing quantum transitions driven by the chemical potential $\mu$. They originate from a nontrivial interplay between noncritical…
We present large scale simulations of a stochastic sandpile model in two dimensions. We use moments analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. The general picture…
We study the short time properties of a two-dimensional film growth model in which incident particles execute advective-diffusive motion with a vertical step followed by $D$ horizontal steps. The model represents some features of the…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
We consider correlated L\'evy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties.…
We study a two-dimensional granular system where external driving force is applied to each particle in the system in such a way that the system is driven into a steady state by balancing the energy input and the dissipation due to inelastic…
The dynamical properties of a dense horizontally vibrated bidisperse granular monolayer are experimentally investigated. The quench protocol produces states with a frozen structure of the assembly, but the remaining degrees of freedom…
The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
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 study time evolution of critical fluctuations of conserved charges near the QCD critical point in the context of relativistic heavy ion collisions. A stochastic diffusion equation is employed in order to describe the diffusion property…
Two-point density-density correlation functions for the diffusive binary reaction system $A+A\to\emptyset$ are obtained in one dimension via Monte Carlo simulation. The long-time behavior of these correlation functions clearly deviates from…
The experiments of Leptos et al. [Phys. Rev. Lett. 103, 198103 (2009)] show that the displacements of small particles affected by swimming microorganisms achieve a non-Gaussian distribution, which nevertheless scales diffusively -- the…
We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and…