Related papers: Transport in disordered systems: the single big ju…
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate…
We consider a coarse-grained description of a system of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial…
We investigate exit times from domains of attraction for the motion of a self-stabilized particle traveling in a geometric (potential type) landscape and perturbed by Brownian noise of small amplitude. Self-stabilization is the effect of…
We study the large space and time scale behavior of a totally asymmetric, nearest-neighbor exclusion process in one dimension with random jump rates attached to the particles. When slow particles are sufficiently rare the system has a phase…
We study a model for flocking given by a $n$-particle system under which each particle jumps forward by a random amount, independently sampled from a given distribution $\theta$, with rate given by a non-increasing function $w$ of its…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
We consider a system of $N$ interacting particles, described by SDEs driven by Poisson random measures, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending on its position.…
In this work, the short-time dynamics of simple liquid is explored both analytically and numerically with the focus on the interplay between the density fluctuations in a volume surrounding a chosen particle and its random walk motion. The…
The diffusion type is determined not only by microscopic dynamics but also by the environment properties. For example, the environment's fractal structure is responsible for the emergence of subdiffusive scaling of the mean square…
Consider a system of particles evolving as independent and identically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity $\vec{v}$, the common mean velocity of the random…
We study the fluctuations of the area $A=\int_0^T x(t) dt$ under a one-dimensional Brownian motion $x(t)$ in a trapping potential $\sim |x|$, at long times $T\to\infty$. We find that typical fluctuations of $A$ follow a Gaussian…
In biological, glassy, and active systems, various tracers exhibit Laplace-like, i.e., exponential, spreading of the diffusing packet of particles. The limitations of the central limit theorem in fully capturing the behaviors of such…
First passage time statistics in disordered systems exhibiting scale invariance are studied widely. In particular, long trapping times in energy or entropic traps are fat-tailed distributed, which slow the overall transport process. We…
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,…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles increases beyond a certain threshold. In this paper, we argue that such a threshold…
We investigate single-particle diffusion in a two-state Langevin model where the friction coefficient randomly switches between low-friction (liquid-like) and high-friction (glassy-like) states. The dynamics are governed by the ratio…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
The relationship between anomalous superdiffusive behavior and particle trapping probability is analyzed on a rocking ratchet potential with spatially correlated weak disorder. The trapping probability density is shown, analytically and…
We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial…
In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…