Related papers: Noisy multistate voter model for flocking in finit…
In this work, we investigate interactions that simultaneously order a system locally, while keeping it globally disordered. The study is done in the context of the emergence of diversity in opinion propagation models with interactions…
Understanding collective self-organization in active matter, such as bird flocks and fish schools, remains a grand challenge in physics. Interactions that induce alignment are essential for flocking; however, alignment alone is generally…
Leader election is a fundamental problem in distributed computing, particularly within programmable matter systems, where coordination among simple computational entities is crucial for solving complex tasks. In these systems, particles…
We study several fundamental properties of a class of stochastic processes called spatial Lambda-coalescents. In these models, a number of particles perform independent random walks on some underlying graph G. In addition, particles on the…
We numerically examine a binary system of particles with repulsive interactions, where one species is driven by a rotating drive and the other is subjected either to a constant drive in a fixed direction or to a rotating drive that is out…
Interactions in active matter systems inherently involve delays due to information processing and actuation lags. We numerically investigate the impact of such delays on the phase behavior of the Vicsek model for motile active matter at a…
We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when…
We consider a branching-selection particle system on $\Z$ with $N \geq 1$ particles. During a branching step, each particle is replaced by two new particles, whose positions are shifted from that of the original particle by independently…
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…
Driven non-equilibrium lattice models have wide-ranging applications in contexts such as mass transport, traffic flow, and transport in biological systems. In this work, we investigate the steady-state properties of a one-dimensional…
We consider a model in which positive and negative particles with equal densities diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent…
We investigate a model where strong noise in a sub-population creates a metastable state in an otherwise unstable two-population system. The induced metastable state is vortex-like, and its persistence time grows exponentially with the…
The symmetric exclusion process and the voter model are two interacting particle systems for which a dual finite particle system allows one to characterize its invariant measures. Adding spontaneous births and deaths to the two processes…
One standard approach to describe the collective behaviour of self-propelled particles is the Vicsek model: point-like self-propelled particles tend to align their migration directions to the ones of their nearer neighbours at each…
Ordering dynamics of self-propelled particles in an inhomogeneous medium in two-dimensions is studied. We write coarse-grained hydrodynamic equations of motion for coarse-grained density and velocity fields in the presence of an external…
A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…
We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They…
Deterministic chaotic dynamics presumes that the state space can be partitioned arbitrarily finely. In a physical system, the inevitable presence of some noise sets a finite limit to the finest possible resolution that can be attained. Much…
We study a binary dynamical process that is a representation of the voter model with opinion makers. The process models an election with two candidates but can also describe the frequencies of a biallelic gene in a population or atoms with…
We study noise sensitivity of the consensus opinion of the voter model on finite graphs, with respect to noise affecting the initial opinions and noise affecting the dynamics. We prove that the final opinion is stable with respect to small…