Related papers: Density-Independent Model of Self-Propelled Partic…
The flocking of self-propelled particles in heterogeneous environments is relevant to both natural and artificial systems. The Vicsek model is a canonical choice to investigate such systems due to the minimal number of parameters required…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
Collective behavior in biological systems was first captured by the Vicsek model, in which particles align their velocities in the average direction of neighbors, leading to coherent motion and showing an order-disorder transition. However,…
We study the collective behavior of binary mixture of self-propelled particles. Particles moves along their heading direction with {\it variable speed} and interact through short range alignment interaction. A variable speed parameter…
Self-propelled particles with alignment, displaying ordered collective motions such as swarming, can be investigated by the well-known Vicsek model. However, challenges still remain regarding the nature of the associated phase transition.…
We study an interacting high-density one-dimensional system of self-propelled particles described by the Active Ornstein-Uhlenbeck particle (AOUP) model where, even in the absence of alignment interactions, velocity and energy domains…
We consider interacting particle dynamics with Vicsek type interactions, and their macroscopic PDE limit, in the non-mean-field regime; that is, we consider the case in which each particle/agent in the system interacts only with a…
We use the method of the microscopic phase density to get the kinetic equation for the system of self-propelled particles with Vicsek-like alignment rule. The hydrodynamic equations are derived for the ordered phase taking into account the…
A model of self-driven particles similar to the Vicsek model [Phys. Rev. Lett. 75 (1995) 1226] but with metric-free interactions is studied by means of a novel Enskog-type kinetic theory. In this model, N particles of constant speed v0 try…
The Vlasov-Poisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like $t^{-3}$ at late times. In this…
Many biological systems form colonies at high density. Passive granular systems will be jammed at such densities, yet for the survival of biological systems it is crucial that they are dynamic. We construct a phase diagram for a system of…
We study collective dynamics of interacting deformable self-propelled particles whose migration velocity increases when the local density of particles is increased. Numerical simulations in two dimensions reveal that traveling bands similar…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
A particle system with a single locally-conserved field (density) in a bounded interval with different densities maintained at the two endpoints of the interval is under study here. The particles interact in the bulk through a long range…
In resent years, Vicsek model has attracted more and more attention and been well developed. However, the in-depth analysis on the convergence time are scarce thus far. In this paper, we study some certain factors that mainly govern the…
Statistical mechanical models with local interactions in $d>1$ dimension can be regarded as $d=1$ dimensional models with regular long range interactions. In this paper we study the critical properties of Ising models having $V$ sites, each…
We investigate self-organized criticality in a two-dimensional electron gas (2DEG) by introducing a lattice-based model that incorporates electron-electron interactions through the concept of coherence length. Our numerical simulations…
We study a Vicsek-style model of self-propelled particles where ferromagnetic and nematic alignment compete in both the usual "metric" version and in the "metric-free" case where a particle interacts with its Voronoi neighbors. We show that…
We consider flocking of self-propelling agents in two dimensions, each of which communicates with its neighbors within a limited vision cone. Also, the communication occurs with some delay. The communication among the agents are modeled by…
Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost…