Related papers: Constrained hydrodynamic flocking models in the li…
Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. The rods have finite size, interact via…
Competition between biological species in marine environments is affected by the motion of the surrounding fluid. An effective 2D compressibility can arise, for example, from the convergence and divergence of water masses at the depth at…
We present an experimental study on the collective behavior of macroscopic self-propelled particles that are externally excited by light. This property allows testing the system response to the excitation intensity in a very versatile…
We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…
Hydrodynamics provides a successful framework to effectively describe the dynamics of complex many-body systems ranging from subnuclear to cosmological scales by introducing macroscopic quantities such as particle densities and fluid…
We study a random model of deep multi-head self-attention in which the weights are resampled independently across layers and heads, as at initialization of training. Viewing depth as a time variable, the residual stream defines a…
In the present paper the macroscopic limits of the kinetic model for inter-acting entities (individuals, organisms, cells) are studied. The kinetic model is one-dimensional and entities are characterized by their position and orientation…
The mechanism of hydrodynamics-induced pairing of soft particles, namely closed bilayer membranes (vesicles, a model system for red blood cells) and drops, is studied numerically with a special attention paid to the role of the confinement…
We propose a dynamical model for group formation and switching behavior in systems where each group competes for members through attraction functions that are inversely proportional to their current sizes. This attraction is modulated by…
Self-propelled microparticles create flow fields that determine how they interact with surfaces, external flows, and each other. These flow fields fall into distinct classes--pushers, pullers, and neutral swimmers--each exhibiting…
We discuss two cases that can be connected to the dynamics of interacting populations: (I.) density waves for the case or negligible random fluctuations of the populations densities, and (II.) probability distributions connected to the…
We consider a hydrodynamic model of swarming behavior derived from the kinetic description of a particle system combining a noisy Cucker-Smale consensus force and self-propulsion. In the large self-propulsion force limit, we provide…
Three-dimensional simulations with fully resolved hydrodynamics are performed to study the collective motion of model swimmers in confinement. We show that certain swimming mechanisms can lead to traveling wave-like collective motion even…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
We study communities emerging from generalised random Lotka--Volterra dynamics with a large number of species with interactions determined by the degree of niche overlap. Each species is endowed with a number of traits, and competition…
We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour…
Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…
We derive the porous medium equation from an interacting particle system which belongs to the family of exclusion processes, with nearest neighbor exchanges. The particles follow a degenerate dynamics, in the sense that the jump rates can…