Related papers: Constrained hydrodynamic flocking models in the li…
This paper is concerned with the derivation and analysis of hydrodynamic models for systems of self-propelled particles subject to alignment interaction and attraction-repulsion. The starting point is the kinetic model considered in earlier…
The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy…
Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the…
We consider a integro-differential nonlinear model that describes the evolution of a population structured by a quantitative trait. The interactions between traits occur from competition for resources whose concentrations depend on the…
We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
We study a system of particles in the interval $[0,\epsilon^{-1}] \cap \mathbb Z$, $\epsilon^{-1}$ a positive integer. The particles move as symmetric independent random walks (with reflections at the endpoints); simultaneously new…
Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
Fish schooling is often modeled with self-propelled particles subject to phenomenological behavioral rules. Although fish are known to sense and exploit flow features, these models usually neglect hydrodynamics. Here, we propose a novel…
We study the (hydro-)dynamics of multi-species driven by alignment. What distinguishes the different species is the protocol of their interaction with the rest of the crowd: the collective motion is described by different communication…
Understanding the organization of collective motion in biological systems is an ongoing challenge. In this Paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish,…
We introduce a model for self-organized dynamics which, we argue, addresses several drawbacks of the celebrated Cucker-Smale (C-S) model. The proposed model does not only take into account the distance between agents, but instead, the…
The collective non-equilibrium dynamics of multi-component mixtures of interacting active (self-propelled) and passive (diffusive) particles have garnered great interest in the physics community. However, the mathematical understanding of…
We study the hydrodynamics of a system of agents who optimize either their individual utility (self-interest) or the collective welfare (cooperation). When agents act selfishly, their interactions are non-reciprocal, driving the system out…
We study the multi-scale description of large-time collective behavior of agents driven by alignment. The resulting multi-flock dynamics arises naturally with realistic initial configurations consisting of multiple spatial scaling, which in…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
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…
We present a hydrodynamic study of a monolayer of squirmer model microswimmers confined to a boundary by strong gravity using the simulation method of multi-particle collision dynamics. The squirmers interact with each other via their…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…