相关论文: On the Mathematics of Swarming: Emergent Behavior …

Laplacian growth is the study of interfaces that move in proportion to harmonic measure. Physically, it arises in fluid flow and electrical problems involving a moving boundary. We survey progress over the last decade on discrete models of…

We consider a one-dimensional hydrodynamic model featuring nonlocal attraction-repulsion interactions and singular velocity alignment. We introduce a two-velocity reformulation and the corresponding energy-type inequality, in the spirit of…

Collective behaviour in biological systems pitches us against theoretical challenges way beyond the borders of ordinary statistical physics. The lack of concepts like scaling and renormalization is particularly grievous, as it forces us to…

We study the systems of Euler equations which arise from agent-based dynamics driven by velocity \emph{alignment}. It is known that smooth solutions of such systems must flock, namely -- the large time behavior of the velocity field…

We construct the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface. The polar order parameter and concentration of a collection of "active" (self-propelled) particles at a planar interface between a…

Particle- and agent-based systems are a ubiquitous modeling tool in many disciplines. We consider the fundamental problem of inferring interaction kernels from observations of agent-based dynamical systems given observations of…

A variety of physical, social and biological systems generate complex fluctuations with correlations across multiple time scales. In physiologic systems, these long-range correlations are altered with disease and aging. Such correlated…

The spontaneous emergence of collective motion patterns is usually associated with the presence of a velocity alignment mechanism that mediates the interactions among the moving individuals. Despite of this widespread view, it has been…

The collective response of a system is profoundly shaped by the interaction dynamics between its constituent elements. In physics, tailoring these interactions can enable the observation of unusual phenomena that are otherwise inaccessible…

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be written as a Laplacian growth model regularized by a `kinetic undercooling' boundary condition. We study the linear stability of uniformly…

Collective motion and self-organization of interacting particles, such as flocking and swarming, can be viewed as nonequilibrium analogues of collective dynamics in gases. Motivated by the analogy between gas mixtures and Cucker--Smale…

We show by means of experiments, theory and simulations, that the slow dynamics of coarsening systems displays dynamic heterogeneity similar to that observed in glass-forming systems. We measure dynamic heterogeneity via novel multi-point…

Swarming behavior, where coherent motion emerges from the interactions of many mobile agents, is ubiquitous in physics and biology. Moreover, there are many efforts to replicate swarming dynamics in mobile robotic systems which take…

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a Laplacian growth model regularized by a 'kinetic undercooling' boundary condition. Using this model we study both the…

The emergence of collective motion, also known as flocking or swarming, in groups of moving individuals who orient themselves using only information from their neighbors is a very general phenomenon that is manifested at multiple spatial…

We investigate the emergent behavior of four types of generic dynamical systems under random environmental perturbations. Sufficient conditions for nearly-emergence in various scenarios are presented. Recent fundamental works of F. Cucker…

Natural flocks (aligned) and swarms (non-aligned) both exhibit features of near-criticality, challenging their treatment as two ends of the same phase transition. We present a model for the aggregation of active individuals, in which their…

Mathematical models for systems of interacting agents using simple local rules have been proposed and shown to exhibit emergent swarming behavior. Most of these models are constructed by intuition or manual observations of real phenomena,…

Understanding the mechanisms behind emergent behaviors in multi-agent systems is critical for advancing fields such as swarm robotics and artificial intelligence. In this study, we investigate how neural networks evolve to control agents'…

We study the limits of linear modeling of swarm behavior by characterizing the inflection point beyond which linear models of swarm collective behavior break down. The problem we consider is a central place object gathering task. We design…