Related papers: Quick Relaxation in Collective Motion
We study the emergent behaviors of the weak solutions to the kinetic Cucker-Smale (in short, KCS) model in a non-compact spatial-velocity support setting. Unlike the compact support situation, non-compact support of a weak solution can…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
A description of the Kibble-Zurek mechanism with linear response theory has been done previously, but ad hoc hypotheses were used, like the use of the rate-dependent impulse window via the Zurek equation in the context of no driving in the…
A simple model of the two dimensional collective motion of a group of mobile agents have been studied. Like birds, these agents travel in open free space where each of them interacts with the first $n$ neighbors determined by the…
In two recent papers the authors study the existence of weak solutions and the hydrodynamic limit of kinetic flocking equations with strong local alignment. The introduction of a strong local alignment term to model flocking behavior was…
The study of the movement of flocks, whether biological or technological is motivated by the desire to understand the capability of coherent motion of a large number of agents that only receive very limited information. In a biological…
We study equilibrium configurations of swarming biological organisms subject to exogenous and pairwise endogenous forces. Beginning with a discrete dynamical model, we derive a variational description of the corresponding continuum…
Animal motion and flocking are ubiquitous nonequilibrium phenomena that are often studied within active matter. In examples such as insect swarms, macroscopic quantities exhibit power laws with measurable critical exponents and ideas from…
We present a novel method for global motion planning of robotic systems that interact with the environment through contacts. Our method directly handles the hybrid nature of such tasks using tools from convex optimization. We formulate the…
Systems with long range interactions present generically the formation of quasi-stationary long-lived non-equilibrium states. These states relax to Boltzmann equilibrium following a dynamics which is not well understood. In this paper we…
We study a new flocking model which has the versatility to capture the physically realistic qualitative behavior of the Motsch-Tadmor model, while also retaining the entropy law, which lends to a similar 1D global well-posedness analysis to…
Collective behavior is all around us, from flocks of birds to schools of fish. These systems are immensely complex, which makes it pertinent to study their behavior through minimal models. We introduce such a minimal model for cohesive and…
This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as \emph{exact} polynomial optimization problems that can be relaxed as…
Counting the number of birds in an open sky setting has been an challenging problem due to the large number of bird flocks and the birds can overlap. Another difficulty is the lack of accurate training samples since the cost of labeling…
The relaxation rates to the invariant density in the chaotic phase space component of the kicked rotor (standard map) are calculated analytically for a large stochasticity parameter, $K$. These rates are the logarithms of the poles of the…
We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem. Our approach combines both speed and heading control and provides global optimality guarantees despite…
Iterative linear solvers have gained recent popularity due to their computational efficiency and low memory footprint for large-scale linear systems. The relaxation method, or Motzkin's method, can be viewed as an iterative method that…
In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups.…
We study the large-time behavior of continuum alignment dynamics based on Cucker-Smale (CS)-type interactions which involve short-range kernels, that is, communication kernels with support much smaller than the diameter of the crowd. We…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…