Collective motion, such as milling, flocking, and collective turning, is a common and
captivating phenomenon in nature, which arises in a group of many self-propelled …

Swarmalators are systems of agents which are both self-propelled particles and oscillators.
Each particle is endowed with a phase which modulates its interaction force with the other …

In this paper we provide a local Cauchy theory both on the torus and in the whole space for
general Vicsek dynamics at the kinetic level. We consider rather general interaction kernels …

We derive an explicit form for the Cucker--Smale (CS) model on the special orthogonal
group SO(3) by identifying closed form expressions for geometric quantities such as …

In this paper, we demonstrate the existence of topological states in a new collective
dynamics model. This individual-based model (IBM) describes self-propelled rigid bodies …

In this article we study a system of N particles, each of them being defined by the couple of a
position (in R^d) and a so-called orientation which is an element of a compact Riemannian …

We consider a model for collective behaviour on Riemannian manifolds, with interactions
modelled through a smooth interaction potential that depends on the squared intrinsic …

Starting from a particle model describing self-propelled particles interacting through nematic
alignment, we derive a macroscopic model for the particle density and mean direction of …

This paper deals with the convergence of the Doi-Navier-Stokes model of liquid crystals to
the Ericksen-Leslie model in the limit of the Deborah number tending to zero. While the …

Abstract Models have proven useful in revealing the mechanisms underlying these
collective behaviors of flocks of birds, schools of fish, swarms of insects, and herds of …