We review a general class of models for self-organized dynamics based on alignment. The
dynamics of such systems is governed solely by interactions among individuals or “agents,” …

We introduce a model for self-organized dynamics which, we argue, addresses several
drawbacks of the celebrated Cucker-Smale (CS) model. The proposed model does not only …

We study the large-time behaviour of Eulerian systems augmented with non-local alignment.
Such systems arise as hydrodynamic descriptions of agent-based models for self-organized …

We present a new hydrodynamic model for the interactions between collision-free Cucker–
Smale flocking particles and a viscous incompressible fluid. Our proposed model consists of …

We study a model of radiating gases that describes the interaction of an inviscid gas with
photons. We show the existence of smooth traveling waves called 'shock profiles', when the …

We study the systems of Euler equations that arise from agent-based dynamics driven by
velocity alignment. It is known that smooth solutions to such systems must flock, namely the …

We study the velocity gradients of the fundamental Eulerian equation,∂ tu+ u·∇ u= F, which
shows up in different contexts dictated by the different modeling of F's. To this end we utilize …

We consider the fractal Burgers equation (that is to say the Burgers equation to which is
added a fractional power of the Laplacian) and we prove that, if the power of the Laplacian …

We study the structure of stationary solutions to the Doi-Onsager equation with Maier-Saupe
potential on the sphere, which arises in the modelling of rigid rod-like molecules of …

In this paper, we develop two efficient numerical methods for a multiscale kinetic equation in
the context of crowd dynamics with emotional contagion [A. Bertozzi, J. Rosado, M. Short …