Bruno Rubino

Flocking and synchronization of particle models

In this note, we present a multi-dimensional flocking model rigorously derived from a vector oscillatory chain model and study the connection between the Cucker-Smale flocking model and the Kuramoto synchronization model appearing in the statistical mechanics of nonlinear oscillators. We provide an alternative direct approach for frequency synchronization to the Kuramoto model as an application of the flocking estimate for the Cucker-Smale model.

A CLASS OF INTERACTING PARTICLE SYSTEMS ON THE INFINITE CYLINDER WITH FLOCKING PHENOMENA

We present a class of extended Kuramoto models describing a flocking motion of particles on the infinite cylinder and provide sufficient conditions for the asymptotic formation of locked solutions where the distance between particles remains constant. Our proposed model includes the complex Kuramoto model for synchronization. We also provide several numerical simulation results and compare them with analytical results.

Global existence to the Cauchy problem for hyperbolic conservation laws with an isolated umbilic point

In this paper the existence of global weak solutions for a 2 × 2 system of non-strictly hyperbolic non-linear conservation laws is established for data in L∞. The result is proven by means of viscous approximation and application of the compensated compactness method. The presence of a degeneracy in the hyperbolicity of the system requires a careful analysis of the entropy functions, whose regularity is necessary to obtain an existence result. For this purpose we combine the classical techniques referring to a singular EulerPoisson-Darboux equation with the compensated compactness method.