368 citations · 558 across the 22 of their papers we have counts for
11 papers · 1 filter
Variational derivation of the homogeneous Boltzmann equation
Giada Basile, Dario Benedetto, Carlo Orrieri
We introduce a variational formulation of the homogeneous Boltzmann equation, with hard-sphere cross section, which selects the unique energy conserving solution. We prove that thi…
Microcanonical phase transitions for the vortex system
Dario Benedetto, Emanuele Caglioti, Margherita Nolasco
We consider the Microcanonical Variational Principle for the vortex system in a bounded domain. In particular we are interested in the thermodynamic properties of the system in dom…
Asymptotic probability of energy increasing solutions to the homogeneous Boltzmann equation
Giada Basile, Dario Benedetto, Lorenzo Bertini +1
Weak solutions to the homogeneous Boltzmann equation with increasing energy have been constructed by Lu and Wennberg. We consider an underlying microscopic stochastic model with bi…
Large deviations for a binary collision model: energy evaporation
Giada Basile, Dario Benedetto, Lorenzo Bertini +1
We analyze the large deviations for a discrete energy Kac-like walk. In particular, we exhibit a path, with probability exponentially small in the number of particles, that looses…
Random assignment problems on manifolds
Dario Benedetto, Emanuele Caglioti, Sergio Caracciolo +3
We consider the assignment problem between two sets of random points on a smooth, two-dimensional manifold of unit area. It is known that the average cost scales as $E_Ω(N)…
Some aspects of the inertial spin model for flocks and related kinetic equations
Dario Benedetto, Paolo Buttà, Emanuele Caglioti
In this paper we study the macroscopic behavior of the inertial spin (IS) model. This model has been recently proposed to describe the collective dynamics of flocks of birds, and i…