Homogeneous Cooling States¶are not always¶Good Approximations to Granular Flows

A widespread belief in the study of granular flow is the existence of “homogeneous cooling states”, i.e., self-similar solutions which would attract all solutions, faster than the equilibrium solution does. In most cases, the existence of these self-similar solutions is an open problem. Here we consider a one-dimensional model, which has been used for some years, and for which simple self-similar solutions do exist. However, we prove that the approximation is quite poor. Our proof makes use of the powerful and simple tools of mass transportation, and exploits the structure of the evolution equation, seen as a nonlinear transport equation.     

A one dimensional Boltzmann equation with inelastic collisions

We consider the Boltzmann equation for inelastic particles on the line and prove some preliminary results on existence and uniqueness of the solutions. We also discuss some connections with another kinetic equation investigated by the same authors. Conferenza tenuta il 3 novembre 1997     

Lattice dynamics and energy channelling in the thermoelastic effect

The physical mechanism of the isentropic thermoelastic effect is investigated in terms of lattice dynamics. The temperature variation arising from a thermal compensation of the strain induced frequency changes of the vibrational modes is the consequence of maintaining constant the entropy (dependent on the phonon population number) during the transformation. The interplay of the mechanical work for elastic deformation of a material and the heat consequently transferred to it is then analyzed according to the principles of thermodynamics within the same frame. The temperature dependence of the energy dissipated during a thermoelastic cycle is numerically evaluated in an appropriate Debye-Grüneisen model.     

Violation of distribution symmetry in statistical evaluation of absolute enantioselective synthesis

Enantiomeric excesses obtained in absolute enantioselective synthesis by chiral autocatalysis (Soai-reaction) were statistically analyzed. Two sets of parallel experiments, which were performed under chemically different conditions, are available. One group contains 37, while the other contains 84 preparative results. The former group shows some interesting tendencies but does not give conclusive statistical results. The sample of 84 parallel experiments, providing 39 R- and 45 S-excesses have shown that these data represent two distinct, non-symmetric sets with different non-Gaussian distributions. Clear S preference was found.     

A special class of stationary flows for two-dimensional euler equations: A statistical mechanics description. Part II

We continue and conclude our analysis started in Part I (see [CLMP]) by discussing the microcanonical Gibbs measure associated to a N-vortex system in a bounded domain. We investigate the Mean-Field limit for such a system and study the corresponding Microcanonnical Variational Principle for the Mean-Field equation. We discuss and achieve the equivalence of the ensembles for domains in which we have the concentration at (–8)⁺ in the canonical framework. In this case we have the uniqueness of the solutions of the Mean-Field equation. For the other kind of domains, for large values of the energy, there is no equivalence, the entropy is not a concave function of the energy, and the Mean-field equation has more than one solution. In both situations, we have concentration when the energy diverges. The Microcanonical Mean Field Limit for the N-vortex system is proven in the case of equivalence of ensembles.Communicated by J.L. Lebowitz     

On a Constrained 2-D Navier-Stokes Equation

The planar Navier-Stokes equation exhibits, in absence of external forces, a trivial asymptotics in time. Nevertheless the appearence of coherent structures suggests non-trivial intermediate asymptotics which should be explained in terms of the equation itself. Motivated by the separation of the different time scales observed in the dynamics of the Navier-Stokes equation, we study the well-posedness and asymptotic behaviour of a constrained equation which neglects the variation of the energy and moment of inertia.