Mean-field model of free-cooling inelastic mixtures

Mean-field model of free-cooling inelastic mixtures.

We consider a mean-field model describing the free-cooling process of a two-component granular mixture, a generalization of the so called scalar Maxwell model. The cooling is viewed as an ordering process and the scaling behavior is attributed to the presence of an attractive fixed point at v=0 for the dynamics. By means of asymptotic analysis of the Boltzmann equation and of numerical simulati...

Steady-state properties of a mean-field model of driven inelastic mixtures.

We investigate a Maxwell model of inelastic granular mixture under the influence of a stochastic driving and obtain its steady-state properties in the context of classical kinetic theory. The model is studied analytically by computing the moments up to the eighth order and approximating the distributions by means of a Sonine polynomial expansion method. The main findings concern the existence o...

Mean field theory of inhomogeneous fluid mixtures

Measurements of electron inelastic mean free paths in materials.

We present a method for determining inelastic mean free paths (IMFPs) in materials using high-accuracy measurements of x-ray absorption fine structure (XAFS). For electron energies below 100 eV, theoretical predictions have large variability and alternate measurement techniques exhibit significant uncertainties. In this regime, the short IMFP makes photoelectrons ideal for structural determinat...

Free energy in the generalized Sherrington-Kirkpatrick mean field model

In [10] Michel Talagrand gave a rigorous proof of the Parisi formula in the SherringtonKirkpatrick model. In this paper we build upon the methodology developed in [10] and extend Talagrand’s result to a more general class of mean field models with spins distributed according to an arbitrary probability measure on the bounded subset of the real line and with external field term given by an arbit...