In this paper we study the integrability properties of a general version of the Boltzmann collision operator that includes inelastic interactions between particles. We prove a Young’s inequality for variable hard potentials, a Hardy-Littlewood-Sobolev inequality for soft potentials, and estimates with Maxwellian weights for variable hard potentials. In addition we obtain sharp constants for Max...

A multiagent architecture is proposed in order to build a physics laboratory in virtual reality. Thermodynamics experiments are used for its validation. Classical numerical resolution of thermodynamics problems comes up against the number and variability of boundary conditions. Based on molecular dynamics, a multiagent approach is proposed, resting upon agent spatial and temporal autonomy. This...

For the space homogeneous Boltzmann equation, we formulate a hybrid Monte Carlo method that is robust in the fluid dynamic limit. This method is based on an analytic representation of the solution over a single time step and involves implicit time differencing derived from a suitable power series expansion of the solution (a generalized Wild expansion). A class of implicit, yet explicitly imple...

There are many papers concerning the propagation of regularity for the solution of the Boltzmann equation (cf. [5, 6, 8, 9, 13] and references therein). In these works, it has been shown that the Sobolev or Lebesgue regularity satisfied by the initial datum is propagated along the time variable. The solutions having the Gevrey regularity for a finite time have been constructed in [15] in which ...

We study the question of what di€erence it makes for the derived ®eld-aligned conductance (K) values if one uses Maxwellian or kappa distributions for the ®tting of low-orbiting satellite electron ̄ux spectra in the auroral region. This question has arisen because sometimes a high-energy tail is seen in the spectra. In principle, the kappa ®ts should always be better, because the kappa distribu...

the adhesion molecules are involved in adhesion of leukocytes to endothelial cells and other immune cells. not only adhesion molecules have membrane form, but they also have soluble form. in this paper, we attempted to investigate the concen¬tration of soluble adhesion molecules in the type 1 diabetic patients (n = 40) and healthy subjects (n = 10). the results indicated that there was an incre...

Maxwellian approximations to linear general relativity are revisited in light of relatively recent results on the degrees freedom gravitational field. The well-known formalism obtained harmonic coordinates is compared with a under coordinate choice where each metric components corresponds coordinate-invariant can be exploited cast field equations into form, but such forms mere mirages -- as vec...