Exponential stability of slowly decaying solutions to the kinetic Fokker-Planck equation

The aim of the present paper is twofold:(1) We carry on with developing an abstract method for deriving decay estimates on the semigroup associated to non-symmetric operators in Banach spaces as introduced in [10]. We extend the method so as to consider the shrinkage of the functional space. Roughly speaking, we consider a class of operators writing as a dissipative part plus a mild perturbation, and we prove that if the associated semigroup satisfies a decay estimate in some reference space then it satisfies the same decay estimate in another-smaller or larger-Banach space under the condition that a certain iterate of the "mild perturba- tion" part of the operator combined with the dissipative part of the semigroup maps the larger space to the smaller space in a bounded way. The cornerstone of our approach is a factorization argument, reminiscent of the Dyson series.(2) We apply this method to the kinetic Fokker-Planck equation when the spatial domain is either the torus with periodic boundary conditions, or the whole space with a confinement potential. We then obtain spectral gap es- timates for the associated semigroup for various metrics, including Lebesgue norms, negative Sobolev norms, and the Monge-Kantorovich-Wasserstein distance W\_1.Comment: Some typos corrected, proof of Lemma 4.7 only sketched to shorten the paper, 41 page

Strong Convergence towards homogeneous cooling states for dissipative Maxwell models

We show the propagation of regularity, uniformly in time, for the scaled solutions of the inelastic Maxwell model for small inelasticity. This result together with the weak convergence towards the homogenous cooling state present in the literature implies the strong convergence in Sobolev norms and in the $L^1$ norm towards it depending on the regularity of the initial data. The strategy of the proof is based on a precise control of the growth of the Fisher information for the inelastic Boltzmann equation. Moreover, as an application we obtain a bound in the $L^1$ distance between the homogeneous cooling state and the corresponding Maxwellian distribution vanishing as the inelasticity goes to zero.Comment: 2 figure

Cauchy problem for the Boltzmann-BGK model near a global Maxwellian

In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth solution if the initial perturbation is sufficiently small in a high order energy norm. We also establish an asymptotic decay estimate and uniform $L^2$-stability for nonlinear perturbations.Comment: 26 page

Water adsorption on amorphous silica surfaces: A Car-Parrinello simulation study

A combination of classical molecular dynamics (MD) and ab initio Car-Parrinello molecular dynamics (CPMD) simulations is used to investigate the adsorption of water on a free amorphous silica surface. From the classical MD SiO_2 configurations with a free surface are generated which are then used as starting configurations for the CPMD.We study the reaction of a water molecule with a two-membered ring at the temperature T=300K. We show that the result of this reaction is the formation of two silanol groups on the surface. The activation energy of the reaction is estimated and it is shown that the reaction is exothermic.Comment: 12 pages, 6 figures, to be published in J. Phys.: Condens. Matte

Towards an HH-theorem for granular gases

The $H$-theorem, originally derived at the level of Boltzmann non-linear kinetic equation for a dilute gas undergoing elastic collisions, strongly constrains the velocity distribution of the gas to evolve irreversibly towards equilibrium. As such, the theorem could not be generalized to account for dissipative systems: the conservative nature of collisions is an essential ingredient in the standard derivation. For a dissipative gas of grains, we construct here a simple functional $\mathcal H$ related to the original $H$, that can be qualified as a Lyapunov functional. It is positive, and results backed by three independent simulation approaches (a deterministic spectral method, the stochastic Direct Simulation Monte Carlo technique, and Molecular Dynamics) indicate that it is also non-increasing. Both driven and unforced cases are investigated

Deconstructing Interrupts with Ara

The emulation of DHTs is a natural issue. After years of important research into lambda calculus, we demonstrate the refinement of multicast frameworks. In order to answer this challenge, we disprove that despite the fact that spreadsheets and kernels are mostly incompatible, 128 bit architectures and active networks are regularly incompatible

Mechanical and electrochemical deterioration mechanisms in the tribocorrosion of Al alloys in NaCl and in NaNO3 solutions

Tribocorrosion of Al-Si-Cu-Mg alloys was investigated in 0.05 M NaCl and 0.1 M NaNO3 solutions under severe sliding and controlled electrochemical conditions. A simple galvanic coupling model was developed to analyze and quantitatively predict the evolution potential of the open circuit potential during tribocorrosion. According to this model and the obtained results, galvanic coupling was established in the NaNO3 solution within the wear track between passive and mechanically depassivated areas. In the NaCl solution, galvanic coupling was established between the whole depassivated wear track and the surrounding area. This difference was attributed to different mechanical properties of the passive surfaces.The research team was financially supported by the Portuguese Foundation for Science and Technology (FCT-Portugal), under a PhD scholarship (SFRH/BD/27911/2006). The authors thank also to Dr. Edith Ariza (University of Minho) and Pierre Mettraux (EPFL) for SEM analysis

Effect of Al2Cu precipitates size and mass transport on the polarisation behaviour of age-hardened Al–Si–Cu–Mg alloys in 0.05M NaCl

The electrochemical behaviour of age-hardened Al–Si–Cu–Mg alloys was investigated in a 0.05 M NaCl solution under controlled mass transport conditions using a rotating disk electrode. This work aimed at getting better understanding of the effect of the alloy microstructure, in particular the size distribution of Al2Cu phase, on the corrosion behaviour of the alloy. Three different size distributions of the Al2Cu phase were obtained through appropriate heat treatments. The cathodic reduction of oxygen was found to occur mainly on the Al2Cu phases acting as preferential cathodes. Small sized Al2Cu phases were found to promote at high rotation rates a transition from a 4 electron to a 2 electron dominated oxygen reduction mechanisms.The research team was financially supported by the Portuguese Foundation for Science and Technology (FCT-Portugal), under a PhD scholarship (SFRH/BD/27911/2006). The authors thank also to Drs. Edith Ariza (University of Minho) and Pierre Mettraux (EPFL) for SEM analysis