Boltzmann entropy and chaos in a large assembly of weakly interacting systems

We introduce a high dimensional symplectic map, modeling a large system consisting of weakly interacting chaotic subsystems, as a toy model to analyze the interplay between single-particle chaotic dynamics and particles interactions in thermodynamic systems. We study the growth with time of the Boltzmann entropy, S_B, in this system as a function of the coarse graining resolution. We show that a characteristic scale emerges, and that the behavior of S_B vs t, at variance with the Gibbs entropy, does not depend on the coarse graining resolution, as far as it is finer than this scale. The interaction among particles is crucial to achieve this result, while the rate of entropy growth depends essentially on the single-particle chaotic dynamics (for t not too small). It is possible to interpret the basic features of the dynamics in terms of a suitable Markov approximation.Comment: 21 pages, 11 figures, submitted to Journal of Statistical Physic

Pancreatic graft outcome after combined whole pancreas and liver retrieval

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Follow-up study of sensory-motor polyneuropathy in Type 1 (insulin-dependent) diabetic subjects after simultaneous pancreas and kidney transplantation and after graft rejection

The influence of successful simultaneous pancreas and kidney transplantation on peripheral polyneuropathy was investigated in 53 patients for a mean observation period of 40.3 months. Seventeen patients were followed-up for more than 3 years. Symptoms and signs were assessed every 6 months using a standard questionnaire, neurological examination and measurement of sensory and motor nerve conduction velocities. While symptoms of polyneuropathy improved (pain, paraesthesia, cramps, restless-legs) and nerve conduction velocity increased, there was no change of clinical signs (sensation, muscle-force, tendon-reflexes). Following kidney-graft-rejection there was a slight decrease of nerve conduction verlocity during the first year, which was not statistically significant. Following pancreas-graft rejection there was no change of nerve conduction velocity during the first year. Comparing the maximum nerve conduction velocity of the patients with pancreas-graft-rejection to the nerve conduction velocities of these patients at the end of the study, there was a statistically significant decrease of 6.5 m/s. In conclusion, we believe that strict normalization of glucose metabolism alters the progressive course of diabetic polyneuropathy. It may be stabilized or partly reversed after successful grafting even in long-term diabetic patients

Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system

We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in J. Math. Pures Appl. 86, 68-79 (2006) to obtain uniqueness results for the Vlasov-Poisson system.Comment: AMS-LaTeX, 21 page

A Compromise Approach to Rendering Urban Place Names: the Case of Ekaterinburg

The paper describes different approaches to the rendering of urban place names, i.e. the names of different city facilities, and argues for the importance of accuracy in the case of Russian-into-English translation. With the balanced account of the two basic translation methods commonly applied to such vocabulary units — the one that makes use of calquing in accordance with the standards of the target language, and the other based exclusively on the use of transliteration for rendering both the statute and the main part of the toponymic unit — the authors develop and justify a compromise approach to rendering toponyms for the urban navigation system. This new one embraces a number of other translation techniques used alongside with transliteration / translation in rendering place names from Russian into English. In practice, this would provide for easier city navigation for non-native Russian speakers. A detailed description of the methodology of rendering the said units into English is exemplified by the names of different urban facilities of Ekaterinburg. The given methodology has been developed by a group of researchers, including the authors of the paper

Self-Similarity for Ballistic Aggregation Equation

We consider ballistic aggregation equation for gases in which each particle is iden- ti?ed either by its mass and impulsion or by its sole impulsion. For the constant aggregation rate we prove existence of self-similar solutions as well as convergence to the self-similarity for generic solutions. For some classes of mass and/or impulsion dependent rates we are also able to estimate the large time decay of some moments of generic solutions or to build some new classes of self-similar solutions

A new approach to quantitative propagation of chaos for drift, diffusion and jump processes

This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstract generator operators (consistency estimate) together with fine stability estimates on the flow of the limiting nonlinear equation (stability estimates). Then we apply this method to a Boltzmann collision jump process (for Maxwell molecules), to a McKean-Vlasov drift-diffusion process and to an inelastic Boltzmann collision jump process with (stochastic) thermal bath. To our knowledge, our approach yields the first such quantitative results for a combination of jump and diffusion processes.Comment: v2 (55 pages): many improvements on the presentation, v3: correction of a few typos, to appear In Probability Theory and Related Field