About the barotropic compressible quantum Navier-Stokes equations

In this paper we consider the barotropic compressible quantum Navier-Stokes equations with a linear density dependent viscosity and its limit when the scaled Planck constant vanish. Following recent works on degenerate compressible Navier-Stokes equations, we prove the global existence of weak solutions by the use of a singular pressure close to vacuum. With such singular pressure, we can use the standard definition of global weak solutions which also allows to justify the limit when the scaled Planck constant denoted by $\epsilon$ tends to 0

From Bloch model to the rate equations II: the case of almost degenerate energy levels

Bloch equations give a quantum description of the coupling between an atom and a driving electric force. In this article, we address the asymptotics of these equations for high frequency electric fields, in a weakly coupled regime. We prove the convergence towards rate equations (i.e. linear Boltzmann equations, describing the transitions between energy levels of the atom). We give an explicit form for the transition rates. This has already been performed in [BFCD03] in the case when the energy levels are fixed, and for different classes of electric fields: quasi or almost periodic, KBM, or with continuous spectrum. Here, we extend the study to the case when energy levels are possibly almost degenerate. However, we need to restrict to quasiperiodic forcings. The techniques used stem from manipulations on the density matrix and the averaging theory for ordinary differential equations. Possibly perturbed small divisor estimates play a key role in the analysis. In the case of a finite number of energy levels, we also precisely analyze the initial time-layer in the rate aquation, as well as the long-time convergence towards equilibrium. We give hints and counterexamples in the infinite dimensional case

The boundary Riemann solver coming from the real vanishing viscosity approximation

We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems: v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx} The conservative case is, in particular, included in the previous formulation. We suppose that the solutions $v^{\epsilon}$ to these problems converge to a unique limit. Also, it is assumed smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $A$ can be $0$. Second, we take into account the possibility that $B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.Comment: 84 pages, 6 figures. Text changes in Sections 1 and 3.2.3. Added Section 3.1.2. Minor changes in other section

Uniform regularity for the Navier-Stokes equation with Navier boundary condition

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in $L^\infty$. This allows to get the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument

An overview on the approximation of boundary Riemann problems through physical viscosity

This note aims at providing an overview of some recent results concerning the viscous approximation of so-called boundary Riemann problems for nonlinear systems of conservation laws in small total variation regimes. \ua9 2016, Sociedade Brasileira de Matem\ue1tica

Death and the Societies of Late Antiquity

Ce volume bilingue, comprenant un ensemble de 28 contributions disponibles en français et en anglais (dans leur version longue ou abrégée), propose d’établir un état des lieux des réflexions, recherches et études conduites sur le fait funéraire à l’époque tardo-antique au sein des provinces de l’Empire romain et sur leurs régions limitrophes, afin d’ouvrir de nouvelles perspectives sur ses évolutions possibles. Au cours des trois dernières décennies, les transformations considérables des méthodologies déployées sur le terrain et en laboratoire ont permis un renouveau des questionnements sur les populations et les pratiques funéraires de l’Antiquité tardive, période marquée par de multiples changements politiques, sociaux, démographiques et culturels. L’apparition de ce qui a été initialement désigné comme une « Anthropologie de terrain », qui fut le début de la démarche archéothanatologique, puis le récent développement d’approches collaboratives entre des domaines scientifiques divers (archéothanatologie, biochimie et géochimie, génétique, histoire, épigraphie par exemple) ont été décisives pour le renouvellement des problématiques d’étude : révision d’anciens concepts comme apparition d’axes d’analyse inédits. Les recherches rassemblées dans cet ouvrage sont articulées autour de quatre grands thèmes : l’évolution des pratiques funéraires dans le temps, l’identité sociale dans la mort, les ensembles funéraires en transformation (organisation et topographie) et les territoires de l’empire (du cœur aux marges). Ces études proposent un réexamen et une révision des données, tant anthropologiques qu’archéologiques ou historiques sur l’Antiquité tardive, et révèlent, à cet égard, une mosaïque de paysages politiques, sociaux et culturels singulièrement riches et complexes. Elles accroissent nos connaissances sur le traitement des défunts, l’emplacement des aires funéraires ou encore la structure des sépultures, en révélant une diversité de pratiques, et permettent au final de relancer la réflexion sur la manière dont les sociétés tardo-antiques envisagent la mort et sur les éléments permettant d’identifier et de définir la diversité des groupes qui les composent. Elles démontrent ce faisant que nous pouvons véritablement appréhender les structures culturelles et sociales des communautés anciennes et leurs potentielles transformations, à partir de l’étude des pratiques funéraires.This bilingual volume proposes to draw up an assessment of the recent research conducted on funerary behavior during Late Antiquity in the provinces of the Roman Empire and on their borders, in order to open new perspectives on its possible developments. The considerable transformations of the methodologies have raised the need for a renewal of the questions on the funerary practices during Late Antiquity, a period marked by multiple political, social, demographic and cultural changes. The emergence field anthropology, which was the beginning of archaeothanatology, and then the recent development of collaborative approaches between various scientific fields (archaeothanatology, biochemistry and geochemistry, genetics, history, epigraphy, for example), have been decisive. The research collected in this book is structured around four main themes: Evolution of funerary practices over time; Social identity through death; Changing burial grounds (organisation and topography); Territories of the Empire (from the heart to the margins). These studies propose a review and a revision of the data, both anthropological and archaeological or historical on Late Antiquity, and reveal a mosaic of political, social, and cultural landscapes singularly rich and complex. In doing so, they demonstrate that we can truly understand the cultural and social structures of ancient communities and their potential transformations, based on the study of funerary practices

A uniqueness criterion for viscous limits of boundary Riemann problems

We deal with initial-boundary value problems for systems of conservation laws in one space dimension and we focus on the boundary Riemann problem. It is known that, in general, different viscous approximations provide different limits. In this paper, we establish sufficient conditions to conclude that two different approximations lead to the same limit. As an application of this result, we show that, under reasonable assumptions, the self-similar second-order approximation and the classical viscous approximation provide the same limit. Our analysis applies to both the characteristic and the non characteristic case. We require neither genuine nonlinearity nor linear degeneracy of the characteristic fields