Global Classical Solutions of the Relativistic Vlasov–Darwin System with Small Cauchy Data: The Generalized Variables Approach

We show that a smooth, small enough Cauchy datum launches a unique classical solution of the relativistic Vlasov–Darwin (RVD) system globally in time. A similar result is claimed in Seehafer (Commun Math Sci 6:749–769, 2008) following the work in Pallard (Int Mat Res Not 57191:1–31, 2006). Our proof does not require estimates derived from the conservation of the total energy, nor those previously given on the transversal component of the electric field. These estimates are crucial in the references cited above. Instead, we exploit the formulation of the RVD system in terms of the generalized space and momentum variables. By doing so, we produce a simple a priori estimate on the transversal component of the electric field. We widen the functional space required for the Cauchy datum to extend the solution globally in time, and we improve decay estimates given in Seehafer (2008) on the electromagnetic field and its space derivatives. Our method extends the constructive proof presented in Rein (Handbook of differential equations: evolutionary equations, vol 3. Elsevier, Amsterdam, 2007) to solve the Cauchy problem for the Vlasov–Poisson system with a small initial datum.     

Asymptotic behavior for doubly degenerate parabolic equations

We use mass transportation inequalities to study the asymptotic behavior for a class of doubly degenerate parabolic equations of the form

(1)$\text{?ρ}\text{?t}\text{=}\text{div}\text{ρ?c}{}^1\text{?}\text{F′(ρ)+V}\text{in}\text{(0,∞)×Ω,}\text{and}\text{ρ(t=0)=ρ}{}_0\text{in}\text{{0}×Ω,}$

where $\text{Ω}$ is $\text{R}{}^{\mathrm{n}}$, or a bounded domain of $\text{R}{}^{\mathrm{n}}$ in which case $\text{ρ?c}{}^1\text{[?(F′(ρ)+V)]·ν=0}$ on $\text{(0,∞)×?Ω}$. We investigate the case where the potential V is uniformly c-convex, and the degenerate case where V=0. In both cases, we establish an exponential decay in relative entropy and in the c-Wasserstein distance of solutions – or self-similar solutions – of (1) to equilibrium, and we give the explicit rates of convergence. In particular, we generalize to all p>1, the HWI inequalities obtained by Otto and Villani (J. Funct. Anal. 173 (2) (2000) 361–400) when p=2. This class of PDEs includes the Fokker–Planck, the porous medium, fast diffusion and the parabolic p-Laplacian equations. To cite this article: M. Agueh, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

A Java-based control system for the Orsay tandem accelerator

A new control system was designed for the tandem MP-9 at Orsay. Because of the existing devices located on high voltage platforms and the lack of space inside the accelerator, in-house electronic cards based on micro-controllers and an optical fieldbus were developed to collect data. VME processors under VxWorks, a real time operating system, manage the fieldbus, concentrate the accelerator information and transmit it to the supervisory software through the ethernet network. This software consists of a collection of Java virtual machines (JVM) running on several Unix work-stations and PCs under Windows. Some of the Java virtual machines manage apparatus, instruments, local display and connections to an object database and VME concentrators. Other manage general synoptics. JVMs communicate between themselves with RMI protocol and JRPC with VME concentrators. So the supervisory software can be spread over several control stations throughout the network.     

Whole‐Genome Sequencing of a Single Viral Species from a Highly Heterogeneous Sample

Metagenomic studies suggest that only a small fraction of the viruses that exist in nature have been identified and studied. Characterization of unknown viral genomes is hindered by the many genomes populating any virus sample. A new method is reported that integrates drop‐based microfluidics and computational analysis to enable the purification of any single viral species from a complex mixed virus sample and the retrieval of complete genome sequences. By using this platform, the genome sequence of a 5243 bp dsDNA virus that was spiked into wastewater was retrieved with greater than 96 % sequence coverage and more than 99.8 % sequence identity. This method holds great potential for virus discovery since it allows enrichment and sequencing of previously undescribed viruses as well as known viruses.     

Yukawa potentials in systems with partial periodic boundary conditions. II. Lekner sums for quasi-two-dimensional systems

Yukawa potentials may be long-ranged when the Debye screening length is large. In computer simulations, such long-ranged potentials have to be taken into account with convenient algorithms to avoid systematic bias in the sampling of the phase space. Recently, we provided Ewald sums for quasi-two-dimensional systems with Yukawa interaction potentials [J. Chem. Phys. 126, 056101 (2007); Molec. Phys. paper I of this series]. Sometimes, Lekner sums are used as an alternative to Ewald sums for Coulomb systems. In the present work, we derive the Lekner sums for quasi-two-dimensional systems with Yukawa interaction potentials and we give numerical tests for practical implementations. The main result of this paper is to emphasize that Lekner sums cannot be considered as an alternative to Ewald sums for Yukawa potentials. As a conclusion to this work: Lekner sums should not be used for quasi-two-dimensional systems with Yukawa interaction potentials.     

EELS measurements of boron concentration profiles in p-a-Si and nip a-Si solar cells

The p-type Si layer in a-Si and μc-Si solar cells on foil needs to fulfil several important requirements. The layer is necessary to create the electric field that separates the photo-generated charge carriers; the doping also increases the conductivity to conduct the photocurrent to the front contact; on the other hand, the p-layer should transmit the incident light efficiently to the intrinsic absorber layer. We show that it is possible to study TEM samples prepared, for analysis of possible layer defects, by focussed ion beam milling to detect boron and carbon concentrations as low as 10²⁰ cm^-3, using core-loss EELS combined with numerical analysis. We control the band gap and activation energy of p-a-SiC by varying the B₂H₆ and CH₄ flow during deposition in the process chamber. We have found a linear relation between the activation energy of the dark conductivity E_act and the optical band gap E₀₄. Modelling shows that the optimum efficiency in nip solar cells is obtained when the p-a-SiC band gap is slightly larger than the band gap of the absorber layer. We have assessed the potential of core-loss EELS for detecting B and C concentrations as low as 10²⁰ cm^-3 in a spatially resolved manner, and of low-loss EELS as a probe of the local variations in plasmon energy.     

Kinematic Fields and Acoustic Emission Observations Associated with the Portevin Le Châtelier Effect on an Al–Mg Alloy

This paper presents experimental tensile test results obtained on flat aluminum magnesium alloy samples on a hard machine. The mechanical response, kinematic fields and acoustic emissions were simultaneously obtained in an experimental setup. Propagation instabilities associated with the Portevin–Le-Chatelier effect were observed as localized intense strain increment bands. Depending on the strain rate, A, B or C types were studied on the basis of stress drops, acoustic emission and strain fields. Then the band characteristics (position, orientation, width, thickness reduction, intensity, acoustic emission, principal strain direction) were presented in various strain rate conditions.     

Inference for the invariance of canonical analysis under linear transformations

Using a recent result about the invariance problem in linear canonical analysis (LCA), we introduce a criterion by means of which one can see if this invariance holds when the related random vectors are transformed by linear maps. Then, the estimation of this criterion is considered as well as the problem of testing for invariance of LCA. Particularly, a new test for additional information in canonical analysis is proposed and simulations are used to gain understanding of the finite sample performance of this test and to compare it with the likelihood ratio test.     

Linear relative canonical analysis of Euclidean random variables,asymptotic study and some applications

We introduce the Linear Relative Canonical Analysis (LRCA) of Euclidean random variables. Then similar properties than for usual linear Canonical Analysis are obtained. Furthermore, we develop an asymptotic study of LRCA and apply the obtained results to tests for lack of relative linear association, dimensionality and invariance.