Recherches sur la convergence des séries de fourier

Sans résumé     

Temperature overshoots for a 4-velocity unidimensional discrete Boltzmann model

We propose a 4-velocity unidimensional discrete Boltzmann model with two different speeds 2, 1 and two different masses 1, 2. With the three conservation laws of mass, momentum, and energy satisfied, we can introduce a nontrivial temperature. First, we determine the similarity shock waves satisfying physical properties: positivity, shock stability, inequalities of the subsonic and supersonic flows, increase or decrease of both mass and temperature across the shock. It results that either the speed of the shock front is higher than the speed 1 of the slow particles and the shocks are compressive or less than 1 and the shocks are rarefactive. We observe overshoots of the temperature, across the shock, with bumps higher and higher as the shock front speed increases. Second, we study the (1+1)-dimensional shock waves. They represent the superposition and collision of two compressive shocks traveling in opposite directions and we observe temperature overshoots for not too large times.     

Gluon-ghost condensate of mass dimension 2 in the Curci-Ferrari gauge

The effective potential for an on-shell BRST invariant gluon-ghost condensate of mass dimension 2 in the Curci-Ferrari gauge in SU(N) Yang-Mills is analysed by combining the local composite operator technique with the algebraic renormalization. We pay attention to the gauge parameter independence of the vacuum energy obtained in the considered framework and discuss the Landau gauge as an interesting special case.     

Hermite and Smith normal form algorithms over Dedekind domains

We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.

     

Hamiltonian Stationary Lagrangian Surfaces in Euclidean Four-Space and Related Minimization Problems. Part II: Some Minimization Results

We study some minimization problems for Hamiltonian stationaryLagrangian surfaces in R⁴. We show that the flat Lagrangian torusS ¹ × S ¹ minimizes the Willmore functional among Hamiltonianstationary tori of its isotopy class, which gives a new proof of thefact that it is area minimizing in the same class. Considering theLagrangian flat cylinder as a torus in some quotient space R⁴/v Z, we show that it is also area minimizing in its isotopy class.     

The Gribov–Zwanziger action in the presence of the gauge invariant,nonlocal mass operator Tr∫d<Superscript>4</Superscript>xF<Subscript>μν</Subscript>(D<Superscript>2</Superscript>)<Superscript>-1</Superscript>F<Subscript>μν</Subscript> in the Landau gauge

We prove that the nonlocal gauge invariant mass dimension 2 operator F_μν(D²)^-1F_μν can be consistently added to the Gribov–Zwanziger action, which implements the restriction of the path integral’s domain of integration to the first Gribov region when the Landau gauge is considered. We identify a local polynomial action and prove the renormalizability to all orders of perturbation theory by employing the algebraic renormalization formalism. Furthermore, we also pay attention to the breaking of the BRST invariance, and to the consequences that this has for the Slavnov–Taylor identity. PACS 11.15.-q; 11.15.Tk     

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.