Complements on disconnected reductive groups

We present various results on disconnected reductive groups, in particular about the characteristic 0 representation theory of such groups over finite fields.Comment: This version takes into account improvements suggested by G. Mall

Tunnel effect for semiclassical random walk

We study a semiclassical random walk with respect to a probability measure with a finite number n_0 of wells. We show that the associated operator has exactly n_0 exponentially close to 1 eigenvalues (in the semiclassical sense), and that the other are O(h) away from 1. We also give an asymptotic of these small eigenvalues. The key ingredient in our approach is a general factorization result of pseudodifferential operators, which allows us to use recent results on the Witten Laplacian

The space of unipotently supported class functions on a finite reductive group

We determine the Lusztig restrictions on the space of class functions with a unipotent support on a finite reductive group. In particular we give a simple expression for the Lusztig restrictions of the generalized Green functions and we describe the Lusztig restrictions of the generalized Gelfand-Graev representations. We make explicit computations for the Gelfand-Graev representations associated to the subregular unipotent class. In the case of SLn we show that the computations can be reduced to the case of GLn' for various n'.Comment: 21 page

Time resolved tracking of a sound scatterer in a turbulent flow: non-stationary signal analysis and applications

It is known that ultrasound techniques yield non-intrusive measurements of hydrodynamic flows. For example, the study of the echoes produced by a large number of particle insonified by pulsed wavetrains has led to a now standard velocimetry technique. In this paper, we propose to extend the method to the continuous tracking of one single particle embedded in a complex flow. This gives a Lagrangian measurement of the fluid motion, which is of importance in mixing and turbulence studies. The method relies on the ability to resolve in time the Doppler shift of the sound scattered by the continuously insonfied particle. For this signal processing problem two classes of approaches are used: time-frequency analysis and parametric high resolution methods. In the first class we consider the spectrogram and reassigned spectrogram, and we apply it to detect the motion of a small bead settling in a fluid at rest. In more non-stationary turbulent flows where methods in the second class are more robust, we have adapted an Approximated Maximum Likelihood technique coupled with a generalized Kalman filter.Comment: 16 pages 9 figure

The Power of Axisymmetric Pulsar

Stationary force-free magnetosphere of an axisymmetric pulsar is shown to have a separatrix inclination angle of 77.3$^\circ$. The electromagnetic field has an $R^{-1/2}$ singularity inside the separatrix near the light cylinder. A numerical simulation of the magnetosphere which crudely reproduces these properties is presented. The numerical results are used to estimate the power of an axisymmetric pulsar: $L=(1\pm 0.1)\mu^2\Omega^4/c^3$. A need for a better numerical simulation is pointed out.Comment: 9 page

The `bare' strange stars might not be bare

It is proposed that the `bare' strange matter stars might not be bare, and radio pulsars might be in fact `bare' strange stars. As strange matter stars being intensely magnetized rotate, the induced unipolar electric fields would be large enough to construct magnetospheres. This situation is very similar to that discussed by many authors for rotating neutron stars. Also, the strange stars with accretion crusts in binaries could act as X-ray pulsars or X-ray bursters. There are some advantages if radio pulsars are `bare' strange stars.Comment: 11 pages, 1 Postscript figures, LaTeX, Chin. Phys. Lett. 1998, Vol.15, Nov.12, p.93

A Methodology to Engineer and Validate Dynamic Multi-level Multi-agent Based Simulations

This article proposes a methodology to model and simulate complex systems, based on IRM4MLS, a generic agent-based meta-model able to deal with multi-level systems. This methodology permits the engineering of dynamic multi-level agent-based models, to represent complex systems over several scales and domains of interest. Its goal is to simulate a phenomenon using dynamically the lightest representation to save computer resources without loss of information. This methodology is based on two mechanisms: (1) the activation or deactivation of agents representing different domain parts of the same phenomenon and (2) the aggregation or disaggregation of agents representing the same phenomenon at different scales.Comment: Presented at 3th International Workshop on Multi-Agent Based Simulation, Valencia, Spain, 5th June 201

Heavy Quark Diffusion from the Lattice

We study the diffusion of heavy quarks in the Quark Gluon Plasma using the Langevin equations of motion and estimate the contribution of the transport peak to the Euclidean current-current correlator. We show that the Euclidean correlator is remarkably insensitive to the heavy quark diffusion coefficient and give a simple physical interpretation of this result using the free streaming Boltzmann equation. However if the diffusion coefficient is smaller than $\sim 1/(\pi T)$, as favored by RHIC phenomenology, the transport contribution should be visible in the Euclidean correlator. We outline a procedure to isolate this contribution.Comment: 24 pages, 5 figure