Motion of Isolated bodies

It is shown that sufficiently smooth initial data for the Einstein-dust or the Einstein-Maxwell-dust equations with non-negative density of compact support develop into solutions representing isolated bodies in the sense that the matter field has spatially compact support and is embedded in an exterior vacuum solution

A certain necessary condition of potential blow up for Navier-Stokes equations

We show that a necessary condition for $T$ to be a potential blow up time is $\lim\limits_{t\uparrow T}\|v(\cdot,t)\|_{L_3}=\infty$.Comment: 16 page

Well-posed and ill-posed behaviour of the μ(I)-rheology for granular flow

In light of the successes of the Navier–Stokes equations in the study of fluid flows, similar continuum treatment of granular materials is a long-standing ambition. This is due to their wide-ranging applications in the pharmaceutical and engineering industries as well as to geophysical phenomena such as avalanches and landslides. Historically this has been attempted through modification of the dissipation terms in the momentum balance equations, effectively introducing pressure and strain-rate dependence into the viscosity. Originally, a popular model for this granular viscosity, the Coulomb rheology, proposed rate-independent plastic behaviour scaled by a constant friction coefficient μ . Unfortunately, the resultant equations are always ill-posed. Mathematically ill-posed problems suffer from unbounded growth of short-wavelength perturbations, which necessarily leads to grid-dependent numerical results that do not converge as the spatial resolution is enhanced. This is unrealistic as all physical systems are subject to noise and do not blow up catastrophically. It is therefore vital to seek well-posed equations to make realistic predictions. The recent μ(I) -rheology is a major step forward, which allows granular flows in chutes and shear cells to be predicted. This is achieved by introducing a dependence on the non-dimensional inertial number I in the friction coefficient μ . In this paper it is shown that the μ(I) -rheology is well-posed for intermediate values of I , but that it is ill-posed for both high and low inertial numbers. This result is not obvious from casual inspection of the equations, and suggests that additional physics, such as enduring force chains and binary collisions, becomes important in these limits. The theoretical results are validated numerically using two implicit schemes for non-Newtonian flows. In particular, it is shown explicitly that at a given resolution a standard numerical scheme used to compute steady-uniform Bagnold flow is stable in the well-posed region of parameter space, but is unstable to small perturbations, which grow exponentially quickly, in the ill-posed domain

Implémentation sur FPGA d'un turbo codeur-décodeur en blocs à haut-débit avec une faible complexité

- Ce papier présente une implémentation sur FPGA (Field Programmable Gate Array) d'un turbo codeur-décodeur en blocs de faible complexité pour des applications à haut débit (i.e. > 25Mbps). Le code retenu pour l'implémentation est le code produit BCH étendu (32, 26, 4)2 (résultant de la concaténation de deux codes BCH étendus (32,26,4)). Les simulations en langage C et la synthèse en VHDL ont permis de montrer que l'utilisation de la structure itérative à traitement par blocs pour l'implémentation du turbo codeur-décodeur peut atteindre un débit de 50 Mbits/s tout en ayant une faible complexité (i.e. < 4500 éléments logiques)

Global wellposedness for a certain class of large initial data for the 3D Navier-Stokes Equations

In this article, we consider a special class of initial data to the 3D Navier-Stokes equations on the torus, in which there is a certain degree of orthogonality in the components of the initial data. We showed that, under such conditions, the Navier-Stokes equations are globally wellposed. We also showed that there exists large initial data, in the sense of the critical norm $B^{-1}_{\infty,\infty}$ that satisfies the conditions that we considered.Comment: 13 pages, updated references for v

Isotopic and velocity distributions of Bi produced in charge-pickup reactions of 208Pb at 1 A GeV

Isotopically resolved cross sections and velocity distributions have been measured in charge-pickup reactions of 1 A GeV 208Pb with proton, deuterium and titanium target. The total and partial charge-pickup cross sections in the reactions 208Pb + 1H and 208Pb + 2H are measured to be the same in the limits of the error bars. A weak increase in the total charge-pickup cross section is seen in the reaction of 208Pb with the titanium target. The measured velocity distributions show different contributions - quasi-elastic scattering and Delta-resonance excitation - to the charge-pickup production. Data on total and partial charge-pickup cross sections from these three reactions are compared with other existing data and also with model calculations based on the coupling of different intra-nuclear cascade codes and an evaporation code.Comment: 20 pages, 12 figures, background information on http://www-w2k.gsi.de/kschmidt

The "Symplectic Camel Principle" and Semiclassical Mechanics

Gromov's nonsqueezing theorem, aka the property of the symplectic camel, leads to a very simple semiclassical quantiuzation scheme by imposing that the only "physically admissible" semiclassical phase space states are those whose symplectic capacity (in a sense to be precised) is nh + (1/2)h where h is Planck's constant. We the construct semiclassical waveforms on Lagrangian submanifolds using the properties of the Leray-Maslov index, which allows us to define the argument of the square root of a de Rham form.Comment: no figures. to appear in J. Phys. Math A. (2002

Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phy