On quantization of quadratic Poisson structures

Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd. We exhibit in this article an example of quadratic Poisson structure which does not arise this way.Comment: Submitted to Comm. Math. Phys. Version 2 : error in introduction correcte

Turbulent-like fluctuations in quasistatic flow of granular media

We analyze particle velocity fluctuations in a simulated granular system subjected to homogeneous quasistatic shearing. We show that these fluctuations share the following scaling characteristics of fluid turbulence in spite of their different physical origins: 1) Scale-dependent probability distribution with non-Guassian broadening at small time scales; 2) Power-law spectrum, reflecting long-range correlations and the self-affine nature of the fluctuations; 3) Superdiffusion with respect to the mean background flow

Scattering by a toroidal coil

In this paper we consider the Schr\"odinger operator in ${\mathbb R}^3$ with a long-range magnetic potential associated to a magnetic field supported inside a torus ${\mathbb{T}}$. Using the scheme of smooth perturbations we construct stationary modified wave operators and the corresponding scattering matrix $S(\lambda)$. We prove that the essential spectrum of $S(\lambda)$ is an interval of the unit circle depending only on the magnetic flux $\phi$ across the section of $\mathbb{T}$. Additionally we show that, in contrast to the Aharonov-Bohm potential in ${\mathbb{R}}^2$, the total scattering cross-section is always finite. We also conjecture that the case treated here is a typical example in dimension 3.Comment: LaTeX2e 17 pages, 1 figur

The Wide-field High-resolution Infrared TElescope (WHITE)

The Wide-field High-resolution Infrared TElescope (WHITE) will be dedicated in the first years of its life to carrying out a few (well focused in terms of science objectives and time) legacy surveys. WHITE would have an angular resolution of ~0.3'' homogeneous over ~0.7 sq. deg. in the wavelength range 1 - 5 um, which means that we will very efficiently use all the available observational time during night time and day time. Moreover, the deepest observations will be performed by summing up shorter individual frames. We will have a temporal information that can be used to study variable objects. The three key science objectives of WHITE are : 1) A complete survey of the Magellanic Clouds to make a complete census of young stellar objects in the clouds and in the bridge and to study their star formation history and the link with the Milky Way. The interaction of the two clouds with our Galaxy might the closest example of a minor merging event that could be the main driver of galaxy evolution in the last 5 Gyrs. 2) The building of the first sample of dusty supernovae at z<1.2 in the near infrared range (1-5 um) to constrain the equation of state from these obscured objects, study the formation of dust in galaxies and build the first high resolution sample of high redshift galaxies observed in their optical frame 3) A very wide weak lensing survey over that would allow to estimate the equation of state in a way that would favourably compete with space projects.Comment: Invited talk to the 2nd ARENA Conference : "The Astrophysical Science Cases at Dome C" Potsdam 17-21 September, 200

Developmental constraints on vertebrate genome evolution

Constraints in embryonic development are thought to bias the direction of evolution by making some changes less likely, and others more likely, depending on their consequences on ontogeny. Here, we characterize the constraints acting on genome evolution in vertebrates. We used gene expression data from two vertebrates: zebrafish, using a microarray experiment spanning 14 stages of development, and mouse, using EST counts for 26 stages of development. We show that, in both species, genes expressed early in development (1) have a more dramatic effect of knock-out or mutation and (2) are more likely to revert to single copy after whole genome duplication, relative to genes expressed late. This supports high constraints on early stages of vertebrate development, making them less open to innovations (gene gain or gene loss). Results are robust to different sources of data-gene expression from microarrays, ESTs, or in situ hybridizations; and mutants from directed KO, transgenic insertions, point mutations, or morpholinos. We determine the pattern of these constraints, which differs from the model used to describe vertebrate morphological conservation ("hourglass" model). While morphological constraints reach a maximum at mid-development (the "phylotypic" stage), genomic constraints appear to decrease in a monotonous manner over developmental time

Criticality of the "critical state" of granular media: Dilatancy angle in the tetris model

The dilatancy angle describes the propensity of a granular medium to dilate under an applied shear. Using a simple spin model (the ``tetris'' model) which accounts for geometrical ``frustration'' effects, we study such a dilatancy angle as a function of density. An exact mapping can be drawn with a directed percolation process which proves that there exists a critical density $\rho_c$ above which the system expands and below which it contracts under shear. When applied to packings constructed by a random deposition under gravity, the dilatancy angle is shown to be strongly anisotropic, and it constitutes an efficient tool to characterize the texture of the medium.Comment: 7 pages RevTex, 8eps figure, to appear in Phys. Rev.

Simulation of neutrophil motion and deformation: influence of rheology and flow configuration

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Dynamic glass transition: bridging the gap between mode-coupling theory and the replica approach

We clarify the relation between the ergodicity breaking transition predicted by mode-coupling theory and the so-called dynamic transition predicted by the static replica approach. Following Franz and Parisi [Phys. Rev. Lett. 79, 2486 (1997)], we consider a system of particles in a metastable state characterized by non-trivial correlations with a quenched configuration. We show that the assumption that in a metastable state particle currents vanish leads to an expression for the replica off-diagonal direct correlation function in terms of a replica off-diagonal static four-point correlation function. A factorization approximation for this function results in an approximate closure for the replica off-diagonal direct correlation function. The replica off-diagonal Ornstein-Zernicke equation combined with this closure coincides with the equation for the non-ergodicity parameter derived using the mode-coupling theory.Comment: revised version; to be published in EP