Long-Time Behavior of Nonautonomous Fokker-Planck Equations and Cooling of Granular Gases

We analyze the asymptotic behavior of linear Fokker-Planck equations with time-dependent coefficients. Relaxation towards a Maxwellian distribution with time-dependent temperature is shown under explicitly computable conditions. We apply this result to the study of Brownian motion in granular gases by showing that the Homogenous Cooling State attracts any solution at an algebraic rate.Проаналізовано асимптотичну поведінку лінійних рівнянь Фоккера - Планка з коефіцієнтами, залежними від часу. Показано, що за явно обчислюваних умов відбувається релаксація до розподілу Максвелла з залежною від часу температурою. Цей результат застосовано до вивчення броунівського руху в гранульованих газах і показано, що однорідний охолоджуючий стан притягує будь-який розв'язок з алгебраїчною швидкістю

Translations in the exponential Orlicz space with Gaussian weight

We study the continuity of space translations on non-parametric exponential families based on the exponential Orlicz space with Gaussian reference density.Comment: Submitted to GSI 2017, Pari

Integral representation of the linear Boltzmann operator for granular gas dynamics with applications

We investigate the properties of the collision operator associated to the linear Boltzmann equation for dissipative hard-spheres arising in granular gas dynamics. We establish that, as in the case of non-dissipative interactions, the gain collision operator is an integral operator whose kernel is made explicit. One deduces from this result a complete picture of the spectrum of the collision operator in an Hilbert space setting, generalizing results from T. Carleman to granular gases. In the same way, we obtain from this integral representation of the gain operator that the semigroup in L^1(\R \times \R,\d \x \otimes \d\v) associated to the linear Boltzmann equation for dissipative hard spheres is honest generalizing known results from the first author.Comment: 19 pages, to appear in Journal of Statistical Physic

Non-Fickian dispersion in porous media : 1. Multiscale measurements using single-well injection withdrawal tracer tests

International audienceWe present a set of single-well injection withdrawal tracer tests in a paleoreef porous reservoir displaying important small-scale heterogeneity. An improved dual-packer probe was designed to perform dirac-like tracer injection and accurate downhole automatic measurements of the tracer concentration during the recovery phase. By flushing the tracer, at constant flow rate, for increasing time duration, we can probe distinctly different reservoir volumes and test the multiscale predictability of the (non-Fickian) dispersion models. First we describe the characteristics, from microscale to meter scale, of the reservoir rock. Second, the specificity of the tracer test setup and the results obtained using two different tracers and measurement methods (salinity-conductivity and fluorescent dye­optical measurement, respectively) are presented. All the tracer tests display strongly tailed breakthrough curves (BTC) consistent with diffusion in immobile regions. Conductivity results, measured over 3 orders of magnitude only, could have been easily interpreted by the conventional mobile-immobile (MIM) diffusive mass transfer model of asymptotic log-log slope of 2. However, the fluorescent dye sensor, which allows exploring much lower concentration values, shows that a change in the log-log slope occurs at larger time with an asymptotic value of 1.5, corresponding to the double-porosity model. These results suggest that the conventional, one-slope MIM transfer rate model is too simplistic to account for the real multiscale heterogeneity of the diffusion-dominant fraction of the reservoir

The dissipative linear Boltzmann equation for hard spheres

We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The equilibrium state is a universal Maxwellian distribution function with the same velocity as field particles and with a non--zero temperature lower than the background one, which depends on the details of the binary collision. Thanks to the H--theorem we then prove strong convergence of the solution to the Boltzmann equation towards the equilibrium.Comment: 17 pages, submitted to Journal of Statistical Physic

A benthic quality index for European alpine lakes

The development of benthic quality indices for European lakes is hindered by the lack of information concerning many national lake types and pressures. Most information is from north European lakes stressed by acidification and from deep lakes subjected to eutrophication; for other lake types (the ones included in the Mediterranean areas for example) and for other pressures (hydro-morphological alteration, toxic stress) there is practically no information about the response of benthic macro-invertebrates; this hinders the possibility of an intercalibration of the indices among the member states (MS) in the EU. In the present communication three benthic quality indices are proposed considering the littoral, sublittoral and profundal zone in 5 reference and 7 non reference lakes from the Alpine region in response to eutrophication. The sensitivity values of the 177 species found in these lakes were calculated taking a weighted average of the values of environmental variables from lakes in which the species were present. The indicator taxa which prevailed in these lakes were Chironomids and Oligochaetes. A coinertia analysis emphasized the importance of trophic variables (transparency, nitrates, total phosphorous) in explaining the species distribution, but geographic (altitude) and morphometric (depth, volume) variables were also important. The indices enabeled a separation of reference from non-reference lakes and to assign the non-reference lakes to different quality classes in agreement with the Water Framework Directive. doi: 10.5324/fn.v31i0.1364. Published online: 17 October 2012.

A Class of Non-Parametric Statistical Manifolds modelled on Sobolev Space

We construct a family of non-parametric (infinite-dimensional) manifolds of finite measures on Rd. The manifolds are modelled on a variety of weighted Sobolev spaces, including Hilbert-Sobolev spaces and mixed-norm spaces. Each supports the Fisher-Rao metric as a weak Riemannian metric. Densities are expressed in terms of a deformed exponential function having linear growth. Unusually for the Sobolev context, and as a consequence of its linear growth, this "lifts" to a nonlinear superposition (Nemytskii) operator that acts continuously on a particular class of mixed-norm model spaces, and on the fixed norm space W²'¹ i.e. it maps each of these spaces continuously into itself. It also maps continuously between other fixed-norm spaces with a loss of Lebesgue exponent that increases with the number of derivatives. Some of the results make essential use of a log-Sobolev embedding theorem. Each manifold contains a smoothly embedded submanifold of probability measures. Applications to the stochastic partial differential equations of nonlinear filtering (and hence to the Fokker-Planck equation) are outlined

Matrix metalloproteinases (MMP-2,9) and their tissue inhibitors (TIMP-1,2) as novel markers of stress response and atherogenesis in children with chronic kidney disease (CKD) on conservative treatment

The system of matrix metalloproteinases (MMPs) and their tissue inhibitors (TIMPs) may play a key role in atherogenesis of chronic kidney disease (CKD) patients by its impact on matrix accumulation. Connections with inflammation, stress, or endothelial dysfunction are also probable. However, the data on correlations between these parameters in CKD patients are scarce in adults and absent in children. The aim of our study was to evaluate serum concentrations of MMP-2, MMP-9, TIMP-1, and TIMP-2, as well as their correlations with markers of stress response (Hsp90-α, anti-Hsp60), endothelial dysfunction (sE-selectin), and inflammation (high-sensitivity C-reactive protein) in CKD children treated conservatively. Thirty-seven patients were divided into two groups according to the CKD stage (gr.CKDI, 19 children with CKD stages 2–3; gr.CKDII, 18 subjects with CKD stages 4–5). Twenty-four age-matched healthy subjects served as controls. Serum concentrations of MMP-2, MMP-9, TIMP-1, TIMP-2, Hsp90-α, anti-Hsp60, and sE-selectin were assessed by ELISA. Median values of MMP-2, MMP-9, TIMP-1, and TIMP-2 were significantly higher in all CKD children vs. controls and were increased in patients with CKD stages 4–5 vs. CKD stages 2–3. Hsp90-α, anti-Hsp60, sE-selectin, and glomerular filtration rate predicted the values of MMPs and TIMPs. Chronic kidney disease in children is characterized by MMP/TIMP system dysfunction, aggravated by the progression of renal failure. Correlations between examined parameters, heat shock proteins, and markers of endothelial damage suggest the possibility of MMP/TIMP application as indicators of stress response and atherogenesis in children with CKD on conservative treatment

Metalloprotease Meprinβ in Rat Kidney: Glomerular Localization and Differential Expression in Glomerulonephritis

Meprin (EC 3.4.24.18) is an oligomeric metalloendopeptidase found in microvillar membranes of kidney proximal tubular epithelial cells. Here, we present the first report on the expression of meprinβ in rat glomerular epithelial cells and suggest a potential involvement in experimental glomerular disease. We detected meprinβ in glomeruli of immunostained rat kidney sections on the protein level and by quantitative RT-PCR of laser-capture microdissected glomeruli on the mRNA level. Using immuno-gold staining we identified the membrane of podocyte foot processes as the main site of meprinβ expression. The glomerular meprinβ expression pattern was altered in anti-Thy 1.1 and passive Heymann nephritis (PHN). In addition, the meprinβ staining pattern in the latter was reminiscent of immunostaining with the sheep anti-Fx1A antiserum, commonly used in PHN induction. Using Western blot and immunoprecipitation assays we demonstrated that meprinβ is recognized by Fx1A antiserum and may therefore represent an auto-antigen in PHN. In anti-Thy 1.1 glomerulonephritis we observed a striking redistribution of meprinβ in tubular epithelial cells from the apical to the basolateral side and the cytosol. This might point to an involvement of meprinβ in this form of glomerulonephritis