Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Exploiting fitness distance correlation of set covering problems

The set covering problem is an NP-hard combinatorial optimization problemthat arises in applications ranging from crew scheduling in airlines todriver scheduling in public mass transport. In this paper we analyze searchspace characteristics of a widely used set of benchmark instances throughan analysis of the fitness-distance correlation. This analysis shows thatthere exist several classes of set covering instances that have a largelydifferent behavior. For instances with high fitness distance correlation,we propose new ways of generating core problems and analyze the performanceof algorithms exploiting these core problems.

Impaired uptake of glutathione by hepatic mitochondria from chronic ethanol-fed rats. Tracer kinetic studies in vitro and in vivo and susceptibility to oxidant stress.

Isolated hepatocytes incubated with [35S]-methionine were examined for the time-dependent accumulation of [35S]-glutathione (GSH) in cytosol and mitochondria, the latter confirmed by density gradient purification. In GSH-depleted and -repleted hepatocytes, the increase of specific activity of mitochondrial GSH lagged behind cytosol, reaching nearly the same specific activity by 1-2 h. However, in hepatocytes from ethanol-fed rats, the rate of increase of total GSH specific radioactivity in mitochondria was markedly suppressed. In in vivo steady-state experiments, the mass transport of GSH from cytosol to mitochondria and vice versa was 18 nmol/min per g liver, indicating that the half-life of mitochondrial GSH was approximately 18 min in controls. The fractional transport rate of GSH from cytosol to mitochondria, but not mitochondria to cytosol, was significantly reduced in the livers of ethanol-fed rats. Thus, ethanol-fed rats exhibit a decreased mitochondrial GSH pool size due to an impaired entry of cytosol GSH into mitochondria. Hepatocytes from ethanol-fed rats exhibited a greater susceptibility to the oxidant stress-induced cell death from tert-butylhydroperoxide. Incubation with glutathione monoethyl ester normalized the mitochondrial GSH and protected against the increased susceptibility to t-butylhydroperoxide, which was directly related to the lowered mitochondrial GSH pool size in ethanol-fed cells.

Diffusive transport properties in monovalent and divalent metal-ion halide melts: A computer simulation study

Self- and cross-velocity correlation functions and related transport coefficients of molten salts are studied by molecular-dynamics simulation. Six representative systems are considered, i.e., NaCl and KCl alkali halides, CuCl and CuBr noble-metal halides, and SrCl2 and ZnCl2 divalent metal-ion halides. Computer simulation results are compared with experimental self-diffusion coefficients and electrical conductivities. Special attention is paid to dynamic cross correlations and their dependence on the Coulomb interactions as well as on the size and mass differences between anions and cations.

External forcings, oceanographic processes and particle flux dynamics in Cap de Creus submarine canyon, NW Mediterranean Sea

Particle fluxes (including major components and grain size), and oceanographic parameters (near-bottom water temperature, current speed and suspended sediment concentration) were measured along the Cap de Creus submarine canyon in the Gulf of Lions (GoL; NW Mediterranean Sea) during two consecutive winter-spring periods (2009 2010 and 2010 2011). The comparison of data obtained with the measurements of meteorological and hydrological parameters (wind speed, turbulent heat flux, river discharge) have shown the important role of atmospheric forcings in transporting particulate matter through the submarine canyon and towards the deep sea. Indeed, atmospheric forcing during 2009 2010 and 2010 2011 winter months showed differences in both intensity and persistence that led to distinct oceanographic responses. Persistent dry northern winds caused strong heat losses (14.2 × 103 W m−2) in winter 2009 2010 that triggered a pronounced sea surface cooling compared to winter 2010 2011 (1.6 × 103 W m−2 lower). As a consequence, a large volume of dense shelf water formed in winter 2009 2010, which cascaded at high speed (up to ∼1 m s−1) down Cap de Creus Canyon as measured by a current-meter in the head of the canyon. The lower heat losses recorded in winter 2010 2011, together with an increased river discharge, resulted in lowered density waters over the shelf, thus preventing the formation and downslope transport of dense shelf water. High total mass fluxes (up to 84.9 g m−2 d−1) recorded in winter-spring 2009 2010 indicate that dense shelf water cascading resuspended and transported sediments at least down to the middle canyon. Sediment fluxes were lower (28.9 g m−2 d−1) under the quieter conditions of winter 2010 2011. The dominance of the lithogenic fraction in mass fluxes during the two winter-spring periods points to a resuspension origin for most of the particles transported down canyon. The variability in organic matter and opal contents relates to seasonally controlled inputs associated with the plankton spring bloom during March and April of both years.