Stability and asymptotic analysis of a fluid-particle interaction model

We are interested in coupled microscopic/macroscopic models describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov-Fokker-Planck equation to describe the microscopic motion of the particles coupled to the Euler equations for a compressible fluid. We investigate dissipative quantities, equilibria and their stability properties and the role of external forces. We also study some asymptotic problems, their equilibria and stability and the derivation of macroscopic two-phase models.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Lower bounds for the number of limit cycles of trigonometric Abel equations

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Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

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.

On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

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Liquid chromatography-tandem mass spectrometry (LC/APCI-MS/MS) methods for the quantification of captan and folpet phthalimide metabolites in human plasma and urine.

Captan and folpet are fungicides largely used in agriculture. They have similar chemical structures, except that folpet has an aromatic ring unlike captan. Their half-lives in blood are very short, given that they are readily broken down to tetrahydrophthalimide (THPI) and phthalimide (PI), respectively. Few authors measured these biomarkers in plasma or urine, and analysis was conducted either by gas chromatography coupled to mass spectrometry or liquid chromatography with UV detection. The objective of this study was thus to develop simple, sensitive and specific liquid chromatography-atmospheric pressure chemical ionization-tandem mass spectrometry (LC/APCI-MS/MS) methods to quantify both THPI and PI in human plasma and urine. Briefly, deuterated THPI was added as an internal standard and purification was performed by solid-phase extraction followed by LC/APCI-MS/MS analysis in negative ion mode for both compounds. Validation of the methods was conducted using spiked blank plasma and urine samples at concentrations ranging from 1 to 250 μg/L and 1 to 50 μg/L, respectively, along with samples of volunteers and workers exposed to captan or folpet. The methods showed a good linearity (R (2) > 0.99), recovery (on average 90% for THPI and 75% for PI), intra- and inter-day precision (RSD, <15%) and accuracy (<20%), and stability. The limit of detection was 0.58 μg/L in urine and 1.47 μg/L in plasma for THPI and 1.14 and 2.17 μg/L, respectively, for PI. The described methods proved to be accurate and suitable to determine the toxicokinetics of both metabolites in human plasma and urine.

Ultra high performance supercritical fluid chromatography coupled with tandem mass spectrometry for screening of doping agents. II: Analysis of biological samples.

The potential and applicability of UHPSFC-MS/MS for anti-doping screening in urine samples were tested for the first time. For this purpose, a group of 110 doping agents with diverse physicochemical properties was analyzed using two separation techniques, namely UHPLC-MS/MS and UHPSFC-MS/MS in both ESI+ and ESI- modes. The two approaches were compared in terms of selectivity, sensitivity, linearity and matrix effects. As expected, very diverse retentions and selectivities were obtained in UHPLC and UHPSFC, proving a good complementarity of these analytical strategies. In both conditions, acceptable peak shapes and MS detection capabilities were obtained within 7min analysis time, enabling the application of these two methods for screening purposes. Method sensitivity was found comparable for 46% of tested compounds, while higher sensitivity was observed for 21% of tested compounds in UHPLC-MS/MS and for 32% in UHPSFC-MS/MS. The latter demonstrated a lower susceptibility to matrix effects, which were mostly observed as signal suppression. In the case of UHPLC-MS/MS, more serious matrix effects were observed, leading typically to signal enhancement and the matrix effect was also concentration dependent, i.e., more significant matrix effects occurred at the lowest concentrations.

Developing discontinuous Galerkin methods for the resolution of the incompressible Navier-Stokes equations

Informe de investigación elaborado a partir de una estancia en el Laboratorio de Diseño Computacional en Aeroespacial en el Massachusetts Institute of Technology (MIT), Estados Unidos, entre noviembre de 2006 y agosto de 2007. La aerodinámica es una rama de la dinámica de fluidos referida al estudio de los movimientos de los líquidos o gases, cuya meta principal es predecir las fuerzas aerodinámicas en un avión o cualquier tipo de vehículo, incluyendo los automóviles. Las ecuaciones de Navier-Stokes representan un estado dinámico del equilibrio de las fuerzas que actúan en cualquier región dada del fluido. Son uno de los sistemas de ecuaciones más útiles porque describen la física de una gran cantidad de fenómenos como corrientes del océano, flujos alrededor de una superficie de sustentación, etc. En el contexto de una tesis doctoral, se está estudiando un flujo viscoso e incompresible, solucionando las ecuaciones de Navier- Stokes incompresibles de una manera eficiente. Durante la estancia en el MIT, se ha utilizado un método de Galerkin discontinuo para solucionar las ecuaciones de Navier-Stokes incompresibles usando, o bien un parámetro de penalti para asegurar la continuidad de los flujos entre elementos, o bien un método de Galerkin discontinuo compacto. Ambos métodos han dado buenos resultados y varios ejemplos numéricos se han simulado para validar el buen comportamiento de los métodos desarrollados. También se han estudiado elementos particulares, los elementos de Raviart y Thomas, que se podrían utilizar en una formulación mixta para obtener un algoritmo eficiente para solucionar problemas numéricos complejos.

Anti-schistosomal drugs: observations on the mechanism of drug resistance to hycanthone, and on the involvement of host antibodies in the mode of action of praziquantel

This paper reports recent observations from our laboratory dealing with the anti-schistosome drugs hycanthone (HC) and praziquantel (PZQ). In particular, we discuss a laboratory model of drug resistance to HC in Schistosoma mansoni and show that drug sensitive and resistant lines of the parasite can be differentiated on the basis of restriction fragment length polymorphisms using homologous ribosomal gene probes. In addition, we summarize data demonstrating that effective chemotherapy of S. mansoni infection with PZQ in mice requires the presence of host anti-parasite antibodies. These antibodies bind to PZQ treated worms and may be involved in an antibody-dependent cellular cytotoxicity reactions which result in the clearance of worms from the vasculature.

Indirect hydrogen analysis by gas chromatography coupled to mass spectrometry (GC-MS).

Gas chromatography (GC) is an analytical tool very useful to investigate the composition of gaseous mixtures. The different gases are separated by specific columns but, if hydrogen (H2 ) is present in the sample, its detection can be performed by a thermal conductivity detector or a helium ionization detector. Indeed, coupled to GC, no other detector can perform this detection except the expensive atomic emission detector. Based on the detection and analysis of H2 isotopes by low-pressure chemical ionization mass spectrometry (MS), a new method for H2 detection by GC coupled to MS with an electron ionization ion source and a quadrupole analyser is presented. The presence of H2 in a gaseous mixture could easily be put in evidence by the monitoring of the molecular ion of the protonated carrier gas. Copyright © 2013 John Wiley & Sons, Ltd.