Detection of a Moving Rigid Solid in a Perfect Fluid

In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem, initially introduced in [3], that consists in recovering the position and the velocity of the solid assuming that the potential function is known at a given time. We show that this problem is in general ill-posed by providing counterexamples for which the same potential corresponds to different positions and velocities of a same solid. However, it is also possible to find solids having a specific shape, like ellipses for instance, for which the problem of detection admits a unique solution. Using complex analysis, we prove that the well-posedness of the inverse problem is equivalent to the solvability of an infinite set of nonlinear equations. This result allows us to show that when the solid enjoys some symmetry properties, it can be partially detected. Besides, for any solid, the velocity can always be recovered when both the potential function and the position are supposed to be known. Finally, we prove that by performing continuous measurements of the fluid potential over a time interval, we can always track the position of the solid.Comment: 19 pages, 14 figure

Homogenization results for chemical reactive flows through porous media

This paper deals with the homogenization of a nonlinear problem mod-elllng chemica! reactive flows through periodically perforated domains. The chemical reactions take place on the walls of the porous médium. The effective behavior of these reactive flows is described by a new elliptic boundary-value problem contalning an extra zero-order term which captures the effect of the chemical reactions

Bloch Approximation in Homogenization and Applications

The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in this paper. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions $u^\varepsilon$ of boundary value problems associated with such operators when the period $\varepsilon>0$ of the coefficients is small. In a previous work by C. Conca and M. Vanninathan [SIAM J. Appl. Math., 57 (1997), pp. 1639--1659], a new proof of weak convergence as $\varepsilon\to 0$ towards the homogenized solution was furnished using Bloch wave decomposition. Following the same approach here, we go further and introduce what we call Bloch approximation, which will provide energy norm approximation for the solution $u^\varepsilon$. We develop several of its main features. As a simple application of this new object, we show that it contains both the first and second order correctors. Necessarily, the Bloch approximation will have to capture the oscillations of the solution in a sharper way. The present approach sheds new light and offers an alternative for viewing classical results

Brillouin light scattering study of Co2_{2}Cr0.6_{0.6}Fe0.4_{0.4}Al and Co2_{2}FeAl Heusler compounds

The thermal magnonic spectra of Co$_{2}$Cr$_{0.6}$Fe$_{0.4}$Al (CCFA) and Co$_2$FeAl were investigated using Brillouin light scattering spectroscopy (BLS). For CCFA, the exchange constant A (exchange stiffness D) is found to be 0.48 $\mu$erg/cm (203 meV A$^2$), while for Co$_2$FeAl the corresponding values of 1.55 $\mu$erg/cm (370 meV A$^2$) were found. The observed asymmetry in the BLS spectra between the Stokes and anti-Stokes frequencies was assigned to an interplay between the asymmetrical profiles of hybridized Damon-Esbach and perpendicular standing spin-wave modes, combined with the optical sensitivity of the BLS signal to the upper side of the CCFA or Co$_2$FeAl film

Insights into the Structure of Dot@Rod and Dot@Octapod CdSe@CdS Heterostructures

CdSe@CdS dot@rods with diameter around 6 nm and length of either 20, 27, or 30 nm and dot@octapods with pod diameters of ?15 nm and lengths of ?50 nm were investigated by X-ray absorption spectroscopy. These heterostructures are prepared by seed-mediated routes, where the structure, composition, and morphology of the CdSe nanocrystals used as a seed play key roles in directing the growth of the second semiconducting domain. The local structural environment of all the elements in the CdSe@CdS heterostructures was investigated at the Cd, S, and Se K-edges by taking advantage of the selectivity of X-ray absorption spectroscopy, and was compared to pure reference compounds. We found that the structural features of dot@rods are independent of the size of the rods. These structures can be described as made of a CdSe dot and a CdS rod, both in the wurtzite phase with a high crystallinity of both the core and the rod. This result supports the effectiveness of high temperature colloidal synthesis in promoting the formation of core@shell nanocrystals with very low defectivity. On the other hand, data on the CdSe@CdS with octapod morphology suggest the occurrence of a core composed of a CdSe cubic sphalerite phase with eight pods made of CdS wurtzite phase. Our findings are compared to current models proposed for the design of functional heterostructures with controlled nanoarchitecture

Functional consequences of mutations in CDKL5, an X-linked gene involved in infantile spasms and mental retardation

Mutations in the X-linked cyclin-dependent kinase-like 5 (CDKL5) gene have been identified in patients with Rett syndrome, West syndrome, and X-linked infantile spasms sharing the common features of generally intractable early seizures and mental retardation. Disease-causing mutations are distributed in both the catalytic domain and in the large COOH terminus. In this report, we examine the functional consequences of some Rett mutations of CDKL5 together with some synthetically designed derivatives useful to underline the functional domains of the protein. The mutated CDKL5 derivatives have been subjected to in vitro kinase assays and analyzed for phosphorylation of the TEY (Thr-Glu-Tyr) motif within the activation loop, their subcellular localization, and the capacity of CDKL5 to interact with itself. Whereas wild-type CDKL5 autophosphorylates and mediates the phosphorylation of the methyl-CpG-binding protein 2 (MeCP2) in vitro, Rett-mutated proteins show both impaired and increased catalytic activity suggesting that a tight regulation of CDKL5 is required for correct brain functions. Furthermore, we show that CDKL5 can self-associate and mediate the phosphorylation of its own TEY (Thr-Glu-Tyr) motif. Eventually, we show that the COOH terminus regulates CDKL5 properties; in particular, it negatively influences the catalytic activity and is required for its proper sub-nuclear localization. We propose a model in which CDKL5 phosphorylation is required for its entrance into the nucleus whereas a portion of the COOH-terminal domain is responsible for a stable residency in this cellular compartment probably through protein-protein interactions

Existence of global strong solutions to a beam-fluid interaction system

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the fluid cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous fluid and a deformable structure

Human Female Genital Tract Infection by the Obligate Intracellular Bacterium Chlamydia trachomatis Elicits Robust Type 2 Immunity

While Chlamydia trachomatis infections are frequently asymptomatic, mechanisms that regulate host response to this intracellular Gram-negative bacterium remain undefined. This investigation thus used peripheral blood mononuclear cells and endometrial tissue from women with or without Chlamydia genital tract infection to better define this response. Initial genome-wide microarray analysis revealed highly elevated expression of matrix metalloproteinase 10 and other molecules characteristic of Type 2 immunity (e.g., fibrosis and wound repair) in Chlamydia-infected tissue. This result was corroborated in flow cytometry and immunohistochemistry studies that showed extant upper genital tract Chlamydia infection was associated with increased co-expression of CD200 receptor and CD206 (markers of alternative macrophage activation) by endometrial macrophages as well as increased expression of GATA-3 (the transcription factor regulating TH2 differentiation) by endometrial CD4+ T cells. Also among women with genital tract Chlamydia infection, peripheral CD3+ CD4+ and CD3+ CD4- cells that proliferated in response to ex vivo stimulation with inactivated chlamydial antigen secreted significantly more interleukin (IL)-4 than tumor necrosis factor, interferon-γ, or IL-17; findings that repeated in T cells isolated from these same women 1 and 4 months after infection had been eradicated. Our results thus newly reveal that genital infection by an obligate intracellular bacterium induces polarization towards Type 2 immunity, including Chlamydia-specific TH2 development. Based on these findings, we now speculate that Type 2 immunity was selected by evolution as the host response to C. trachomatis in the human female genital tract to control infection and minimize immunopathological damage to vital reproductive structures. © 2013 Vicetti Miguel et al

Gout, allopurinol intake and clinical outcomes in the hospitalized multimorbid elderly

Background: Increased serum uric acid has been considered a cardiovascular risk factor but no study has assessed its relation with hospital mortality or length of stay. On the basis of data obtained from a prospective registry, the prevalence of gout/hyperuricemia and its association with these and other clinical parameters was evaluated in an Italian cohort of elderly patients acutely admitted to internal medicine or geriatric wards. Methods: While the prevalence of gout was calculated by counting patients with this diagnosis hyperuricemia was inferred in patients taking allopurinol at hospital admission or discharge, on the assumption that this drug was only prescribed owing to the \ufb01nding of high serum levels of uric acid. A series of clinical and demographic variables were evaluated for their association with gout/hyperuricemia. Results: Of 1380 patients, 139 (10%) had a diagnosis of gout or were prescribed allopurinol. They had more co-morbidities (7.0 vs 5.6; P b 0.0001) and consumed more drugs (6.8 vs 5.0; P b 0.0001). The CIRS (co-morbidity index) was worse in these patients (OR 1.28 95% CI 1.15\u20131.41). Multivariable regression analysis showed that only renal and heart failures were independently associated with gout/allopurinol intake. Moreover, this combined event was associated with an increased risk of adverse events during hospitalization (OR 1.66, 95% CI 1.16\u20132.36), but not with the risk of re-hospitalization, length of hospital stay or death. Conclusions: Gout/allopurinol intake has a high prevalence in elderly patients acutely admitted to hospital and are associated with renal and cardiovascular diseases, an increased rate of adverse events and a high degree of drug consumption. In contrast, this \ufb01nding did not affect the length of hospitalization nor hospital mortality