The Inviscid, Compressible and Rotational, 2D Isotropic Burgers and Pressureless Euler-Coriolis Fluids; Solvable models with illustrations

The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler-Coriolis fluids respectively modeled by single vortices confined in compressible, local, inertial and global, rotating, environments. The field equations are established, inductively, starting from the equations of the characteristics solved with an initial Helmholtz decomposition of the velocity fields namely a vorticity free and a divergence free part and, deductively, by means of a canonical Hamiltonian Clebsch like formalism, implying two pairs of conjugate variables. Two vector valued fields are constants of the motion: the velocity field in the Burgers case and the momentum field per unit mass in the Euler-Coriolis one. Taking advantage of this property, a class of solutions for the mass densities of the fluids is given by the Jacobian of their sum with respect to the actual coordinates. Implementation of the isotropy hypothesis results in the cancellation of the dilatation-rotational cross terms in the Jacobian. A simple expression is obtained for all the radially symmetric Jacobians occurring in the theory. Representative examples of regular and singular solutions are shown and the competition between dilatation and vorticity is illustrated. Inspired by thermodynamical, mean field theoretical analogies, a genuine variational formula is proposed which yields unique measure solutions for the radially symmetric fluid densities investigated. We stress that this variational formula, unlike the Hopf-Lax formula, enables us to treat systems which are both compressible and rotational. Moreover in the one-dimensional case, we show for an interesting application that both variational formulas are equivalent

Coulomb system equivalent to the energy spectrum of the Calogero-Sutherland-Moser (CSM) model

The purpose of this paper is to prove an equivalence between the energy spectrum of the CSM model and the electrostatic energy of a one-dimensional lattice of quantized point charges interacting via Coulomb potential with Dirichlet boundary condition

Psychomotor Development of 18-Months Children With Orofacial Clefts

Objective - To describe the global and language development of children with cleft palate or cleft lip and palate at the age of 18 months, and to evaluate whether the type of cleft has an impact on psychomotor development. Study Design - Prospective cohort study. Settings - Tertiary care hospital Patients - All children born between December 2002 and November 2009 with an orofacial cleft, operated and seen at the developmental unit (UD) of the same hospital at the age of 18 months. Outcome Measures - Developmental quotients of the Griffiths Mental Development Scale and the French Communicative Development Inventory (IFDC) were used to assess the overall and language development of the children. Statistics- The population characteristics were described with means for continuous variables, and frequencies for binary or categorical variables. Chi-squared and regression analysis were used to analyse the results. Results - 69 children with clefts were examined at the age of 18 months with the IFDC and the Griffith test. The results showed that there was no significant difference in the test results of language development and global psychomotor development between the children with different types of clefts, and all were within the normal range. Conclusion - Psychomotor development is not affected by orofacial clefts, and there is no difference between children with cleft palate or cleft lip and palate

The One-Dimensional Schrödinger-Newton Equations

We prove an existence and uniqueness result for ground states of one-dimensional Schrödinger-Newton equation

Surface correlations for two-dimensional Coulomb fluids in a disc

After a brief review of previous work, two exactly solvable two-dimensional models of a finite Coulomb fluid in a disc are studied. The charge correlation function near the boundary circle is computed. When the disc radius is large compared to the bulk correlation length, a correlation function of the surface charge density can be defined. It is checked, on the solvable models, that this correlation function does have the generic long-range behaviour, decaying as the inverse square distance, predicted by macroscopic electrostatics. In the case of a two-component plasma (Coulomb fluid made of two species of particles of opposite charges), the density correlation function on the boundary circle itself is conjectured to have a temperature-independent behaviour, decaying as the -4 power of the distance.Comment: 15 pages, Latex, submitted to J.Phys.:Condens.Matte

Évaluation de six moteurs de recherche comme sources de veille dans le cadre d’une veille concernant trois sujets sur une période de deux semaines

La mise en place d’un dispositif de veille est devenue aujourd’hui d’une importance capitale pour les entreprises qui veulent gérer la surcharge informationnelle et rester compétitives. Cependant, elles ne disposent pas toujours des ressources nécessaires et utilisent principalement les moteurs de recherche pour surveiller les marchés. Ce projet de recherche a l’ambition d’évaluer les qualités de six moteurs de recherche en tant que sources de veille et d’utiliser exclusivement le flux RSS pour les surveiller, de manière à fournir des recommandations les concernant et poser quelques jalons pour une future étude. Quatre questions de recherche ont d’abord été établies, touchant à la pertinence, la précision, l’éclectisme et l’exhaustivité, afin de pouvoir explorer notre sujet et satisfaire nos objectifs d’évaluation des moteurs. Nous avons consulté la littérature pour la mise en place d’une méthodologie, mais n’avons pas trouvé d’études équivalentes. Afin de pallier ce manque, nous avons mené une réflexion sur les outils et le processus à employer, consacrant ainsi une majorité du temps imparti à cette phase de la recherche. Notre travail se déploie ainsi en six chapitres. Nous contextualisons d’abord notre recherche, puis nous fournissons les éléments méthodologiques, nous analysons ensuite les données collectées pour enfin en proposer une interprétation. Les résultats démontrent que globalement Bing est la source plus précise avec un taux de 40.27%, cependant notre recherche révèle qu’un moteur ne peut pas répondre à tous les besoins informationnels. En effet, lorsqu’il s’agit d’évaluer les résultats sous le prisme de différents sujets de veille, d’autres moteurs se montrent plus performants. Notre projet de recherche constitue une proposition tant pour l’approche méthodologique que pour l’analyse des données, nous espérons donc qu’il fournisse des bases propices à des réflexions futures

Lattice dynamics of anharmonic solids from first principles

An accurate and easily extendable method to deal with lattice dynamics of solids is offered. It is based on first-principles molecular dynamics simulations and provides a consistent way to extract the best possible harmonic - or higher order - potential energy surface at finite temperatures. It is designed to work even for strongly anharmonic systems where the traditional quasiharmonic approximation fails. The accuracy and convergence of the method are controlled in a straightforward way. Excellent agreement of the calculated phonon dispersion relations at finite temperature with experimental results for bcc Li and bcc Zr is demonstrated

Mass loss and longevity of gravitationally bound oscillating scalar lumps (oscillatons) in D-dimensions

Spherically symmetric oscillatons (also referred to as oscillating soliton stars) i.e. gravitationally bound oscillating scalar lumps are considered in theories containing a massive self-interacting real scalar field coupled to Einstein's gravity in 1+D dimensional spacetimes. Oscillations are known to decay by emitting scalar radiation with a characteristic time scale which is, however, extremely long, it can be comparable even to the lifetime of our universe. In the limit when the central density (or amplitude) of the oscillaton tends to zero (small-amplitude limit) a method is introduced to compute the transcendentally small amplitude of the outgoing waves. The results are illustrated in detail on the simplest case, a single massive free scalar field coupled to gravity.Comment: 23 pages, 2 figures, references on oscillons added, version to appear in Phys. Rev.