A new class of two-layer Green-Naghdi systems with improved frequency dispersion

We introduce a new class of Green-Naghdi type models for the propagation of internal waves between two (1+1)-dimensional layers of homogeneous, immiscible, ideal, incompressible, irrotational fluids, vertically delimited by a flat bottom and a rigid lid. These models are tailored to improve the frequency dispersion of the original bi-layer Green-Naghdi model, and in particular to manage high-frequency Kelvin-Helmholtz instabilities, while maintaining its precision in the sense of consistency. Our models preserve the Hamiltonian structure, symmetry groups and conserved quantities of the original model. We provide a rigorous justification of a class of our models thanks to consistency, well-posedness and stability results. These results apply in particular to the original Green-Naghdi model as well as to the Saint-Venant (hydrostatic shallow-water) system with surface tension.Comment: to appear in Stud. Appl. Mat

An improved result for the full justification of asymptotic models for the propagation of internal waves

We consider here asymptotic models that describe the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with uneven bottoms. The aim of this paper is to show that the full justification result of the model obtained by Duch\^ene, Israwi and Talhouk [{\em SIAM J. Math. Anal.}, 47(1), 240--290], in the sense that it is consistent, well-posed, and that its solutions remain close to exact solutions of the full Euler system with corresponding initial data, can be improved in two directions. The first direction is taking into account medium amplitude topography variations and the second direction is allowing strong nonlinearity using a new pseudo-symmetrizer, thus canceling out the smallness assumptions of the Camassa-Holm regime for the well-posedness and stability results.Comment: arXiv admin note: substantial text overlap with arXiv:1304.4554; text overlap with arXiv:1208.6394 by other author

Shallow water asymptotic models for the propagation of internal waves

Proceeding of the workshop " mécanique des fluides et dynamique de populations : modèles, existence de solutions, stabilité et méthodes numériques ", Beirut, Sept. 10-14, 2012.International audienceWe are interested in asymptotic models for the propagation of internal waves at the interface between two shallow layers of immiscible fluid, under the rigid-lid assumption. We review and complete existing works in the literature, in order to offer a unified and comprehensive exposition. Anterior models such as the shallow water and Boussinesq systems, as well as unidirectional models of Camassa-Holm type, are shown to descend from a broad Green-Naghdi model, that we introduce and justify in the sense of consistency. Contrarily to earlier works, our Green-Naghdi model allows a non-flat topography, and horizontal dimension d = 2. Its derivation follows directly from classical results concerning the one-layer case, and we believe such strategy may be used to construct interesting models in different regimes than the shallow-water/shallow-water studied in the present work

A new fully justified asymptotic model for the propagation of internal waves in the Camassa-Holm regime

A discussion on Kelvin-Helmholtz instabilities has been added. To appear in SIAM J. Math. Anal.This study deals with asymptotic models for the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with a flat bottom. We present a new Green-Naghdi type model in the Camassa-Holm (or medium amplitude) regime. This model is fully justified, in the sense that it is consistent, well-posed, and that its solutions remain close to exact solutions of the full Euler system with corresponding initial data. Moreover, our system allows to fully justify any well-posed and consistent lower order model; and in particular the so-called Constantin-Lannes approximation, which extends the classical Korteweg-de Vries equation in the Camassa-Holm regime

ASSESSMENT OF THE LEBANESE REAL ESTATE MARKET: A CONTENT ANALYSIS APPROACH

The purpose of this study is to assess the real estate market in Lebanon. The study was conducted by a group of MBA students at the Lebanese American University. A content analysis of the classified advertisements of the Lebanese Real Estate was conducted. Results identified four major elements that affect the Lebanese Real Estate market: Advertisements (R2=0.795559), Season of the advertisements (R2=0.741338), Location of the advertisement (R2= 0.594345), and Area of the advertisement (R2= 0.099588).The variable, advertisements, was most affected by the other variables. A recursive system test was conducted to show the relationship between advertisements, and the rest of the variables. (P43= 0.628947)real estate market, Lebanon, content analysis

Estudio documental sobre la viabilidad de la seguridad electrónica para la protección de estudiantes y docentes en instituciones educativas de básica primaria y media vocacional en Bogotá

En Colombia, específicamente en Bogotá, uno de cada dos estudiantes ha sido víctima de robo en el colegio, asimismo uno de cada tres ha sido agredido a golpes y expuesto a maltrato físico por parte de sus compañeros, un alto porcentaje de los agredidos requirió atención médica por esta causa y un alto porcentaje de los agredidos fue amenazado con arma de fuego, corto-punzante y contundente, todo esto asociado a la realidad del país, la cual está marcada por un conflicto armado prolongado, afecta de manera manifiesta la dinámica educativa e influye en las conductas agresivas de los estudiantes de cada región. Durante el 2007, y aún en años anteriores, se ha podido ver en diferentes partes del país manifestaciones de violencia en las instituciones educativas. La pobreza, el pandillismo, las drogas, la violencia intrafamiliar, los medios de comunicación, el conflicto armado y otros factores, se suman a las causas que liberan la violencia en las aulas clases. Por eso se hace necesario saber cómo es el estado del arte acerca de la implementación de tecnologías de vigilancia en escuelas de la ciudad de Bogotá, para lo cual se realizo una búsqueda bibliográfica y su posterior tabulación y análisis estadístico encontrando que el 52.9% de la información hallada es de procedencia colombiana, 54.5% de la información encontrada se hayo por medio del buscador Google y el 52.9% del fue escrito en formato de publicación de articulo de internetPregrad

Local and global solution for a nonlocal Fokker–Planck equation related to the adaptive biasing force process

International audienceWe prove global existence, uniqueness and regularity of the mild, L p and classical solution of a non-linear Fokker-Planck equation arising in an adaptive importance sampling method for molecular dynamics calculations. The non-linear term is related to a conditional expectation, and is thus non-local. The proof uses tools from the theory of semigroups of linear operators for the local existence result, and an a priori estimate based on a supersolution for the global existence result