Aproximación numérica de quinto orden de las ecuaciones de Hamilton-Jacobi

En este trabajo aproximamos la solución de viscosidad de las ecuaciones de Hamilton-Jacobi asociadas al problema de la reinicialización de curvas de nivel. Utilizamos para ello un método de quinto orden de precisión espacial óptimo para la aproximación de las ecuaciones de Hamilton-Jacobi. Como aplicación calculamos la aproximación a alto orden de funciones distancia euclidea signadas de curvas en R2

Analysis and numerical approximation of viscosity solutions with shocks : application to the plasma equation

We consider a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion function that depends on the unknown and on the gradient of the unknown. The new class of Hamilton-Jacobi equations represents the propagation of fronts with speed that is a nonlinear function of the signal. The equations contain a nonstandard Hamiltonian that allows the presence of shocks in the solution and these shocks propagate with nonlinear velocity. We focus on the one-dimensional plasma equation as an example of the general Fokker-Planck equations having the features we are interested in analyzing. We explore features of the solution of the corresponding Hamilton-Jacobi plasma equation and propose a suitable fifth order finite difference numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We present numerical results performed under different initial data with compact support

Implementación de las herramientas del e-marketing en el sector hotelero de Bogotá, durante el 2008-2009, en hoteles de 4 y 5 estrellas

Internet es un fenómeno básicamente tecnológico, en lo relacional y en lo humano, que permite la interacción entre todas las comunidades del planeta. En 1991 fue presentada la tecnología World Wide Web (WWW), con la cual se deseaba que la gente pudiera buscar documentos a través de internet, y así implementar un intercambio de información entre las personas de una forma estratégica, a partir de esto internet se convirtió en la herramienta principal de contacto entre las personas, gracias a esto más adelante se pude observar como este medio ofrece implementar el comercio en la red y surge los conceptos de e-bussines, e-marketing, e- commerce.Administrador (a) de EmpresasPregrad

High order accurate shock capturing schemes for hyperbolic conservation laws based on a new class of limiters.

We have introduced new shock capturing schemes that reduce the numerical diusion at discontinuities, sharpen the discontinuities in derivative and avoid spurious oscillations, improving the behavior of essentially non oscillatory schemes and piecewise hyperbolic methods. We have introduced and analyzed in this work a new class of limiter functions, the so called power limiters", which are an essential tool for the construction of these schemes. When power limiters are used as limiters of rst or second order dierences, the resulting methods behave essentially non-oscillatory near discontinuities and they allow simple expressions of the local truncation errors when they are used as limiters of second order dierences. We have used the powereno limiter as a slope limiter for the design of a new piecewise hyperbolic method called the Power PHM method. The third order accurate Power PHM scheme improves the behavior of PHM at local extrema and contact discontinuities, and it shares the advantages of the PHM. Since these are compact schemes (three point stencil), Power PHM is recommended over PHM when this condition is convenient for the computation (e.g., relaxation schemes). We have also used the powereno limiter applied to consecutive second order nite dierences to construct the Power ENO method. We have analyzed a new fth order accurate Weighted Power ENO method as a nonlinear convex combination of the three Power ENO parabolas. Our fth order accurate Weighted PowerENO scheme improves the behavior of WENO5 reducing the numerical viscosity at contact discontinuities and local extrema. It captures ner scales for a xed computational grid. Our scheme is recommended when high order accuracy is a goal and when dealing with numerical schemes and simulations where a reduced (compact) stencil is not necessary. We have checked the robustness, stability and accuracy of the proposed schemes in a set of model problems by means of several numerical tests, including the shock entropy wave interaction, two interacting blast waves, the two dimensional four contacts Riemann problem and the two dimensional four shocks problem. Finally, we have shown the ability of the presented schemes in resolving ne scales near unstable interfaces by computing Rayleigh-Taylor and Richtmyer-Meshkov instabilities. ____________________________________________________________________________________________________ RESUMEN Hemos introducido nuevos metodos de captura de ondas de choque que reducen la difusion numerica en las discontinuidades, denen ntidamente las discontinuidades en derivada y evitan las oscilaciones espureas, mejorando el comportamiento de los esquemas esencialmente no oscilatorios y los metodos hiperbolicos a trozos. Hemos introducido y analizado en este trabajo una nueva clase de funciones limitadoras, los llamados power limiters" que son una herramienta esencial para la construccion de estos esquemas. Hemos utilizado el limitador powereno" como limitador de pendiente para el dise~no de un nuevo metodo hiperbolico a trozos que llamamos metodo Power PHM. Tambien hemos utilizado el limitador powereno aplicado a segundas diferencias contiguas para construir el metodo Power ENO. Hemos analizado un nuevo metodo de quinto orden de precisi on espacial, el metodo Weighted PowerENO, como una combinacion convexa no lineal de las tres parabolas PowerENO. Hemos comprobado la robustez, estabilidad y precision de los esquemas propuestos para un conjunto de problemas modelo mediante varios experimentos numericos. Finalmente hemos demostrado la capacidad de los esquemas presentados en la resolucion de las escalas nas en el entorno de interfases inestables mediante el calculo de inestabilidades de Rayleigh-Taylor y Richtmyer-Meshkov

Razón y tradición: los partidos en Argentina y Uruguay

La ponencia aborda el análisis de la perspectiva actual de los partidos Colorado en Uruguay y el Radical en Argentina, vistos desde un doble enfoque, primero observando el desempeño de sus estructuras internas, y segundo, a partir de una comparación de ambos en el contexto de la política partidaria rioplatense. marcando la particularidades y desaj!os comunes que presentan en los recientes procesos de transición democrática. Intentamos, por último, delinear las principales estrategias y respuestas ensayados desde los partidos reformistas tradicionales en la transición democrática. mostrando al mismo tiempo, las limitantes que tuvieron en su accionar tanto por el legado político y cultural de las experiencias autoritarias de la década del 70, el contexto económico internacional desfavorable, la crisis del Estado Social, la persistencia de actores corporativos, y las dificultades consecuentes para que los partidos pudieran efectivamente articular las demandas crecientes provenientes de la sociedad en políticas públicas coherentes y satisfactorias

Numerical approximation of MHD equations for real gases

We consider the MHD equations for real gases described by a Van der Waals equation of state. We present an explicit calculation of the spectral decomposition of the Jacobian of the fluxes and we propose a characteristic-based upwind numerical scheme to approximate the solution of the system of equations in the one dimensional case. We show a numerical example where we observe wave dynamics significantly stronger than the one obtained for the ideal MHD case

Fronts propagating with signal dependent speed in limited diffusion and related Hamilton-Jacobi formulations

We consider a class of limited diffusion equations and explore the formation of diffusion fronts as the result of a combination of diffusive and hyperbolic transport. We analyze a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion coefficient that depends on the unknown and on the gradient of the unknown. We explore the main features of the solution of the Hamilton-Jacobi equations that contain shocks and propose a suitable numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We analyze three model problems covering different scenarios. One is the relativistic heat equation model where the speed of propagation of fronts is constant. A second one is a standard porous media model where the speed of propagation of fronts is a function of the density, is unbounded and can exceed any fixed value. We propose a third one which is a porous media model whose speed of propagating fronts depends on the density media and is limited. The three model problems satisfy a general Darcy law. We perform a set of numerical experiments under different piecewise smooth initial data with compact support and compare the behavior of the three different model problems

Fast Hyigens sweeping methods for Schrodinger equations in the semi-classical regime

Agraïments: This paper is dedicated to Prof. Stan Osher on the occasion of his 70th birthday. Leung is supported in part by the Hong Kong RGC under Grant GRF603011. Qian is supported by NS.We propose fast Huygens sweeping methods for Schrodinger equations in the semi-classical regime by incorporating short-time Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) propagators into Huygens' principle. Even though the WKBJ solution is valid only for a short time period due to the occurrence of caustics, Huygens' principle allows us to construct the global-in-time semi-classical solution. To improve the computational efficiency, we develop analytic approximation formulas for the short-time WKBJ propagator by using the Taylor expansion in time. These analytic formulas allow us to develop two classes of fast Huygens sweeping methods, among which one is posed in the momentum space, and the other is posed in the position space, and both of these methods are of computational complexity O(N log N ) for each time step, where N is the total number of sampling points in the d-dimensional position space. To further speed up these methods, we also incorporate the soft-thresholding sparsification strategy into our new algorithms so that the computational cost can be further reduced. The methodology can also be extended to nonlinear Schrodinger equations. One, two, and three dimensional examples demonstrate the performance of the new algorithms