Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction

We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers. The problem is reformulated as a nonautonomous recurrence in a space of time-periodic functions, where the dynamics is considered along the discrete spatial coordinate. We show that small amplitude oscillations are determined by finite-dimensional nonautonomous mappings, whose dimension depends on the solutions frequency. We consider the case of two-dimensional reduced mappings, which occurs for frequencies close to the edges of the phonon band. For an homogeneous chain, the reduced map is autonomous and reversible, and bifurcations of reversible homoclinics or heteroclinic solutions are found for appropriate parameter values. These orbits correspond respectively to discrete breathers, or dark breathers superposed on a spatially extended standing wave. Breather existence is shown in some cases for any value of the coupling constant, which generalizes an existence result obtained by MacKay and Aubry at small coupling. For an inhomogeneous chain the study of the nonautonomous reduced map is in general far more involved. For the principal part of the reduced recurrence, using the assumption of weak inhomogeneity, we show that homoclinics to 0 exist when the image of the unstable manifold under a linear transformation intersects the stable manifold. This provides a geometrical understanding of tangent bifurcations of discrete breathers. The case of a mass impurity is studied in detail, and our geometrical analysis is successfully compared with direct numerical simulations

Memoria del curso académico 2007-2008

Por orden cronológico destacamos los siguientes acontecimientos: Durante el curso 2007/2008 se elaboró la Memoria de Implantación del título de Graduado/a en Ingeniería de Edificación por la UPCT, título adaptado al EEES que va a sustituir al de Arquitectura Técnica. La memoria, tras su aprobación por unanimidad en la Junta de Centro de 04/03/2008 y por la Comisión de Convergencia Europea de 06/06/2008, fue enviada a ANECA para su verificación. El 11 de julio de 2008 se crea la Escuela de Arquitectura e Ingeniería de la Edificación para la gestión y organización de las enseñanzas del título vigente de Arquitecto Técnico, de los programas de postgrado y de los títulos de Master y Doctorado y del nuevo título de Grado en Arquitectura (Decreto nº 205/2008, de 11 de julio) con el informe previo favorable del Consejo Social y del Consejo Interuniversitario de la Región de Murcia. Por tanto, desde el curso 2008/2009 el título de Arquitecto Técnico ya no se impartirá en la Escuela Universitaria de Ingeniería Técnica Civil. El día 6 de junio se produce la triste y lamentable pérdida de nuestro compañero Salvador Martínez González, profesor del Departamento de Expresión Gráfic

JOSÉ MANUEL PASTOR

Abstract: A real application of simulation in the design of public transportation facilities is presented. The flow of passengers is modelled using discrete-event simulation, which facilitates the abstraction of the emptying and filling of the passengers into the buses, rather than the more usual continuous simulation for crowd movement. The decision variables include not only the physical layout of the queues but also some tactical variables that will help in future negotiations with labour unions and owners of the lines. A regression analysis has been performed using the simulation results to study the relationship between the maximum queue length and the input/output ratio in the gates