Spectral averaging techniques for Jacobi matrices

Spectral averaging techniques for one-dimensional discrete Schroedinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discussed. Special focus is put on proving lower bounds on the density of the averaged spectral measures. These Wegner type estimates are used to analyze stability properties for the spectral types of Jacobi matrices under local perturbations

Transient situations in traffic flow: Modelling the Mexico City Cuernavaca Highway

In this paper a recent variable anticipation cellular automata model for single-lane traffic flow is extended to analyze the situation of free and congested flow in the Highway from Mexico City to Cuernavaca. This highway presents free flow in standard days; but in the returning day of long weekends or holidays it exhibits congested flow and in rush hours jamming appears. We illustrate how our CA model for traffic flow can deal appropriately with transient situations and can be used to search new alternatives that allow to improve the traffic flow in Mexican highways.Comment: Paper accepted to be published in the Proceedings of Second Mexican Meeting on Mathematical and Experimental Physics (September 2004), El Colegio Nacional, Mexico City, Mexic

Estimating a pressure dependent thermal conductivity coefficient with applications in food technology

In this paper we introduce a method to estimate a pressure dependent thermal conductivity coefficient arising in a heat diffusion model with applications in food technology. To address the known smoothing effect of the direct problem, we model the uncertainty of the conductivity coefficient as a hierarchical Gaussian Markov random field (GMRF) restricted to uniqueness conditions for the solution of the inverse problem established in Fraguela et al. Furthermore, we propose a Single Variable Exchange Metropolis-Hastings algorithm to sample the corresponding conditional probability distribution of the conductivity coefficient given observations of the temperature. Sensitivity analysis of the direct problem suggests that large integration times are necessary to identify the thermal conductivity coefficient. Numerical evidence indicates that a signal to noise ratio of roughly 1000 suffices to reliably retrieve the thermal conductivity coefficient