Catálogo de publicaciones - libros

A matrix is defined to be rank stable if rank() is unchanged for all relatively small perturbations of its elements. In this paper we investigate some properties and zero patterns of such matrices.

In this paper we present main points in the process of application of numerical schemes for hyperbolic balance laws to water wave propagation and flooding. The appropriate mathematical models are the one-dimensional open channel flow equations and the two-dimensional shallow water equations. Therefore good simulation results can only be obtained with well-balanced numerical schemes such as the ones developed by Bermùdez and Vázquez, Hubbard and García-Navarro, LeVeque, etc. as well as the ones developed by the authors of this paper. We also propose a modification of the well-balanced Q-scheme for the two-dimensional shallow water equations that solves the wetting and drying problem. Finally, we present numerical results for three simulation tasks: the CADAM dam break experiment, the water wave propagation in the Toce river, and the catastrophic dam break on the Malpasset river.

The behavior of springs in linearized theory can be expressed by the stiffness coefficient of the spring. In this paper we derive the stiffness coefficient for leaf springs in terms of geometric properties of the spring and elastic properties of material the spring is made of.

We consider the quantum site percolation model on graphs with a amenable group action. It consists of a random family of Hamiltonians. Basic spectral properties of these operators are derived: non-randomness of the spectrum and its components, existence of an self-averaging integrated density of states and an associated trace-formula.

Extended finite difference WENO schemes for hyperbolic balance laws with spatially varying flux and geometrical source term were developed by the authors. In these schemes high order ENO and WENO reconstruction for flux and source term characteristicwise components are used, therefore schemes give high resolution results.

In this paper these high order properties are analyzed through several convergence tests: on two shallow water tests, one linear acoustics test, and one test for the Burgers equation with a source term. Experimentally established orders of accuracy vs. the theoretically expected orders are compared for the new schemes, as well as for the original WENO schemes combined with pointwise source term evaluation.