Convergence time to equilibrium distributions of autonomous and periodic non-autonomous graphs

We present some estimates of the time of convergence to the equilibrium distribution in autonomous and periodic non-autonomous graphs, with ergodic stochastic adjacency matrices, using the eigenvalues of these matrices. On this way we generalize previous results from several authors, that only considered reversible matrices.

Acoustic Propagation over Periodic and Quasi-Period Rough Surfaces Proceedings

Numerical techniques such as the Boundary Element Method, Finite Element Method and Finite Difference Time Domain have been used widely to investigate plane and curved wave-front scattering by rough surfaces. For certain shapes of roughness elements (cylinders, semi-cylinders and ellipsoids) there are semi-analytical alternatives. Here, we present a theory for multiple scattering by cylinders on a hard surface to investigate effects due to different roughness shape, the effects of vacancies and variation of roughness element size on the excess attenuation due to a periodically rough surfaces.