Application of Random Walk Methods to Wave Propagation

Application of Random Walk Methods to Wave Propagation

Here we present an approach to problems of diffraction that has its roots in a number of well-established theories such as the geometric theory of diffraction, the method of parabolic equations, the theory of Wiener functional integration, and the theory of stochastic processes. We start our analysis of the Helmholtz equation following closely the scheme of the ray method, but instead of approx...

Wave - Propagation Methods and

Multilevel Aggregation Methods for Small-World Graphs with Application to Random-Walk Ranking

We describe multilevel aggregation in the specific context of using Markov chains to rank the nodes of graphs. More generally, aggregation is a graph coarsening technique that has a wide range of possible uses regarding information retrieval applications. Aggregation successfully generates efficient multilevel methods for solving nonsingular linear systems and various eigenproblems from discret...

Wave Propagation and Imaging in Random Waveguides

Electromagnetic Wave Propagation in Random Waveguides

Abstract. We study long range propagation of electromagnetic waves in random waveguides with rectangular cross-section and perfectly conducting boundaries. The waveguide is filled with an isotropic linear dielectric material, with randomly fluctuating electric permittivity. The fluctuations are weak, but they cause significant cumulative scattering over long distances of propagation of the wave...