American Institute of Mathematical Sciences

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March  2010, 28(1): 147-159. doi: 10.3934/dcds.2010.28.147

Wave propagation in random waveguides

Chang-Yeol Jung 1, and  Alex Mahalov 2,

1. 

Ulsan National Institute of Science and Technology, San 194, Banyeon-ri, Eonyang-eup, Ulju-gun, Ulsan, South Korea
2. 

Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, United States

Received  October 2009 Revised  February 2010 Published  April 2010

We study uncertainty bounds and statistics of wave solutions through a random waveguide which possesses certain random inhomogeneities. The waveguide is composed of several homogeneous media with random interfaces. The main focus is on two homogeneous media which are layered randomly and periodically in space. Solutions of stochastic and deterministic problems are compared. The waveguide media parameters pertaining to the latter are the averaged values of the random parameters of the former. We investigate the eigenmodes coupling due to random inhomogeneities in media, i.e. random changes of the media parameters. We present an efficient numerical method via Legendre Polynomial Chaos expansion for obtaining output statistics including mean, variance and probability distribution of the wave solutions. Based on the statistical studies, we present uncertainty bounds and quantify the robustness of the solutions with respect to random changes of interfaces.
Keywords: Evolution of probability distribution; Monte Carlo simulation; Stochastic partial differential equation; random media; random interface..
Mathematics Subject Classification: 11K45, 65C20, 65C30, 82B3.
Citation: Chang-Yeol Jung, Alex Mahalov. Wave propagation in random waveguides. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 147-159. doi: 10.3934/dcds.2010.28.147
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