Abstract We develop an approach to wave propagation that may be considered as a natural extension of the convenient ray approximation to a theoretically accurate description of the wave fields. We start by following closely the scheme of the ray method and represent solutions of the Helmholtz equation in the Liouville form with the phase defined by the classical eikonal equations and with the amplitude that has to satisfy the second order transport equation. Then, instead of approximating the transport equation by a first order equation, as is done in ray theory, we treat it directly and obtain its exact solution in the form of a probabilistic Feynman-Kac formula, which employs an averaging in Wiener space. This approach to wave propagation is shown to be an effective tool for the analysis of numerous wave propagation problems some of which are notoriously difficult for standard methods, such as the problem of 3-D wave diffraction by a screen occupying a plane angular sector.
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David B. Bogy received his M.S. and M.S. degrees in Mechanical Engineering at Rice University in 1959 and 1961. After serving in the US Army and working as an engineer at Shell Development Company in Houston, Texas he entered Brown University in 1963 and received his Ph.D. in Applied Mathematics (Solid and Fluid Mechanics) in 1966. He was a postdoctoral fellow at Caltech in Applied Mechanics and joined the faculty in the ME Department at Berkeley in 1967, where he remains today. He has authored or co-authored more than 300 papers in refereed archival journals, most of them in the last 30 years in the mechanics of data storage systems. He has supervised 50 Ph.D’s. He served as Chair of the ME Department at Berkeley from 1991-1999. He was named the William S. Floyd Jr. Distinguished Professor in Engineering in 1993, and he was elected to the National Academy of Engineering in 1994. He is a Fellow of the American Academy of Mechanics, the American Society of Mechanical Engineers and the Institute of Electrical and Electronic Engineers.
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