Applications of Random Differential Equations to Engineering Science. Wave Propagation in Turbulent Media and Random Linear Hyperbolic Systems

摘要

Research has been conducted in two major problem areas: Applications of Random Differential Equations to Engineering Science. Wave Propagation in Turbulent Media and Random Linear Hyperbolic Systems. These two area are not disjoint. In fact the second problem area is a follow-up study on problems in the first one with emphasis on wave propagation in turbulent media. We have investigated several turbulence-related problems arising from engineering science. They include problems in wave propagation through turbulent media, turbulent transport theory, the surface roughness effect on hydrodynamic lubrication and wave scattering, and stability of elastic structures under random loading or with imperfections. In the theoretical aspect, the research is mainly concerned with the development of new methodology in solving differential equations with random coefficients, examination of the existing closure approximations with regards to their validity and possible improvements. Certain related mathematical questions are also studied.