A New Geometric Approach To Study One Dimensional Complex Data Sets

A New Geometric Approach to Study One-dimensional Complex Data Sets

Dissertation Abstracts International

Wave Propagation in Complex Environments

The problem of wave propagation, such as elastic waves, acoustic waves, and electromagnetic waves, are commonly encountered in a wide range of areas, including civil engineering, mechanical engineering, wireless communication, remote sensing, meteorology, etc. In realistic scenarios, waves normally propagate in complex environments. Electromagnetic waves are transmitted through the medium with small particles that have significant scattering and absorbing effects. Sound waves radiated by underwater vehicles in shallow seas are reflected by the sea surface and seabed. Wave propagation in complex environments is often associated with multi-physics fields. Ultrasound waves propagation in porous media can generate heat, and elastic waves in piezoelectric materials induce electric fields. In addition, the physical mechanism of wave propagation in complex environments should be investigated across different scales. For example, to understand the interaction between light transmission and the matters in the surrounding medium, it is necessary to couple particle physics, electromagnetics, and geometric optics.