Inverse Scattering in the Recovery of a Single Concave and a Finite Union of Disjoint Convex Obstacles

Inverse scattering theory investigates whether sets of obstacles can be recovered from measurements of scattered particles/waves. This project aims to investigate the scattering properties of a concave obstacle and its interaction with scattered rays from a finite set of convex obstacles. Specifically, we wish to determine whether a single concave obstacle can be recovered from measurements of the travelling time distribution of billiard-like rays. Further, we will investigate whether the combination of a single concave and finitely many convex obstacles can be recovered from a measurement of the travelling time distribution.

Joshua Crawford

The University of Western Australia

Josh has recently completed his undergraduate studies in Physics and Mathematics at the University of Western Australia and is intending to further his studies in Physics through an Honours program in 2021. Previously, Josh had worked as a Mineral Processing Engineer for a small engineering consulting company, however he returned to university to complete his degree in Physics to work towards a career in academia. The opportunity to contribute to the body of knowledge in a field he is strongly passionate about has been a strong motivator for the career change, and drives his desire to continue to learn. He has research interests in elementary particle physics and mathematical physics, motivated by a desire to understand how mathematics underpins physical interactions on a fundamental level.

Josh also works as a high-school tutor where he has the opportunity to share his passion with his students and to promote interest in the Mathematical Sciences. One of the most satisfying aspects of teaching is to see your students develop an interest in the field and to ask bigger questions than the syllabus asks for. He hopes to continue teaching throughout his career. Outside of work and studying, Josh enjoys exploring the outdoors or grabbing a coffee with friends.

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