Anomalous Reflections Near a Caustic
RICE UNIV HOUSTON TX DEPT OF COMPUTATIONAL AND APPLIED MATHEMATICS
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We consider scattering associated to the reduced scalar wave equation. High frequency asymptotic solutions of this equation leads to the theory of geometrical optics. In this theory energy is transported along rays orthogonal trajectories to wavefronts. However this theory breaks down as soon as the ray field forms an envelope called a caustic. This signals that a dramatic change in nature of wave propagation occurs in the vicinity of a caustic. To illustrate this change of character we study an experiment which shows that reflected waves may have arbitrarily high energy content relative to the size of the scatterer. Moreover a theorem is proved showing that this unbounded behaviour can only occur when a caustic develops.
- Physical Chemistry
- Numerical Mathematics