The two‐way parabolic wave equation and reverberation from boundaries.

Self-averaging in time reversal for the parabolic wave equation

We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows us to construct an approximate martingale for the phase space Wigner transform of two wave fields. Using a priori L-bounds available in the time-reversal setting, we prove that the Wigner transform ...

Inverse Diffraction Parabolic Wave Equation Localisation System (IDPELS)

While GPS is a relatively mature technology, its susceptibility to radio frequency interference (RFI) is substantial. Various investigations, including the Volpe Report (Volpe, 2001) which was the result of a US Presidential Decision Directive (PDD-63) assigned to the Department of Transportation (DOT), have recommended that methods should be developed to monitor, report and locate interference...

A Parabolic Equation for Wave Propagation over Porous Structures

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Derivation of Dirac’s Equation from the Evans Wave Equation

The Evans wave equation [1] of general relativity is expressed in spinor form, thus producing the Dirac equation in general relativity. The Dirac equation in special relativity is recovered in the limit of Euclidean or flat spacetime. By deriving the Dirac equation from the Evans equation it is demonstrated that the former originates in a novel metric compatibility condition, a geometrical cons...