Traveltime, or geodesic distance, is locally the solution of the eikonal equation of geometric optics. However traveltime between sufficiently distant points is generically multivalued. Finite difference eikonal solvers approximate only the viscosity solution, which is the smallest value of the (multivalued) traveltime (‘‘first arrival time’’). The slowness matching method stitches together loc...

We investigate how a catastrophic event (modeled as a temporary fall of the reproduction rate) increases the extinction probability of an isolated self-regulated stochastic population. Using a variant of the Verhulst logistic model as an example, we combine the probability generating function technique with an eikonal approximation to evaluate the exponentially large increase in the extinction ...

In these notes, we present an introduction to the classical Fast Marching Method (FMM). The FMM has been first introduced to find numerical approximations of the solutions to the stationary eikonal equation. More generally we show that this method allows to find exactly the solutions of numerical schemes that satisfy a certain causality assumption. In order to motivate this method, we present t...

An eikonal expansion is developed in order to provide systematic corrections to the eikonal approximation through order 1/k, where k is the wave number. The expansion is applied to wave functions for the Klein-Gordon equation and for the Dirac equation with a Coulomb potential. Convergence is rapid at energies above about 250 MeV. Analytical results for the eikonal wave functions are obtained f...

We discuss an approach to compute two-particle scattering amplitudes for spinless particles colliding at Planckian centre-of-mass energies, with increasing momentum transfer away from the eikonal limit. For electrically neutral particles, the amplitude exhibits poles on the imaginary squared cm energy axis at locations that are distinct from those appearing in the eikonal limit. For charged par...

The rst arrival quasi-P wave traveltime eld in an anisotropic elastic solid solves a rst order nonlinear partial diierential equation, the qP eikonal equation. Since the qP slowness surface is convex, the rst arrival traveltime along downward propagating rays solves the paraxial qP eikonal equation, an evolution equation in depth. A second order upwind nite diierence scheme solves this paraxial...

Calculations which improve upon the eikonal model description of the scattering of loosely bound n-cluster composite nuclei at low and medium energies are studied. Each cluster-target eikonal phase shift is replaced by the continuation of the corresponding exact partial wave phase shift to noninteger angular momenta. Comparisons with fully quantum mechanical calculations for two-body projectile...