The Fradkin–Schwinger functional methods to represent a Green function in an external gravitational field are used study the eikonal and next-to-eikonal limit, including nonlinear interactions, of scattering amplitudes ultra-relativistic scalar particle on static super-massive target nearly forward limit. approach confirms exponentiation leading which also applies first non-leading power energy...

A simple algorithm to calculate the maximum torsional load for a cylindrical shaft is presented. The algorithm is based on the notion of viscosity solutions to the eikonal equation, and is not restricted to simply-connected cross-sections. Applications to other, related problems, such as ferromagnetic thin lms, and elastic buckling of thin lm blisters are also discussed. 1. Introduction A class...

S U M M A R Y The growth of the Earthscope/USArray Transportable Array (TA) has prompted the development of new methods in surface wave tomography that track phase fronts across the array and map the traveltime field for each earthquake or for each station from ambient noise. Directionally dependent phase velocities are determined locally by measuring the gradient of the observed traveltime fie...