We prove that any 2-dimensional solution ψ ∈ W 1+ 1 3,3 loc of the eikonal equation has locally Lipschitz gradient ∇ψ except at a locally finite number of vortex-points. A related regularizing effect is also obtained for general solutions of the Burgers’ equation. DOI: https://doi.org/10.1080/03605302.2014.999939 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: h...

A functional formulation and partial solution is given of the non-abelian eikonal problem associated with the exchange of non-interacting, charged or colored bosons between a pair of fermions, in the large s/small t limit. A simple, functional “contiguity” prescription is devised for extracting those terms which exponentiate, and appear to generate the leading, high-energy behavior of each pert...

A method for determining the internal structure of a localized scattering potential from field measurements performed outside the scattering volume is developed by using the Rytov approximation. The theory is compared with the inverse-scattering method within the Born and eikonal approximations and found to reduce to these methods in the weak-scattering (Born) and very-short-wavelength (eikonal...

We present an analytic calculation of electron and tau O(α) loop effects on the muon anomalous magnetic moment. Computation of such three-loop diagrams with three mass scales is possible using asymptotic and eikonal expansions. An evaluation of a new type of eikonal integrals is presented in some detail.

a method has been presented for finding the solution surface of the npde: u  c , bounded by a general space curve. the method is based on the geometric characteristics of the surface, and is called the “cone-slot method”. it has been shown that such a surface can be obtained by movement of a cone inside the slot formed by the boundary space curve. an algorithm has been suggested on the basis ...

We propose an efficient computational solver for the eikonal equations on parametric three-dimensional manifolds. Our approach is based on the fast marching method for solving the eikonal equation in O(n log n) steps by numerically simulating wavefront propagation. The obtuse angle splitting problem is reformulated as a set of small integer linear programs, that can be solved in O(n). Numerical...

We describe recent work on striped patterns in a system of block copolymers. A by-product of the characterization of such patterns is a new formulation of the eikonal equation. In this formulation, the unknown is a field of projection matrices of the form P=e⊗e, where e is a unit vector field. We describe how this formulation is better adapted to the description of striped patterns than the cla...

The first-arrival quasi-P wave travel-time field in an anisotropic elastic solid solves a first-order nonlinear partial differential equation, the qP eikonal equation, which is a stationary Hamilton–Jacobi equation. The solution of the paraxial quasi-P eikonal equation, an evolution Hamilton–Jacobi equation in depth, gives the first-arrival travel time along downward propagating rays. We devise...