Methods of the kind obtain the viscosity solution of the eikonal
equation through numerical analysis.
In the present paper, the emergence of gauge-fixing independence (the fundamental formulation of the QCD partition function is subjected to gauge fixing) of nonperturbative, fermionic Green's functions is discussed in a sequence of relaxed high-energy approximations (quenching, eikonal
, Fradkin's representation of fermionic Green's functions and, finally, no Fradkin's representation) to scattering of quarks off quarks.
where the phase path (eikonal
) [phi] and the amplitude A satisfy equations
Pomphrey, 1983: Eikonal
description of internal wave interactions: A non-diffusive picture of "induced diffusion." Dyn.
where [psi] is the phase of the wave (the eikonal
It describes SIMD, shared memory, and distributed memory machine models; decomposition as a fundamental activity in parallel algorithmic design; key programming models; key concepts of performance analysis and optimization; and three case studies applying these concepts to the Single Shortest Path Problem, the Eikonal
equation, and computation of the two-dimensional convex hull.
An approximate solution which is valid for short wavelengths is the eikonal
equation (see, e.g., [22, 23]).
Traditionally, if [[OMRGA].sub.[phi]] is a subset of the Euclidean space with a smooth boundary, then the signed distance function (SDF) of this subset is differentiable practically everywhere, and its gradient satisfies the Eikonal
equation , that is,
The envelope of these wave- fronts is then used to construct a new set of points, and the process is repeated in the limit the Eikonal
solution is obtained.
Thus, in this paper we propose a polar representation of electromagnetic fields and we look for the conditions that the proposed functional form must fulfill under the hypotheses of smooth eikonal
and propagation in metamaterials, in order to be an exact solution.
Chapters four through six are heavy with mathematics, discussing wave reduction with data processing, integral solutions to the wave equation with boundary and initial value conditions--using a variety of mathematical tools including Green's functions, Kirchoff integral formula, and the eikonal
equation--and decomposition and continuation of seismic wave field using Fourier integrals.