Eikonal equation

The unmistakable similarity between the eikonal equation of geometrical... 

Quantum theory was developed primarily to find an explanation for the stability of atomic matter, specifically the planetary model of the hydrogen atom. In the Schrodinger formulation the correct equation was obtained by recognizing the wave-like properties of an electron. The first derivation by Schrodinger [30] was done by analogy with the relationship that was known to exist between wave optics and geometrical optics in the limit where the index of refraction, n does not change appreciably over distances of order A. This condition leads to the eikonal equation (T3.15)... 

A great deal is known about the behavior of spiral waves in excitable media from both the mathematical and the experimental points of view. One feature of particular interest is the center or core from which the spiral waves emanate. The eikonal equation (6.31) allows us to obtain a rough estimate of the size of a spiral core. Chemical waves typically travel at speeds of millimeters per minute, or perhaps (4-10) xl0 cms. Diffusion constants of monomeric species in aqueous solution tend to be around 2 x 10 cm s. If we consider an expanding circle (which has a negative curvature) on the perimeter of the core, and plug these values for c and D into eq. (6.31), we find that A = 0 when... 

Keywords Shallow water equations Wave front amplitude Impulse source Eikonal equation Finite difference method... 

The main idea of calculation the moving tsunami wave height for problem (2) consists of the change of variables 2 = r x,y) [8]. Here r x,y) is a solution of the problem for eikonal equation... 

The temporal evolution of these cusps was used for an experimental verification of the relationship between the normal velocity N and the curvature K of a wave front, given by the Eikonal equation [13,16]... 

When the refractive-index profile is graded, the trajectory of a ray is determined by the ray path, or eikonal equation, in terms of the profile n(r) according to [1,2]... 

For a given profile, the path p is determined from the ray-path, or eikonal equation, as we showed in Chapters 1 and 2. 

This stationary soiution is obtained through the differential equation in (5), called eikonal equation [18], The eikonal equation contains the spatial differential of a function T(x), given the velocity function F,... 

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