eikonal equation

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eikonal equation

[ī′kōn·əl i‚kwā·zhən]
(physics)
An equation for propagation of electromagnetic or acoustic waves in a nonhomogeneous medium; it is valid only when the variation of the properties of the medium is small over the distance of a wavelength.
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He covers some variational problems in Hilbert spaces, iterative methods in Hilbert spaces, operator-splitting and alternating directions methods, augmented Lagrangians and alternating direct methods of multipliers, the least-squares solution of linear and nonlinear problems, obstacle problems and Bingham flow with applications to control, nonlinear eigenvalue problems, Eikonal equations, and fully nonlinear elliptic equations.
The linear refractive index (25a), (25b) is sufficient to highlight that the geometrical attenuation is modelled just by the transport equation, and, therefore, the dissipative absorption just by the complex eikonal equations (21a)-(21b); in fact if n(h) [congruent to] [[alpha].sub.R]h, then I([h.sub.2])/I([h.sub.1]) [congruent to] n([h.sub.1])/n([h.sub.2]) = [h.sub.1]/[h.sub.2] [11].
The complex eikonal equations were derived assuming a material medium as optically isotropic.
The simple complex eikonal equations for calculating the QL approximation of nondeviative amplitude absorption due to the propagation across the Dlayer were encoded as subroutine of an ionospheric raytracing (IONORT) program [20].
As regards the scientific review, the eikonal equation is expressed, and some complex-valued solutions are defined corresponding to complex rays and caustics.
Menze et al., "Ayache Image guided personalization of reaction-diffusion type tumour growth models using modified anisotropic Eikonal equations," Journal of Medical Imaging, vol.