The analysis of the Magneto-Optical (M. 0.) effects when the magnetization is inhomogeneous is separated in two cases : first, when no diffraction occurs inside the medium, the geometrical optics approximation is used to derive the phase of the optical fields and the ray paths. Second, with no negligible diffraction inside themedium, extensions of the previous theory are presented and applied t...

The first and most important step in processing data in transversely isotropic (TI) media for which velocities vary with depth is parameter estimation. The multilayer normal-moveout (NMO) equation for a dipping reflector provides the basis for extending the TI velocity analysis of Alkhalifah and Tsvankin to vertically inhomogeneous media. This NMO equation is based on a root-mean-square (rms) a...

This paper presents efficient algorithms for free path sampling in heterogeneous participating media defined either by high-resolution voxel arrays or generated procedurally. The method is based on the concept of mixing “virtual” material or particles to the medium, augmenting the extinction coefficient to a function for which the free path can be sampled in a straightforward way. The virtual m...

The method of investigation of non-stationary boundary value problems of the theory of thermodiffusion using the Laplace integral transform is described. In the classical theory of elasticity this method was first used by V. Kupradze and the author. The interconnection of deformation, thermal conductivity and diffusion processes in an elastic isotropic solid body is described by a system of fiv...

Casimir forces arise from vacuum fluctuations. They are fully understood only for simple models, and are important in nanoand microtechnologies. We report our experience of computer algebra calculations towards the Casimir force for models involving inhomogeneous dielectrics. We describe a methodology that greatly increases confidence in any results obtained, and use this methodology to demonst...

This paper settles the existence question for a rather general class of convex optimal design problems with a volume constraint. In low dimensions, we prove the existence of an optimal configuration for general convex minimization problems ruled by bounded measurable degenerate elliptic operators. Under a mild continuity assumption on the medium, the free boundary is proven to enjoy the appropr...

In this paper we consider a free boundary problem which describes contact angle dynamics on inhomogeneous surface. We obtain an estimate on convergence rate of the free boundaries to the homogenization limit in periodic media. The method presented here also applies to more general class of free boundary problems with oscillating boundary velocities.

In the framework of a comprehensive theory for a new class of evolutionary problems wellposedness of associated initial boundary value problems is considered. The dynamic linear model for electroseismic waves in anisotropic, inhomogeneous, time-shift invariant media is used as an illustration of the theory.

In this paper we consider a free boundary problem which describes contact angle dynamics on inhomogeneous surface. We obtain an estimate on convergence rate of the free boundaries to the homogenization limit in periodic media. The method presented here also applies to more general class of free boundary problems with oscillating boundary velocities.

This paper is concerned with the fast iterative solution of linear systems arising from finite difference discretizations in electromagnetics. The sweeping preconditioner with moving perfectly matched layers previously developed for the Helmholtz equation is adapted for the popular Yee grid scheme for wave propagation in inhomogeneous, anisotropic media. Preliminary numerical results are presen...