Linearized internal functionals for anisotropic conductivities

Convergence of Linearized and Adjoint Approximations for Discontinuous Solutions of Conservation Laws. Part 1: Linearized Approximations and Linearized Output Functionals

This paper analyzes the convergence of discrete approximations to the linearized equations arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. A simple modified Lax–Friedrichs discretization is used on a uniform grid, and a key point is that the numerical smoothing increases the number of points across the nonlinear discontinuity as the grid is refined. It ...

Conductivities of heterogeneous media with graded anisotropic constituents

Anisotropic ionic conductivities in lyotropic supramolecular liquid crystals.

The designed aromatic amide discotic molecule with sulfonic acid groups at its periphery exhibits a hexagonal supramolecular columnar liquid crystalline phase, which leads to the achievement of anisotropic ionic conductivity through macroscopically aligning the ionic channels.

Partial Regularity For Anisotropic Functionals of Higher Order

Higher order variational functionals, emerging in the study of problems from materials science and engineering, have attracted a great deal of attention in last few years (e.g. [4], see [5]). In particular, the regularity of minimizers of such functionals has been studied very recently. In [15] and [16] the partial Ck,α regularity has been established for quasiconvex integrals with a p-power gr...

Linearized 2.5-dimensional parameter imaging inversion in anisotropic elastic media

S U M M A R Y In this paper we derive 2.5-D short-period seismic modelling and imaging-inversion formulae in the Born approximation for anisotropic elastic media. The 2.5-D approach encompasses 3-D wave scattering measured in a common-azimuth acquisition geometry subject to 2-D computations under appropriate assumptions. The lowest possible symmetry of the medium in this approach, in principle,...