We derive an asymptotic formula for the electrostatic voltage potential in the presence of a nite number of diametrically small inhomogeneities with conductivity dierent from the background conductivity. W e use this formula to establish continuous dependence estimates and to design an eective computational identication procedure.
Let X' be a Dirichlet eigenvalue of the 'periodically, rapidly oscillating' elliptic operator -V • (a(x/s)V) and let X be a corresponding (simple) eigenvalue of the homogenised operator -V • {AV). We characterise the possible limit points of the ratio (X c -X)/e as s -> 0. Our characterisation is quite explicit when the underlying domain is a (planar) convex, classical polygon with sides of rational or infinite slopes. In particular, in this case it implies that there is often a continuum of such limit points.
We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence, stability and approximation error of the series.
Abstract. In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.Mathematics Subject Classification. 35J25, 35R30, 65R99.
We consider the evolution of small amplitude, long wavelength initial data by a polyatomic Fermi-Pasta-Ulam lattice differential equation whose material properties vary periodically. Using the methods of homogenization theory, we prove rigorous estimates that show that the solution breaks up into the linear superposition of two appropriately scaled and modulated counterpropagating waves, each of which solves a Korteweg-de Vries equation, plus a small error. The estimates are valid over very long time scales.
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