Anisotropic Kepler and anisotropic two fixed centres problems

The Kepler Problem with Anisotropic Perturbations

We study a 2-body problem given by the sum of the Newtonian potential and an anisotropic perturbation that is a homogeneous function of degree −β, β ≥ 2. For β > 2, the sets of initial conditions leading to collisions/ejections and the one leading to escapes/captures have positive measure. For β > 2 and β 6= 3, the flow on the zero-energy manifold is chaotic. For β = 2, a case we prove integrab...

Anisotropic inverse problems in two dimensions

Let g be a Riemannian metric on a bounded domain in two dimensions with a Lipschitz boundary. We show that one can determine the equivalent class of g and β in the W 1,p topology, p > 2, from knowledge of the associated Dirichletto-Neumann (DN) map g,β to the elliptic equation divg(β∇gu) = 0. The DN map encodes all the voltage and current measurements at the boundary.

Fixed Obstacle in Anisotropic Myocardium

Background. The aim of this study was to test the hypothesis that electrical uncoupling and depression of the fast sodium channels have differential effects on propagation of the electrical impulse relative to the fiber orientation. Methods and Results. In a model of reentrant ventricular tachycardia (VT) (mean cycle length, 144±13 msec) around a ring of anisotropic myocardium in 10 Langendorff...

Classical and Quantum Correspondence in Anisotropic Kepler Problem

Anisotropic High-Contrast Problems

In this paper, we study robust two-level domain decomposition preconditioners for 10 highly anisotropic multiscale problems. We present a construction of coarse spaces 11 that emploies initial multiscale basis functions and discuss techniques to achieve 12 smaller dimensional coarse spaces without sacrificing the robustness of the precon13 ditioner. We also present numerical results and conside...