Numerical resonances for Schottky surfaces via Lagrange–Chebyshev approximation

Density of Resonances for Schottky Groups

High order numerical approximation of minimal surfaces

preprint numerics no. 7/2010 norwegian university of science and technology trondheim, norway We present an algorithm for finding high order numerical approximations of minimal surfaces with a fixed boundary. The algorithm employs parametriza-tion by high order polynomials and a linearization of the weak formulation of the Laplace-Beltrami operator to arrive at an iterative procedure to evolve ...

Distribution of Resonances for Hyperbolic Surfaces

For non-compact hyperbolic surfaces, the appropriate generalization of the eigenvalue spectrum is the resonance set, the set of poles of the resolvent of a meromoprhic continuation of the Laplacian. Hyperbolic surfaces serve as a model case for quantum theory when the underlying classical dynamics is chaotic. In this talk Ill explain how the resonances are defined and discuss our current unders...

Uniform approximation to Mie resonances

Uniform asymptotic approximations for the positions and widths of Mie resonances are reported . The results improve the accuracy of previous approximations, typically, by several orders of magnitude . They are suitable for fast numerical evaluation, allowing every resonance to be located well within its width, for all resonances of practical interest . The relative errors are very small even fo...

Approximation algorithms for developable surfaces

By its dual representation, a developable surface can be viewed as a curve of dual projective 3-space. After introducing an appropriate metric in the dual space and restricting ourselves to special parametrizations of the surfaces involved, we derive linear approximation algorithms for developable NURBS surfaces, including multiscale approximations. Special attention is paid to controlling the ...