Kernels with prescribed surface tension & mobility for threshold dynamics schemes

Kernels with prescribed surface tension & mobility for threshold dynamics schemes

We show how to construct a convolution kernel that has a desired anisotropic surface tension and desired anisotropic mobility to be used in threshold dynamics schemes for simulating weighted motion by mean curvature of interfaces, including networks of them, in both two and three dimensions. Moreover, we discuss necessary and sufficient conditions for the positivity of the kernel which, in the ...

Maps With Prescribed Tension Fields

We consider maps into a Riemannian manifold of nonpositive sectional curvature with prescribed tension field. We derive a priori estimates and solve a Dirichlet problem.

Threshold Dynamics for Anisotropic Surface Energies∗

We study extensions of Merriman, Bence, and Osher’s threshold dynamics scheme to weighted mean curvature flow, which arises as gradient descent for anisotropic (normal dependent) surface energies. In particular, we investigate, in both two and three dimensions, those anisotropies for which the convolution kernel in the scheme can be chosen to be positive and / or to possess a positive Fourier t...

Threshold Dynamics for Networks with Arbitrary Surface Tensions

Threshold Schemes with Disenrollment

When a shadow of a threshold scheme is publicized, new shadows have to be reconstructed and redistributed in order to maintain the same level of security. In this paper we consider threshold schemes with disenrollment capabilities where the new shadows can be created by broadcasts through a public channel. We establish a lower bound on the size of each shadow in a scheme that allows L disenroll...