Threshold Dynamics for Networks with Arbitrary Surface Tensions

Threshold Dynamics for Networks with Arbitrary Surface Tensions

Supersymmetric branes with (almost) arbitrary tensions

We present a supersymmetric version of the two-brane Randall-Sundrum scenario, with arbitrary brane tensions T1 and T2, subject to the bound |T1,2| ≤ √ −6Λ5, where Λ5 < 0 is the bulk cosmological constant. Dimensional reduction gives N = 1, D = 4 supergravity, with cosmological constant Λ4 in the range 1 2Λ5 ≤ Λ4 ≤ 0. The case with Λ4 = 0 requires T1 = −T2 = √ −6Λ5. This work unifies and genera...

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...

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 ...

Surface tensions

With so many fish stocks under pressure, increasing catch levels for one population by 30 per cent might appear catastrophic. But European fishing ministers believe such a move might help tackle two problems. Fishermen in the North Sea will be able to catch more cod this year, but cod fisheries elsewhere around Europe will be further restricted. EU ministers agreed late last month the fish quot...