An efficient numerical method for estimating the average free boundary velocity in an inhomogeneous Hele-Shaw problem

We develop a numerical method to estimate the average speed of the free boundary in a Hele-Shaw problem with periodic coefficients in both space and time. We test the accuracy of the method and present a few examples. We show numerical evidence of flat parts (facets) on the free boundary in the homogenization limit.Comment: 18 page

Periodic total variation flow of non-divergence type in Rn

We introduce a new notion of viscosity solutions for a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of arbitrary dimension, whose diffusion on flat parts with zero slope is so strong that it becomes a nonlocal quantity. The problems include the classical total variation flow and a motion of a surface by a crystalline mean curvature. We establish a comparison principle, the stability under approximation by regularized parabolic problems, and an existence theorem for general continuous initial data.Comment: 36 pages, 2 figure

Anisotropic total variation flow of non-divergence type on a higher dimensional torus

We extend the theory of viscosity solutions to a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of an arbitrary dimension with diffusion given by an anisotropic total variation energy. We give a proof of a comparison principle, an outline of a proof of the stability under approximation by regularized parabolic problems, and an existence theorem for general continuous initial data, which extend the results recently obtained by the authors.Comment: 27 page

Microstrip Yagi array for MSAT vehicle antenna application

A microstrip Yagi array was developed for the MSAT system as a low-cost mechanically steered medium-gain vehicle antenna. Because its parasitic reflector and director patches are not connected to any of the RF power distributing circuit, while still contributing to achieve the MSAT required directional beam, the antenna becomes a very efficient radiating system. With the complete monopulse beamforming circuit etched on a thin stripline board, the planar microstrip Yagi array is capable of achieving a very low profile. A theoretical model using the Method of Moments was developed to facilitate the ease of design and understanding of this antenna