We introduce a new notion of viscosity solutions for the level set formulation of the motion by crystalline mean curvature in three dimensions. The solutions satisfy the comparison principle, stability with respect to an approximation by regularized problems, and we also show the uniqueness and existence of a level set flow for bounded crystals.

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To ...

Recently there have been several advances in instrumental methods for the flame emission analysis of electrolytecations of clinical significance. Greater precision and increased ease of operation are among today’s clinical requirements. This study compares a new automated flame photometer, “Klina Flame” (Beckman Instruments) with a “Techtron-AA5” atomic absorption emission unit (Varian Instrume...

We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized model systems, as well as the synergy of synthesis-characterization, rheometry and modeling/simulations. The theoretical framework for understanding the obs...

We present the first internally consistent calculation which leads to a narrow 'conduit' of rapid vertical advection and melting of mantle under a spreading center. In this model, mantle flow is driven by plate separation and compositional buoyancy. Melt segregation is described as flow through a permeable media. The major new feature is that the viscosity of the mantle is considered to be a st...

The author studies on a hedging problem for an European contingent claim in a certain incomplete market model by using a homogeneous filtered value measure. He considers the minimal hedging risk in discrete time model and its continuous limit. As a result, he shows that this limit is described by a viscosity solution of some HamiltonJacobi-Bellman equation.

In this paper we prove that a function u ∈ C(Ω) is the continuous value of the Tug-of-War game described in [19] if and only if it is the unique viscosity solution to the infinity laplacian with mixed boundary conditions

The current work focuses on applying an artificial viscosity approach to the Spectral Difference (SD) method to enable high-order computation of compressible fluid flows with discontinuities. The study uses an artificial viscosity approach similar to the high-wavenumber biased artificial viscosity approach introduced by Cook and Cabot, and modified by Kawai and Lele. The model employs a bulk vi...