Electro-chemical polishing is a process of improving micro smoothness, micro topology, and material brightness by anodic dissolving of the substrate in an electrolyte with an external source of electricity. The resulting surface improvements depend on the uniformity of the material microstructure, the lack of surface inclusions, and the consistency of the surface finish all over the target area...

We prove a pointwise version of the multi-dimensional central limit theorem for convex bodies. Namely, let μ be an isotropic, log-concave probability measure on Rn. For a typical subspace E ⊂ Rn of dimension nc, consider the probability density of the projection of μ onto E. We show that the ratio between this probability density and the standard gaussian density in E is very close to 1 in larg...

We investigate collective phenomena with rotationally driven spinners of concave shape. Each spinner experiences a constant internal torque in either a clockwise or counterclockwise direction. Although the spinners are modeled as hard, otherwise noninteracting rigid bodies, their active motion induces an effective interaction that favors rotation in the same direction. With increasing density a...

In this paper the turnpike property is established for convex optimal control problems, involving undiscounted utility function and differential inclusions defined by multi-valued mapping having convex graph. Utility function is concave but not necessarily strictly concave. The turnpike theorem is proved under the main assumption that over any given line segment, either multi-valued mapping is ...

Distance determination, i.e. obtaining the distance between a pair of objects, is used in di¤erent applications such as the simulation of physical systems and robot path planning. Most of the existing algorithms focus on obtaining the separation distance and are limited to deal only with convex objects. In this work, a novel method for solving the minimum separation distance between convex and/...

Ice aprons are poorly studied and not well-defined thin ice bodies adhering to high altitude steep rock faces, but present in most Alpine-type mountain environments worldwide. This study aims precisely define based on a detailed analysis of their topographical characteristics the Mont Blanc massif (western European Alps). For this, we accurately identified mapped 423 using combination high-reso...

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