The theory of scale relativity generalizes the application domain of Einstein's principle of relativity to scale transformations of space-time resolutions. In this theory, we no longer assume that the space-time continuum is differentiable, this implying its fractal character. Both classical and quantum laws may emerge from a unique, more profound, scale law. The effects of nondifferentiability...

A fast local refinement algorithm based on feature extraction is developed. In the mesh-based Reynolds equation solutions, two features physical parameters of fluid lubrication are firstly defined, namely, pressure value and gradient feature. Then, a adaptive strategy different from traditional methods residuals or recovery errors constructed according to features, which expected determine elem...

During the support period July 1, 2011 June 30, 2012, seven research papers were published. They consist of three types: • Research that directly addresses the kernel selection problem in machine learning [1, 2]. • Research that closely relates to the fundamental issues of the proposed research of this grant [3, 4, 5, 6]. • Research that is in the general context of computational mathematics [7...

The quad/triangular subdivision, whose control net and refined meshes consist of both quads and triangles, provides better visual quality of subdivision surfaces. While some theoretical results such as polynomial reproduction and smoothness analysis of quad/triangle schemes have been obtained in the literature, some issues such as the basis functions at quad/triangle vertices and design of inte...

A domain equation for refinement of partial systems MICHAEL R. A. HUTH†, RADHA JAGADEESAN‡ and DAVID A. SCHMIDT§ †Department of Computing, Imperial College London, South Kensington campus, London SW7 2AZ, England Email: [email protected] ‡School of Computer Science, Telecommunications, and Information Sciences, DePaul University, 243 S. Wabash Avenue, Chicago, Illinois 60604-2287 Email:...

We present an adaptive mesh and algorithmic refinement (AMAR) scheme for modeling multi-scale hydrodynamics. The AMAR approach extends standard conservative adaptive mesh refinement (AMR) algorithms by providing a robust flux-based method for coupling an atomistic fluid representation to a continuum model. The atomistic model is applied locally in regions where the continuum description is inva...