An elastoviscoplastic finite element model of aluminum alloys is used to compare mechanical response among meshes formed with several different grain shapes. Tetrahedral elements are used to form grains of cubic, rhombic dodecahedral and truncated octahedral shape. The influence of the grain shape on the aggregate response is examined in terms of the stress variation and the aggregate elastic m...

Shape Approximation requires simplifying a polygonalization of a smooth shape S with another polygonalization that has fewer number of vertices. The computed polygonalization should be homeomorphic to S and geometrically close to it. We present an algorithm that can provably simplify the initial polygonalization when the sampling density is high enough with respect to the feature size of the bo...

A filled rubber network consists of polymer chains which are suspended between filler aggregates. In this contribution, the nonlinear elastic behavior of the aggregated filler particles inside the rubber matrix is investigated. Previously, by using scaling theory, the influence of initial length and fractal dimension of aggregates on the elastic response of aggregated structures was studied. He...

Initial results have been obtained for automatic synthesis of MEMS mask-layouts using a genetic algorithm. An initial random population of mask-layouts is produced. An initial fabrication process sequence is also generated. The fabrication of each geometrically valid layout is simulated using a 3-D simulation of etching. The 3-D results of the fabrication simulation are compared to the desired ...

This paper displays a closed model structure for the category of cubical sets and shows that the resulting homotopy category is equivalent to the ordinary homotopy category for topological spaces. The main results are Theorem 19, which gives the model structure, and Theorem 29 and Corollary 30 which together imply the equivalence of homotopy categories. The cofibrations and weak equivalences fo...

The goal of this work is to establish a new algorithm for computing the cohomology ring of cubical complexes. The cubical structure enables an explicit recurrence formula for the cup product. We derive this formula and, next, show how to extend the Mrozek and Batko [7] homology coreduction algorithm to the cohomology ring structure. The implementation of the algorithm is a work in progress. Thi...

In this paper we give a method to geometrically modify an open set such that the first k eigenvalues of the Dirichlet Laplacian and its perimeter are not increasing, its measure remains constant, and both perimeter and diameter decrease below a certain threshold. The key point of the analysis relies on the properties of the shape subsolutions for the torsion energy.

Aggregates need to pass numerous tests to ensure the performance of asphalt and concrete structures and pavements. Some of these tests are fairly onerous, requiring manual, labor intensive, cost ineffective measurements that do not provide significant statistical validity, and are prone to errors through ignorance, negligence, or even in some cases through deliberate misrepresentation. This pap...

A certain inequality is shown to hold for the values of the Möbius function of the poset obtained by attaching a maximum element to a lower Eulerian Cohen– Macaulay poset. In two important special cases, this inequality provides partial results supporting Stanley’s nonnegativity conjecture for the toric h-vector of a lower Eulerian Cohen–Macaulay meet-semilattice and Adin’s nonnegativity conjec...