Computational simulation of physical phenomena plays a central role in many important applications, including scientific visualization and the generation visual effects for entertainment. Typically, these simulations rely on high-quality meshes to model physical objects. Meshes with badly shaped elements degrade both the accuracy and efficiency of the simulation. Traditionally, mesh optimizatio...

Tetrahedral groups are defined as groups of complex reflections on four planes, such that those planes form a tetrahedral configuration with vertices in the boundary of HC. We prove that the complex tetrahedral groups that are complexifications of real groups (i.e. subgroups of PO(3, 1)) do not admit discrete deformations. To achieve this, the structure of the subgroups that stabilize the verti...

Automatic hexahedral mesh generation for complex geometries is still a challenging problem, and therefore tetrahedral or mixed meshes are preferred. Unfortunately the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper we propose a new linear tetrahedral element based on the average nodal Jacobian. This ele...

The abrupt green-to-yellow thermochromism observed for certain A2CuCl4 compounds has long been attributed to the presence of strong N-H hydrogen bonding in the low-temperature phase that favors square-planar CuCl4(2-) (green in color) through reduction of ligand-ligand repulsion. Weakening of the hydrogen bonding at higher temperature results in the transformation to (far more common) flattened...

High Pressure Raman scattering measurements of KDP:Mn were performed at room temperatures. The X-ray powder diffraction patterns taken at room temperature by Rietveld refinement showed that doped samples of KDP-Mn have the same tetragonal structure of a pure KDP crystal, but with a contraction of the crystalline cell. The behavior of the Raman spectra, in particular the emergence of a new modes...

This paper uses simplicial complexes and simplicial (co)homology theory to expose a foundation for data structures for tetrahedral finite element meshes. Identifying tetrahedral meshes with simplicial complexes leads, by means of Whitney forms, to the connection between simplicial cochains and fields in the region modeled by the mesh. Furthermore, lumped field parameters are tied to matrices as...

The reaction of CoCl2.6H2O, 1,2,4-triazole, and H(2)O at 200 degrees C for 96 h yields purple rods of [Co2(trz)3Cl] (1; trz = 1,2,4-triazolate) in 90% yield. The structure of 1 consists of {Co(trz)3}n(n-) chains of Co(II) sites linked through tetrahedral sites of {CoN(3)Cl} geometry into a three-dimensional framework. The competing antiferromagnetic interactions of the octahedral and tetrahedra...

We consider the soap bubble problem on the sphere S2, which seeks a perimeter-minimizing partition into n regions of given areas. For n = 4, it is conjectured that a tetrahedral partition is minimizing. We prove that there exists a unique tetrahedral partition into given areas, and that this partition has less perimeter than any other partition dividing the sphere into the same four connected a...

This paper presents a new method for creating a thick shell tetrahedral mesh from a triangular surface mesh. Our main goal is to create the thickest possible shell mesh with the lowest possible number of tetrahedrons. Low count tetrahedral meshes is desirable for animating deformable objects where accuracy is less important and to produce shell maps and signed distance fields. In this work we p...

Let v1; : : : ; vn be unit vectors in R such that vi ¢ vj = ¡w for i 6= j where ¡1 < w < 1 n¡1 . The points Pn i=1 ‚ivi (1 ‚ ‚1 ‚ ¢ ¢ ¢ ‚ ‚n ‚ 0) form a “Hill-simplex of the first type”, denoted by Qn(w). It was shown by Hadwiger in 1951 that Qn(w) is equidissectable with a cube. In 1985, Schöbi gave a three-piece dissection of Q3(w) into a triangular prism cQ2(2) £ I, where I denotes an interv...