Quadrilateral surface meshes without self-intersecting dual cycles for hexahedral mesh generation

Several promising approaches for hexahedral mesh generation work as follows: Given a prescribed quadrilateral surface mesh they first build the combinatorial dual of the hexahedral mesh. This dual mesh is converted into the primal hexahedral mesh, and finally embedded and smoothed into the given domain. Two such approaches, the modified whisker weaving algorithm by Folwell and Mitchell, as well as a method proposed by the author, rely on an iterative elimination of certain dual cycles in the surface mesh. An intuitive interpretation of the latter method is that cycle eliminations correspond to complete sheets of hexahedra in the volume mesh.

Although these methods can be shown to work in principle, the quality of the generated meshes heavily relies on the dual cycle structure of the given surface mesh. In particular, it seems that difficulties in the hexahedral meshing process and poor mesh qualities are often due to self-intersecting dual cycles. Unfortunately, all previous work on quadrilateral surface mesh generation has focused on quality issues of the surface mesh alone but has disregarded its suitability for a high-quality extension to a three-dimensional mesh.

In this paper, we develop a new method to generate quadrilateral surface meshes without self-intersecting dual cycles. This method reuses previous b-matching problem formulations of the quadrilateral mesh refinement problem. The key insight is that the b-matching solution can be decomposed into a collection of simple cycles and paths of multiplicity two, and that these cycles and paths can be consistently embedded into the dual surface mesh.

A second tool uses recursive splitting of components into simpler subcomponents by insertion of internal two-manifolds. We show that such a two-manifold can be meshed with quadrilaterals such that the induced dual cycle structure of each subcomponent is free of self-intersections if the original component satisfies this property. Experiments show that we can achieve hexahedral meshes with a good quality.     

Crystal structure and magnetic ordering of RNi Si compounds

The element distributions and the magnetic ordering behaviour of compounds RNi₁₀Si₂ (R = Tb, Dy, Ho, Er, Tm) have been studied by neutron powder diffraction down to temperatures of 1.6 K. The compounds crystallize in an ordered variant of the ThMn₁₂ structure type in the tetragonal space group P4/nmm. An ordered 1:1 distribution of Ni and Si on sites 4d and 4e, respectively, corresponds to a modulation vector [0, 0, 1] with respect to the space group I4/mmm of the ThMn₁₂ structure. TbNi₁₀Si₂ orders antiferromagnetically below T _N = 4.5 K with a magnetic propagation vector of [0, 0, 1/2]. The magnetic Tb moments, 8.97(2) /Tb atom at 1.6 K, are aligned along the c-axis. The Ni sites in TbNi₁₀Si₂ do not carry any ordered magnetic moments. The compounds with R = Dy, Ho, Er, and Tm are paramagnetic down to 1.6 K and 3.0 K, respectively. Received 10 July 2002 / Received in final form 12 September 2002 Published online 29 October 2002     

Static atomic displacements of Sn in disordered NiAs/Ni2In type HT-Ni1+δSn

The crystal structures of the intermediate solid solution HT (high temperature) Ni_1+δSn with δ=0.28, 0.52 and 0.61 (refined Ni contents) have been analyzed in detail by X-ray diffraction on single crystals. The previously reported basic atomic arrangement, i.e., a NiAs/Ni₂In structure type (P6₃/mmc, Ni(1) on 2a, 0 0 0, Ni(2) with an occupancy δ on 2d, and Sn on 2c, ), is confirmed. However, strong anisotropic atomic displacements occur for Sn within the a-b plane of the hexagonal unit cell, which require a Gram-Charlier expansion of the probability density function of Sn in order to obtain a good fit to the diffraction data. Direction, magnitude and the concentration dependence of the displacements can be interpreted in terms of the geometrical requirements of the different local atomic configurations in the planes z=±1/4, so that the displacements can be identified as static ones.     

Cohomology of the Orlik–Solomon Algebras and Local Systems

The paper provides a combinatorial method to decide when the space of local systems with nonvanishing first cohomology on the complement to an arrangement of lines in a complex projective plane has as an irreducible component a subgroup of positive dimension. Partial classification of arrangements having such a component of positive dimension and a comparison theorem for cohomology of Orlik–Solomon algebra and cohomology of local systems are given. The methods are based on Vinberg–Kac classification of generalized Cartan matrices and study of pencils of algebraic curves defined by mentioned positive dimensional components.     

The anionic chemistry of ynamides: A review

Ynamides have recently evolved as remarkably reactive and versatile building blocks for chemical synthesis. The development of efficient and robust methods for their preparation combined with their recent commercialization have facilitated both the design of an ever-growing number of original methods based on their unique reactivity and their use in other areas such as medicinal chemistry. One crucial aspect of the reactivity of these building blocks is based on their anionic chemistry, which has been extensively studied during the last decade and enabled not only the design and development of remarkably efficient and original reactions but also brought general answers to long-standing problems in organic chemistry and contributed to the emergence of new synthetic paradigms. In this short review, the anionic chemistry of ynamides is overviewed.     

On the Pseudolinear Crossing Number

A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing number of a graph G is the minimum number of pairwise crossings of edges in a pseudolinear drawing of G. We establish several facts on the pseudolinear crossing number, including its computational complexity and its relationship to the usual crossing number and to the rectilinear crossing number. This investigation was motivated by open questions and issues raised by Marcus Schaefer in his comprehensive survey of the many variants of the crossing number of a graph.     

New inequalities for subspace arrangements

For each positive integer n?4, we give an inequality satisfied by rank functions of arrangements of n subspaces. When n=4 we recover Ingleton's inequality; for higher n the inequalities are all new. These inequalities can be thought of as a hierarchy of necessary conditions for a (poly)matroid to be realizable. Some related open questions about the “cone of realizable polymatroids” are also presented.     

Portraits of some representatives of metal boride carbide and boride silicide compounds

Different ternary alkaline-earth and rare-earth metal boron carbide and silicide compounds are examined using the solid-state language of Zintl-Klemm concept, band structures, and density of states, in order to show that the topology of the non-metal sub-lattice is highly dependent on the electron count. It is also shown that the chemistry of rare-earth metal-boron-silicon does not parallel that of rare-earth metal-boron-carbon. B-C bonds are easily formed in the latter, leading to a large variety of different structural arrangements, whereas Si-B bonds are hardly observed in the former, except in insertion compounds.     

A note on Mustaţă's computation of multiplier ideals of hyperplane arrangements

In 2006, M. Mustaţă used jet schemes to compute the multiplier ideals of reduced hyperplane arrangements. We give a simpler proof using a log resolution and generalize to non-reduced arrangements. By applying the idea of wonderful models introduced by De Concini-Procesi in 1995, we also simplify the result. Indeed, Mustaţă's result expresses the multiplier ideal as an intersection, and our result uses (generally) fewer terms in the intersection.