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.     

Covering vertices of a graph by k disjoint cycles

Let d, k and n be three integers with k3, d4k−1 and n3k. We show that if d(x)+d(y)d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d,n} vertices of G.     

A bound on the total size of a cut cover

A cycle cover (cut cover) of a graph G is a collection of cycles (cuts) of G that covers every edge of G at least once. The total size of a cycle cover (cut cover) is the sum of the number of edges of the cycles (cuts) in the cover.We discuss several results for cycle covers and the corresponding results for cut covers. Our main result is that every connected graph on n vertices and e edges has a cut cover of total size at most 2e-n+1 with equality precisely when every block of the graph is an odd cycle or a complete graph (other than K₄ or K₈). This corresponds to the result of Fan [J. Combin. Theory Ser. B 74 (1998) 353-367] that every graph without cut-edges has a cycle cover of total size at most e+n-1.     

图中相互独立的4圈和含4个点的路

设k是一个正整数，G是一个顶点数为|G|=4k的图. 假设σ\-2(G)≥4k-1, 则G有一个支撑子图含k-1个4圈和一条顶点数为4的路，使得所有这些圈和路都是相互独立的. 设G=(V\-1,V \-2;E)是一个二分图使得|V\-1|=|V\-2|=2k. 如果对G中每一对满足x∈V\-1和y∈V\-2的不 相邻的顶点x和y 都有d(x)+d(y)≥2k+1, 则G包含k-1个相互独立的4圈和一条顶点数为4的路，使得所有这些圈和路都是相互独立的，并且此度条件是最好的.     

Permutation graphs, fast forward permutations, and sampling the cycle structure of a permutation

PS_N is a fast forward permutation if for each m the computational complexity of evaluating P^m(x) is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions. By studying the evolution of permutation graphs, we prove that the number of queries needed to distinguish a random cyclus from a random permutation in S_N is Θ(N) if one does not use queries of the form P^m(x), but is only Θ(1) if one is allowed to make such queries. We construct fast forward permutations which are indistinguishable from random permutations even when queries of the form P^m(x) are allowed. This is done by introducing an efficient method to sample the cycle structure of a random permutation, which in turn solves an open problem of Naor and Reingold.     

纳米MnO2超级电容器的研究

用固相合成法制备纳米MnO2，作为超级电容器材料，通过循环伏安、交流阻抗与恒电流充放电等测试手段对MnO2电极进行分析.结果表明,以1 mol•L－1 KOH为电解液， MnO2电极在－0.1～0.6 V(vs. Hg/HgO)的电压范围内具有良好的法拉第电容性能.在不同电流密度下，电极比容量达240.25到325.21 F•g－1.恒电流充放电5000次后，电极容量衰减不超过10％.     

PVC DISULFIDE AS CATHODE MATERIALS FOR SECONDARY LITHIUM BATTERIES

PVC disulfide (2SPVC) was synthesized by solution crosslink and its molecular structure was confirmed by infrared spectrum. 2SPVC's specific area is 36.1 m2·g-1 tested by stand BET method, and granularity experiment gives out the particle size of d0.5= 11.3μm. With SEM (Scanning Electron Microscope) experiment the surface morphology and particle shape of 2SPVC were observed. Cyclic voltammetry (scan rate: 0.5 mV·s-1) shows that 2SPVC experience an obvious S-S redox reaction in charge-discharge process. When 2SPVC was used as cathode material for secondary lithium battery in a 1 mol·L-1 solution of lithium bis(trifluoromethylsulfonyl) imide (Li(CF3SO2)2N) in a 5:45:50 volume ratio mixture of o-xylene (oxy), diglyme (DG) and dimethoxymethane (DME) at 30℃, the first discharge capacity of 2SPVC is about 400.3 mAh·g-1 which is very close to its theoretical value (410.5 mAh·g-1) at a constant discharge current of 15 mA·g-1. It can retain at about 346.1 mAh·g-1 of discharge capacity after 30 charge-discharge cycles. So 2SPVC is a very promising cathode candidate for rechargeable lithium batteries.     

聚1-氨基蒽醌在二次锂电池正极材料中的应用

采用化学方法合成聚1-氨基蒽醌并用于二次锂电池正极材料,通过红外光谱、扫描电镜、粒度测试、循环伏安以及充放电测试等方法对材料的官能团结构、微观形貌、颗粒大小以及电化学性能等进行了研究与分析.实验表明,与金属锂组成二次锂电池后,聚1-氨基蒽醌达到了218.3 mAh•g－1的首次放电容量,经过25次循环后仍可保持较高的充放电效率.由于材料具有较高的能量密度且不含对环境有污染的元素S,因此是二次锂电池非常有希望的正极材料.     

Graphs to chemical structures. 4: Combinatorial enumeration of planted three-dimensional trees as stereochemical models of monosubstituted alkanes

Planted three-dimensional (3D) trees, which are defined as a 3D version of planted trees, are enumerated by means of Fujita’s proligand method formulated in Parts 1–3 of this series [Fujita in Theor Chem Acc 113:73–79, 80–86, 2005; Fujita in Theor Chem Acc 115:37–53, 2006]. By starting from the concepts of proligand and promolecule introduced previously [Fujita in Tetrahedron 47:31–46, 1991], a planted promolecule is defined as a 3D object in which the substitution positions of a given 3D skeleton are occupied by a root and proligands. Then, such planted promolecules are introduced as models of planted 3D-trees. Because each of the proligands in a given planted promolecule is regarded as another intermediate planted promolecule in a nested fashion, the given planted promolecule is recursively constructed by a set of such intermediates planted promolecules. The recursive nature of such intermediate planted promolecules is used to derive generating functions for enumerating planted promolecules or planted 3D-trees. The generating functions are based on cycle indices with chirality fittingness (CI-CFs), which are composed of three kinds of sphericity indices (SIs), i.e., a _d for homospheric cycles, c _d for enantiospheric cycles, and b _d for hemispheric cycles. For the purpose of evaluating c _d recursively, the concept of diploid is proposed, where the nested nature of c _d is demonstrated clearly. The SIs are applied to derive functional equations for recursive calculations, i.e., a(x), c(x ²), and b(x). Thereby, planted 3D-trees or equivalently monosubstituted alkanes as stereoisomers are enumerated recursively by counting planted promolecules. The resulting values are collected up to 20 carbon content in a tabular form. Now, the enumeration problem initiated by mathematician Cayley [Philos Mag 47(4):444–446, 1874] has been solved in such a systematic and integrated manner as satisfying both mathematical and chemical requirements.