Computing a Minimum Weight Triangulation of a Sparse Point Set*

Investigating the minimum weight triangulation of a point set with constraint is an important approach for seeking the ultimate solution of the minimum weight triangulation problem. In this paper, we consider the minimum weight triangulation of a sparse point set, and present an O(n ⁴) algorithm to compute a triangulation of such a set. The property of sparse point set can be converted into a new sufficient condition for finding subgraphs of the minimum weight triangulation. A special point set is exhibited to show that our new subgraph of minimum weight triangulation cannot be found by any currently known methods.     

The number of cycle lengths in graphs of given minimum degree and girth

This paper determines lower bounds on the number of different cycle lengths in a graph of given minimum degree k and girth g. The most general result gives a lower bound of ck^g/8.     

DNS and LES of spark ignition with an automotive coil

The cycle to cycle combustion variability which is observed in spark-ignition engines is often caused by fluctuations of the early flame development. LES can be exploited for a better understanding and mastering of their origins. For that purpose appropriate models taking into account energy deposition, mixture ignition and transition to propagation are necessary requirements. This paper presents first DNS and LES of spark ignition with a real automotive coil and simplified pin-pin electrodes. The electrical circuit characteristics are provided by ISSIM while the energy deposition is modelled by Lagrangian particles. The ignition model is first evaluated in terms of initial spark radius on a pin-pin ignition experiment in pure air performed at CORIA and EM2C laboratories, showing that it pilots the radius of the torus formed by the initial shock wave. DNS of a quiescent lean propane/air mixture are then performed with this ignition system and a two-step mechanism. The impact of the modelled transferred energy during glow phase as well as the initial arc radius on the minimum ignition energy (MIE) are examined and compared to experimental values. Replacing the two-step chemistry by an analytically reduced mechanism leads to similar MIE but shows a different ignition kernel shape. Finally, LES of turbulent ignition using a Lagrangian arc model show a realistic prediction of the arc shape and its important role on the energy transfer location and thus on the flame kernel shape.     

Partially dynamic maintenance of minimum weight hyperpaths

We address the problem of dynamically maintaining minimum weight hyperpaths in a directed hypergraph in a decremental setting. For such a problem, we provide a new efficient algorithm that works for a wide class of hyperpath weight measures. This algorithm explicitly updates minimum weight hyperpaths in

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worst case time under a sequence of L hyperarc weight increments and hyperarc deletions, where C is the maximum weight of minimum hyperpaths in and is the size of the representation of the hypergraph. Hyperpath weight measures are only required to belong to the class of strict weakly superior functions.     

变分量子Monte Carlo的一个新算法

提出变分量子MonteCarlo(VMC)计算的新算法-极小化方差(MV)方法.它从局域能的内部结构出发,直接削减其波动以达到将VMC的方差减到极小的目的.给出了局域能的分析表达式,导出VMC的极小方差原理,并建立方差极小化的计算步骤.     

Mixing of electronic states in molybdenum complexes involved in nitrogen activation

The mechanism for nitrogen activation by molybdenum complexes is a complicated one, involving as it does the coupling of a quartet molybdenum reactant with a singlet nitrogen molecule, passing via a series of quartet and doublet encounter complexes to a triplet intermediate, with the subsequent spin crossing to the singlet surface which then leads via a singlet transition state to the final pair of singlet products. We have investigated in detail a variety of levels of theory to describe the crossing of these electronic surfaces and have calculated both lower-bound and actual minimum energy crossing points for the key spin inversion processes.     

气相中W~+活化CO_2分解的自旋禁阻反应机理

用密度泛函理论中的UB3LYP方法,对W采用相对论校正赝势基组(SDD),对C、O采用6-311+G(3d)基组,研究了气相中不同自旋态W+活化CO2分解的反应机理.计算结果表明,W+活化CO2分解反应以六重态进入反应通道,经过六重态势能面到四重态势能面的系间窜越(ISC),最后产物WO+和CO以四重态离开反应通道.运用Harvey方法优化出最低能量交叉点(MECP),并计算了MECP处的自旋-轨道耦合(SOC)常数(494.95cm-1),势能面的交叉和在MECP处较强的自旋-轨道耦合作用降低了自旋禁阻反应能垒,为反应提供了一条低能反应路径,反应总放热量为122.33kJ.mol-1.     

Computing finest mincut partitions of a graph and application to routing problems

Let G=(V,E,w) be an n-vertex graph with edge weights w>0. We propose an algorithm computing all partitions of V into mincuts of G such that the mincuts in the partitions cannot be partitioned further into mincuts. There are O(n) such finest mincut partitions. A mincut is a non-empty proper subset of V such that the total weight of edges with exactly one end in the subset is minimal. The proposed algorithm exploits the cactus representation of mincuts and has the same time complexity as cactus construction. An application to the exact solution of the general routing problem is described.