Atomic charges,dipole moments,and Fukui functions using the Hirshfeld partitioning of the electron density

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.     

Localization maps by orbital partitioning of the electron density

Summary We define a localization measure for one-determinantal wave-functions based on the partitioning of the total electron density to orbital contributions. The set of occupied orbitals is the more localized the fewer terms are necessary to describe the total density. This measure varies from point to point in space which leads to characteristic localization maps for molecules.Supported in part by the grant Hungarian Research Fund OTKA 517/1990     

Hybrid spectral finite difference simulations of stratified turbulent flows on distributed memory architectures

A method for efficient implementation of a combined spectral finite difference algorithm for computation of incompressible stratified turbulent flows on distributed memory computers is presented. The solution technique is the fractional step method with a semi-implicit time advancement scheme. A single-programme multiple-data abstraction is used in conjunction with a static data-partitioning scheme. The distributed FFTs required in the explicit step are based on the transpose method and the large sets of independent tridiagonal systems of equations arising in the implicit steps are solved using the pipelined Thomas algorithm. A speed-up analysis of a model problem is presented for three partitioning schemes, namely unipartition, multipartition and transpose partition. It is shown that the unipartitioning scheme is best suited for this algorithm. Performance measurements of the overall as well as individual stages of the algorithm are presented for several different grids and are discussed in the context of associated dependency and communication overheads. An unscaled speed-up efficiency of up to 91% on doubling the number of processors and up to 60% on an eightfold increase in the number of processors was obtained on the Intel Paragon and iPSC/860 Hypercube. Absolute performance of the code was evaluated by comparisons with performance on the Cray-YMP. On 128 Paragon processors, performance up to five times that of a single-processor Cray-YMP was obtained. The validation of the method and results of grid refinement studies in stably stratified turbulent channel flows are presented. © 1997 John Wiley & Sons, Ltd.     

多道预测反褶积

就多维最小平方预测准测,推导了一种分块Toeplitzt矩阵方程组求解的递推公式,并对人工模型进行了实验,实验结果表明采用多道处理反褶积优于单道结果。文中还给出了多道最小相位的定义,并给出了在一步预测下多维反褶积算子确定性稳定的结论。     

Cluster Structure of Optimal Solutions in Bipartitioning of Small Worlds

Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions.     

Overlapping Domain Decomposition Algorithms for General Sparse Matrices

Domain decomposition methods for finite element problems using a partition based on the underlying finite element mesh have been extensively studied. In this paper, we discuss algebraic extensions of the class of overlapping domain decomposition algorithms for general sparse matrices. The subproblems are created with an overlapping partition of the graph corresponding to the sparsity structure of the matrix. These algebraic domain decomposition methods are especially useful for unstructured mesh problems. We also discuss some difficulties encountered in the algebraic extension, particularly the issues related to the coarse solver.     

On the validity of a front-oriented approach to partitioning large sparse graphs with a connectivity constraint

In this paper we consider the problem of partitioning large sparse graphs, such as finite element meshes. The heuristic which is proposed allows to partition into connected and quasi-balanced subgraphs in a reasonable amount of time, while attempting to minimize the number of edge cuts. Here the goal is to build partitions for graphs containing large numbers of nodes and edges, in practice at least 10⁴. Basically, the algorithm relies on the iterative construction of connected subgraphs. This construction is achieved by successively exploring clusters of nodes called fronts. Indeed, a judicious use of fronts ensures the connectivity of the subsets at low cost: it is shown that locally, i.e. for a given subgraph, the complexity of such operations grows at most linearly with the number of edges. Moreover, a few examples are given to illustrate the quality and speed of the heuristic.The work of this author was partially supported by the DGA/DRET under contract 93-1192 and by the Army Research Office under contract DAAL03-91-C-0047 (Univ. Tenn. subcontract ORA4466.04 Amendment 1).The work of this author was partially supported by the National Science Foundation under contract ASC 92-01266, the Army Research Office under contract DAAL03-91C-0047 (Univ. Tenn. subcontract ORA4466.04 Amendment 1), and ONR under contract ONR-N00014-92-J-1890.     

Comparing Metaheuristic Algorithms for Sonet Network Design Problems

This paper considers two problems that arise in the design of optical telecommunication networks when a ring-based topology is adopted, namely the SONET Ring Assignment Problem and the Intraring Synchronous Optical Network Design Problem. We show that these two network topology problems correspond to graph partitioning problems with capacity constraints: the first is a vertex partitioning problem, while the latter is an edge partitioning problem. We consider solution methods for both problems, based on metaheuristic algorithms. We first describe variable objective functions that depend on the transition from one solution to a neighboring one, then we apply several diversification and intensification techniques including Path Relinking, eXploring Tabu Search and Scatter Search. Finally we propose a diversification method based on the use of multiple neighborhoods. A set of extensive computational results is used to compare the behaviour of the proposed methods and objective functions.     

Performance of a genetic algorithm for the graph partitioning problem

The performance of the genetic algorithm (GA) for the graph partitioning problem (GPP) is investigated by comparison with standard heuristics on well-known benchmark graphs. In general, there is a case where a practical performance of a conventional genetic approach, which performs only simple operations without a local search strategy, is not sufficient. However, it is known that a combination of GA and local search can produce better solutions. From this practice, we incorporate a simple local search algorithm into the GA. In particular, the search ability of the GA is compared with standard heuristics such as multistart local search and simulated annealing, which use the same neighborhood structure of the simple local search, for solving the GPP. Experimental results show that the GA performs better than its competitors.