On the local structure of doubly laced crystals

Let g be a Lie algebra all of whose regular subalgebras of rank 2 are type A₁×A₁, A₂, or C₂, and let B be a crystal graph corresponding to a representation of g. We explicitly describe the local structure of B, confirming a conjecture of Stembridge.     

The harmonic consistency index for the analytic hierarchy process

A new consistency measure, the harmonic consistency index, is obtained for any positive reciprocal matrix in the analytic hierarchy process. We show how this index varies with changes in any matrix element. A tight upper bound is provided for this new consistency measure when the entries of matrix are at most 9, as is often recommended. Using simulation, the harmonic consistency index is shown to give numerical values similar to the standard consistency index but it is easier to compute and interpret. In addition, new properties of the column sums of reciprocal matrices are obtained.     

Completely Simple Semigroups,Lie Algebras,and the Road Coloring Problem

Consider a semigroup generated by matrices associated with an edge-coloring of a strongly connected, aperiodic digraph. We call the semigroup Lie-solvable if the Lie algebra generated by its elements is solvable. We show that if the semigroup is Lie-solvable then its kernel is a right group. Next, we study the Lie algebra generated by the kernel. Lie algebras generated by two idempotents are analyzed in detail. We find that these have homomorphic images that are generalized quaternion algebras. We show that if the kernel is not a direct product, then the Lie algebra generated by the kernel is not solvable by describing the structure of these algebras. Finally, we discuss an infinite class of examples that are shown to always produce strongly connected aperiodic digraphs having kernels that are not right groups.     

Epimerization, diastereoselectivity and hemilability in dicationic chiral ruthenium complexes with bidentate (PS) bisphosphine monosulfide ligands

The binding of heterobidentate P^∧S ligands introduces metal-centered chirality to the planar chiral parent complex Ru(η⁶:η¹-NMe₂C₆H₄C₆H₄PCy₂)Cl₂. Observed diastereomeric ratios for the kinetic product vary dramatically depending upon ring size of the chelate formed with the P^∧S ligand. The complexes epimerize very slowly to thermodynamic product ratios that are substantially different from the kinetic product ratios.     

A mixed directed-undirected data structure for a parallel implementation of a domain decomposition algorithm

The choice of data structures influences the parallelization, efficiency and the manageability of a mesh refinement program. We introduce a mixed directed-undirected graph that combines both communication and scheduling needs. An inverted index is maintained for the directed graph to improve code performance and readability.This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.     

Dispersion modeling by kinematic simulation: Cloud dispersion model

A new technique has been developed to compute mean and fluctuating concentrations in complex turbulent flows (tidal current near a coast and deep ocean). An initial distribution of material is discretized into any small clouds which are advected by a combination of the mean flow and large scale turbulence. The turbulence can be simulated either by kinematic simulation (KS) or direct numerical simulation. The clouds also diffuse relative to their centroids; the statistics for this are obtained from a separate calculation of the growth of individual clouds in small scale turbulence, generated by KS. The ensemble of discrete clouds is periodically re-discretized, to limit the size of the small clouds and prevent overlapping. The model is illustrated with simulations of dispersion in uniform flow, and the results are compared with analytic, steady state solutions. The aim of this study is to understand how pollutants disperses in a turbulent flow through a numerical simulation of fluid particle motion in a random flow field generated by Fourier modes. Although this homogeneous turbulent is rather a “simple” flow, it represents a building block toward understanding pollutant dispersion in more complex flow. The results presented here are preliminary in nature, but we expect that similar qualitative results should be observed in a genuine turbulent flow.