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This work considers the organization and performance of computations on parallel computers of tree algorithms for the N-body problem where the number of particles is on the order of a million. The N-body problem is formulated as a set of recursive equations based on a few elementary functions, which leads to a computational structure in the form of a pyramid-like graph, where each vertex is a process, and each arc a communication link. The pyramid is mapped to three different processor configurations: (1) A pyramid of processors corresponding to the processes pyramid graph; (2) A hypercube of processors, e.g., a connection-machine like architecture; (3) A rather small array, e.g., $2 \\times 2 \\ times 2$, of processors faster than the ones considered in (1) and (2) above. Simulations of this size can be performed on any of the three architectures in reasonable time.

When a semi-infinite body of homogeneous fluid initially at rest behind a vertical retaining wall is suddenly released by the removal of the barrier the resulting flow over a horizontal or sloping bed is referred to as a dam-break flow. When resistance to the flow is neglected the exact solution, in the case of a stable horizontal bed with or without `tail water', may be obtained on the basis of shallow-water theory via the method of characteristics and the results are well known. Discrepancies between these shallow-water based solutions and experiments have been partially accounted for by the introduction of flow resistance in the form of basal friction. This added friction significantly modifies the wave speed and flow profile near the head of the wave so that the simple exact solutions no longer apply and various asymptotic or numerical approaches must be implemented to solve these frictionally modified depth-averaged shallow-water equations. When the bed is no longer stable so that solid particles may be exchanged between the bed and the water column the dynamics of the flow becomes highly complex as the buoyancy forces vary in space and time according to the competing rates of erosion and deposition. Furthermore, when the Froude number of the flow is close to unity perturbations in the height and velocity profiles grow into N-waves and the bed below develops ripples which act to sustain the N-waves in the fluid above. It is our intention here to study dam-break flows over erodible sloping beds as agents of sediment transport taking into account basal friction as well as the effects of particle concentrations on flow dynamics including both erosion and deposition. We shall consider shallow flows over initially dry beds and investigate the effects of changes in the depositional and erosional models employed as well as in the nature of the drag acting on the flow and the slope of the bed. These models include effects hitherto neglected in such studies and offer insights into the transport of sediment in the worst case scenario of the complete and instantaneous collapse of a dam. / Mathematics

When a semi-infinite body of homogeneous fluid initially at rest behind a vertical retaining wall is suddenly released by the removal of the barrier the resulting flow over a horizontal or sloping bed is referred to as a dam-break flow. When resistance to the flow is neglected the exact solution, in the case of a stable horizontal bed with or without `tail water', may be obtained on the basis of shallow-water theory via the method of characteristics and the results are well known. Discrepancies between these shallow-water based solutions and experiments have been partially accounted for by the introduction of flow resistance in the form of basal friction. This added friction significantly modifies the wave speed and flow profile near the head of the wave so that the simple exact solutions no longer apply and various asymptotic or numerical approaches must be implemented to solve these frictionally modified depth-averaged shallow-water equations. When the bed is no longer stable so that solid particles may be exchanged between the bed and the water column the dynamics of the flow becomes highly complex as the buoyancy forces vary in space and time according to the competing rates of erosion and deposition. Furthermore, when the Froude number of the flow is close to unity perturbations in the height and velocity profiles grow into N-waves and the bed below develops ripples which act to sustain the N-waves in the fluid above. It is our intention here to study dam-break flows over erodible sloping beds as agents of sediment transport taking into account basal friction as well as the effects of particle concentrations on flow dynamics including both erosion and deposition. We shall consider shallow flows over initially dry beds and investigate the effects of changes in the depositional and erosional models employed as well as in the nature of the drag acting on the flow and the slope of the bed. These models include effects hitherto neglected in such studies and offer insights into the transport of sediment in the worst case scenario of the complete and instantaneous collapse of a dam. / Mathematics

To examine how dietary n-3 polyunsaturated fatty acids affect Th2 cell development, female C57BL/6 mice were fed a washout corn oil (CO) diet for 1 wk followed by 2 wk of either the same CO diet or a fish oil (FO) diet. CD4+ T cells were isolated from spleens and cultured under both neutral (anti-CD3 and phorbol myristate acetate (PMA)) and Th2 polarizing conditions (anti-CD3 and PMA, in presence of rIL-4, rIL-2, and anti-IFN-γ) in the presence of homologous mouse serum (HMS) or fetal bovine serum (FBS) for 2 d. Dietary n-3 PUFA significantly enhanced Th2 cell development and suppressed Th1 development under neutral conditions as assessed by intracellular cytokine staining for IL-4 and IFN-γ as the two prototypic Th2 and Th1 cytokines, respectively. However, under Th2 polarizing conditions, while the suppression of Th1 cells was maintained in FO-fed mice, no dietary effect was observed in Th2 cells. Dietary FO increased the Th2/Th1 ratio under both neutral and Th2 polarizing conditions with HMS in the cultures. To examine the effect of dietary n-3 PUFA on Th1 development, DO11.10 Rag2-/- mice expressing transgenic T cell receptor specific for ovalbumin (OVA) peptide were used. CD4+ T cells were isolated from spleens and lymph nodes and stimulated with ovalbumin (OVA) peptide and irradiated BALB/c splenocytes in the presence of rIL-12, anti-IL-4, and rIL-2 in HMS for 2d. Cells were expanded for another 3 d in the presence of rIL-2 and rIL-12. Dietary n-3 PUFA did not affect Th1 differentiation as assessed by the proportion of IFN-γ+, IL-4- T cells in the cultures, but suppressed rIL-2 induced expansion. The suppressed expansion was due to suppressed proliferation (p<0.05). In vivo expansion of antigen-specific T cells was visualized by flow cytometric analysis of CFSE-positive transgenic T cells. Dietary n-3 PUFA did not appear to affect antigen-induced CD4+ T cell cycle progression in vivo. Overall, these results suggest dietary n-3 PUFA have no direct effect on Th2 cell development but do directly suppress Th1 cell development following both mitogenic and antigenic stimulation in vitro.

Hydrogenation of "largely unfunctionalized" alkenes has been an active area of research for about a decade. Many catalysts have been prepared but we noticed that comparatively few substrates have been studied and none of these hydrogenations provided useful chirons for the organic synthesis area. That motivated us to investigate asymmetric hydrogenations of chiral acyclic alkenes, which are seldom used for hydrogenations and usually the reactions are fully substrate controlled. It emerged that such reactions could provide a concise entry points into chirons that can be used to prepare many natural products. Asymmetric hydrogenations of functionalized, but not coordinatively functionalized, alkenes have been used to prepare several chirons for syntheses ofpolyketide natural products using our N,carbene Crabtree's catalyst analog. Starting from optically active starting materials (eg Roche esters, lactic acid, glyceraldehyde dimethyl ketals, amino acids), highly optically active chiral alkenes can be made in several steps with high yield. With the iridium catalyzed asymmetric hydrogenations, chiral ethers, 1,3-hydroxymethyl chiron, alpha-methyl-beta-hydroxy-gamma-methyl chiron, alpha-methyl-gamma-alkyl-gamma-amino acid can be obtained with high stereoselectivities. With those well developed methodologies, (-)-dihydromyoporone, (-)-spongidepsin, (-)-invictolide have been prepared with high efficiency. Not like the vinyl acetate, which can be hydrogenated quite well with many Rh catalysts, the alkyl vinyl ether does not have a coordination functional group nearby, hence it is a difficult substrate for asymmetric hydrogenation and there are relatively few iv reports. Also the simple alkyl enol ether is quite acid sensitive and the Pfatlz's type N,PIr catalysts cannot hydrogenate the simple alkyl enol ethers well under the standard hydrogenation conditions. We explored many alkyl enol ethers and found some of them can be hydrogenated efficiently (50 bar H2, 1 mol percent N,carbene-Ir catalyst, 25 degree C) with high enantioselectivities (up to 98 percent ee). This study led us to suspect that more protons were produced when N,P-Ir catalyst precursors were used relative to the corresponding carbene catalyst since the former only gave complex mixture when being used. DF calculations and several other experiments supported this postulation.

Linear dichroism in Near Edge X-ray Absorption Fine Structure (NEXAFS) spectroscopy has been used to determine molecular orientation at surfaces and in microscopic domains. However, the molecular orientation of n-alkanes cannot be derived unambiguously from their NEXAFS spectra due to the inadequate understanding of the character of the relevant spectroscopic features in the NEXAFS spectra of n-alkanes (i.e. C 1s to sigma*C-H, C 1s to sigma*C-C transitions).<p>We have studied the linear dichroism in the NEXAFS spectra of n-alkane thin films by using angular dependent NEXAFS spectroscopy to explore the molecular orientation of hexacontane (HC, n-C60H122). The HC thin films were epitaxially grown onto the cleaved NaCl (001) surfaces by physical vapor deposition. NEXAFS spectra of the HC thin film were acquired at different angles using STXM microscopy. A detailed analysis of the angular dependence of the NEXAFS spectra of the HC thin film helps to understand the relationship between the linear dichroism and the molecular orientation in n-alkane molecules. This linear dichroism in the NEXAFS spectroscopy of n-alkanes is relevant for quantitative measurements of molecular orientation, such as for the microanalysis of crystalline organic materials. <p>The linear dichroism of the NEXAFS resonances for n-alkanes has also been studied by ab initio calculations. These calculations were carried out on an isolated n-alkane molecule and a cluster of n-alkane molecules. The calculations on an isolated n-alkane molecule are used to study the linear dichroism for the NEXAFS resonances above the C 1s IP. The cluster calculations account for matrix effects in the NEXAFS features of condensed n-alkanes. A comparison of calculations on an isolated molecule and on a cluster of molecules provides information on how the NEXAFS spectra change from gas phase to condensed phase and determines the linear dichroism of each NEXAFS feature below the C 1s IP.<p>In the process of preparing n-alkane thin films for the study of linear dichroism, the morphology and molecular orientation of n-alkane thin films with different chain length (n-C36H74 and n-C60H122) have also been investigated by the NEXAFS spectroscopy and microscopy. These thin films were epitaxially grown onto cleaved NaCl (001) surfaces by physical vapor deposition. The results revealed that the morphology and molecular orientation of n-alkane thin films depend on the chain length and deposition parameters, such as substrate temperature. These observations have been rationalized by the thermodynamics of nucleation and the kinetics of growth.