Evaluation of the SSC/LHNC,SSCF and PY approximations for short ranged,anisotropic potentials

Three approximations for the orientational correlation function of molecular fluids—the single super chain/linearized hypernetted chain (SSC/LHNC), single super chain f-expansion (SSCF) and Percus-Yevick (PY) approximation—are evaluated in the dense liquid state for a fluid inter-acting with short ranged anisotropic interactions. These interactions are prototypical of the forces that determine the non-spherical shape of symmetric linear molecules. We find that SSC/LHNC is very poor, failing to predict many of the structural features present in the Monte Carlo (MC) simulation results. The PY and SSCF approximations produce much better results; however, neither approximation is completely satisfactory.     

Douglas Henderson: a life in statistical mechanics

In a previous study (Wang, L. S., Nicholas, J. B., Dupuis, M., Wu, H., and Colson, S. D., 1997, Phys. Rev. Lett., 78, 4450) of small silicon oxide clusters with stochiometry Si3Oy(y = 1-6), it was found that the molecule Si3O2 and its anion required special theoretical attention. This is due to a particular electronic structure feature of the neutral cluster: the s,p hybrid atomic orbitals of the two bonded silicon atoms give rise to a low lying empty π molecular orbital. As a result the ground state of Si3O2 has a triplet spin, and a state of singlet spin is a low lying excited electronic state at about 0.5 eV above the triplet state. Ab initio molecular orbital calculations show that photoelectron detachment proceeds from the 2B1 state of the anion to the 3B1 ground state of the neutral cluster. Detachment via the 1A1 state of the neutral cluster lies in the shoulder of the detachment via the triplet state.     

Co-registration of the distribution of wall shear stress and 140 complex plaques of the aorta

Previous studies provide evidence that atherosclerosis develops in vascular regions exposed to low wall shear stress (WSS) and high oscillatory shear index (OSI). 4D flow MRI was analyzed in 70 stroke patients with complex plaques (≥ 4 mm thickness, ulcerated or superimposed thrombi) and in 12 young healthy volunteers. The segmental distribution of peak systolic WSS_systole and OSI was quantified in analysis planes positioned directly at the location of 140 complex plaques found in the 70 patients. In addition, WSS_systole and OSI were evaluated in 8 standard analysis planes distributed along the aorta. Complex plaques were predominantly found at the inner curvature of the aortic arch and of the descending aorta. High OSI was co-located with the segments mostly affected by complex plaque while WSS_systole demonstrated a homogenous distribution. In standard analysis planes, patients demonstrated significantly (p < 0.01) altered distribution of wall parameters compared to volunteers (reduced WSS_systole in 91% of aortic wall segments, increased OSI in 48% of segments). OSI distribution was asymmetric with higher values at the inner curvature of the aorta. While WSS and OSI showed expected changes in patients compared to healthy controls, their distribution pattern at complex plaques indicated a more complex and heterogeneous relationship than previously anticipated.     

Direct analysis of psychoactive tryptamine and harmala alkaloids in the Amazonian botanical medicine ayahuasca by liquid chromatography–electrospray ionization-tandem mass spectrometry

A direct injection/liquid chromatography–electrospray ionization-tandem mass spectrometry procedure has been developed for the simultaneous quantitation of 11 compounds potentially found in the increasingly popular Amazonian botanical medicine and religious sacrament ayahuasca. The method utilizes a deuterated internal standard for quantitation and affords rapid detection of the alkaloids by a simple dilution assay, requiring no extraction procedures. Further, the method demonstrates a high degree of specificity for the compounds in question, as well as low limits of detection and quantitation despite using samples for analysis that had been diluted up to 200:1. This approach also appears to eliminate potential matrix effects. Method bias for each compound, examined over a range of concentrations, was also determined as was inter- and intra-assay variation. Its application to the analysis of three different ayahuasca preparations is also described. This method should prove useful in the study of ayahuasca in clinical and ethnobotanical research as well as in forensic examinations of ayahuasca preparations.     

Algebraic multigrid preconditioning of the Hessian in optimization constrained by a partial differential equation

We construct an algebraic multigrid (AMG) based preconditioner for the reduced Hessian of a linear‐quadratic optimization problem constrained by an elliptic partial differential equation. While the preconditioner generalizes a geometric multigrid preconditioner introduced in earlier works, its construction relies entirely on a standard AMG infrastructure built for solving the forward elliptic equation, thus allowing for it to be implemented using a variety of AMG methods and standard packages. Our analysis establishes a clear connection between the quality of the preconditioner and the AMG method used. The proposed strategy has a broad and robust applicability to problems with unstructured grids, complex geometry, and varying coefficients. The method is implemented using the Hypre package and several numerical examples are presented.     

Stability of Viscous St. Venant Roll Waves: From Onset to Infinite Froude Number Limit

We study the spectral stability of roll wave solutions of the viscous St. Venant equations modeling inclined shallow water flow, both at onset in the small Froude number or “weakly unstable” limit \(F\rightarrow 2^+\) and for general values of the Froude number F, including the limit \(F\rightarrow +\infty \). In the former, \(F\rightarrow 2^+\), limit, the shallow water equations are formally approximated by a Korteweg-de Vries/Kuramoto–Sivashinsky (KdV–KS) equation that is a singular perturbation of the standard Korteweg-de Vries (KdV) equation modeling horizontal shallow water flow. Our main analytical result is to rigorously validate this formal limit, showing that stability as \(F\rightarrow 2^+\) is equivalent to stability of the corresponding KdV–KS waves in the KdV limit. Together with recent results obtained for KdV–KS by Johnson–Noble–Rodrigues–Zumbrun and Barker, this gives not only the first rigorous verification of stability for any single viscous St. Venant roll wave, but a complete classification of stability in the weakly unstable limit. In the remainder of the paper, we investigate numerically and analytically the evolution of the stability diagram as Froude number increases to infinity. Notably, we find transition at around \(F=2.3\) from weakly unstable to different, large-F behavior, with stability determined by simple power-law relations. The latter stability criteria are potentially useful in hydraulic engineering applications, for which typically \(2.5\le F\le 6.0\).     

Crystallographic determination of metal surfaces with helium scattering

Helium-surface diffraction data has been used to construct the interaction potential between a Helium atom and a metal surface. The constructed potential fits experimental data for all beam energies and angles of incidence and more importantly is independent of beam energy. Such a potential essentially consists of two parts: a short range repulsive corrugated potential due to electronic overlap, and a long range attractive potential due to dispersion forces. We have generated potentials for He scattering for Ni, Cu and Au and in all cases found excellent agreement with experiments. We also report that the repulsive part of the He scattering potential can be obtained rather simply from first principles without adjustable parameters. This suggests that one can determine surface crystallography from first principles without adjustable parameters.