High Performance Computing With A Conservative Spectral Boltzmann Solver

We present new results building on the conservative deterministic spectral method for the space inhomogeneous Boltzmann equation developed by Gamba and Tharkabhushaman. This approach is a two-step process that acts on the weak form of the Boltzmann equation, and uses the machinery of the Fourier transform to reformulate the collisional integral into a weighted convolution in Fourier space. A constrained optimization problem is solved to preserve the mass, momentum, and energy of the resulting distribution. We extend this method to second order accuracy in space and time, and explore how to leverage the structure of the collisional formulation for high performance computing environments. The locality in space of the collisional term provides a straightforward memory decomposition, and we perform some initial scaling tests on high performance computing resources. We also use the improved computational power of this method to investigate a boundary-layer generated shock problem that cannot be described by classical hydrodynamics.Mathematic

Conservative Deterministic Spectral Boltzmann Solver Near The Grazing Collisions Limit

We present new results building on the conservative deterministic spectral method for the space homogeneous Boltzmann equation developed by Gamba and Tharkabhushaman. This approach is a two-step process that acts on the weak form of the Boltzmann equation, and uses the machinery of the Fourier transform to reformulate the collisional integral into a weighted convolution in Fourier space. A constrained optimization problem is solved to preserve the mass, momentum, and energy of the resulting distribution. Within this framework we have extended the formulation to the case of more general case of collision operators with anisotropic scattering mechanisms, which requires a new formulation of the convolution weights. We also derive the grazing collisions limit for the method, and show that it is consistent with the Fokker-Planck-Landau equations as the grazing collisions parameter goes to zero.Mathematic

A Fast Conservative Spectral Solver For The Nonlinear Boltzmann Collision Operator

We present a conservative spectral method for the fully nonlinear Boltzmann collision operator based on the weighted convolution structure in Fourier space developed by Gamba and Tharkabhushnanam.. This method can simulate a broad class of collisions, including both elastic and inelastic collisions as well as angularly dependent cross sections in which grazing collisions play a major role. The extension presented in this paper consists of factorizing the convolution weight on quadrature points by exploiting the symmetric nature of the particle interaction law, which reduces the computational cost and memory requirements of the method to O(M(2)N(4)logN) from the O(N-6) complexity of the original spectral method, where N is the number of velocity grid points in each velocity dimension and M is the number of quadrature points in the factorization, which can be taken to be much smaller than N. We present preliminary numerical results.Mathematic

Calabi-Yau Fourfolds with Flux and Supersymmetry Breaking

In Calabi-Yau fourfold compactifications of M-theory with flux, we investigate the possibility of partial supersymmetry breaking in the three-dimensional effective theory. To this end, we place the effective theory in the framework of general N=2 gauged supergravities, in the special case where only translational symmetries are gauged. This allows us to extract supersymmetry-breaking conditions, and interpret them as conditions on the 4-form flux and Calabi-Yau geometry. For N=2 unbroken supersymmetry in three dimensions we recover previously known results, and we find a new condition for breaking supersymmetry from N=2 to N=1, i.e. from four to two supercharges. An example of a Calabi-Yau hypersurface in a toric variety that satisfies this condition is provided.Comment: 26 page

2P/Encke, the Taurid complex NEOs and the Maribo and Sutter’s Mill meteorites

Aims. 2P/Encke is a short period comet that was discovered in 1786 and has been extensively observed and studied for more than 200 years. The Taurid meteoroid stream has long been linked with 2P/Encke owing to a good match of their orbital elements, even though the comet’s activity is not strong enough to explain the number of observed meteors. Various small near-Earth objects (NEOs) have been discovered with orbits that can be linked to 2P/Encke and the Taurid meteoroid stream. Maribo and Sutter’s Mill are CM type carbonaceous chondrite that fell in Denmark on January 17, 2009 and April 22, 2012, respectively. Their pre-atmospheric orbits place them in the middle of the Taurid meteoroid stream, which raises the intriguing possibility that comet 2P/Encke could be the parent body of CM chondrites. Methods. To investigate whether a relationship between comet 2P/Encke, the Taurid complex associated NEOs, and CM chondrites exists, we performed photometric and spectroscopic studies of these objects in the visible wavelength range. We observed 2P/Encke and 10 NEOs on August 2, 2011 with the FORS instrument at the 8.2 m Very Large Telescope on Cerro Paranal (Chile). Results. Images in the R filter, used to investigate the possible presence of cometary activity around the nucleus of 2P/Encke and the NEOs, show that no resolved coma is present. None of the FORS spectra show the 700 nm absorption feature due to hydrated minerals that is seen in the CM chondrite meteorites. All objects show featureless spectra with moderate reddening slopes at λ10 and 1999 VT25, which show a flatter spectrum, the spectral slope of the observed NEOs is compatible with that of 2P/Encke. However, most of the NEOs show evidence of a silicate absorption in lower S/N data at λ> 800 nm, which is not seen in 2P/Encke, which suggests that they are not related. Conclusions. Despite similar orbits, we find no spectroscopic evidence for a link between 2P/Encke, the Taurid complex NEOs and the Maribo and Sutter’s Mill meteorites. However, we cannot rule out a connection to the meteorites either, as the spectral differences may be caused by secondary alteration of the surfaces of the NEOs

Patterns of richness across forest beetle communities—A methodological comparison of observed and estimated species numbers

Abstract Species richness is a frequently used measure of biodiversity. The compilation of a complete species list is an often unattainable goal. Estimators of species richness have been developed to overcome this problem. While the use of these estimators is becoming increasingly popular, working with the observed number of species is still common practice. To assess whether patterns of beetle communities based on observed numbers may be compared among each other, we compared patterns from observed and estimated numbers of species for beetle communities in the canopy of the Leipzig floodplain forest. These patterns were species richness and the number of shared species among three tree species and two canopy strata. We tested the applicability of the asymptotic Chao1 estimator and the estimate provided by the nonasymptotic rarefaction–extrapolation method for all tree species and both upper canopy and lower canopy. In the majority of cases, the ranking patterns of species richness for host tree species and strata were the same for the observed and estimated number of species. The ranking patterns of the number of species shared among host tree species and strata, however, were significantly different between observed and estimated values. Our results indicate that the observed number of species under‐represents species richness and the number of shared species. However, ranking comparisons of published patterns based on the number of observed species may be acceptable for species richness but likely not reliable for the number of shared species. Further studies are needed to corroborate this conclusion. We encourage to use estimators and to provide open access to data to allow comparative assessments

Synthesis of a quinolone library from ynones

A library of 72 quinolones was synthesized from substituted anthranilic acids, using ynone intermediates. These masked β-dicarbonyl synthons allowed cyclization under milder conditions than previously reported quinolone syntheses

Phase diagram for non-axisymmetric plasma balls

Plasma balls and rings emerge as fluid holographic duals of black holes and black rings in the hydrodynamic/gravity correspondence for the Scherk-Schwarz AdS system. Recently, plasma balls spinning above a critical rotation were found to be unstable against m-lobed perturbations. In the phase diagram of stationary solutions the threshold of the instability signals a bifurcation to a new phase of non-axisymmetric configurations. We find explicitly this family of solutions and represent them in the phase diagram. We discuss the implications of our results for the gravitational system. Rotating non-axisymmetric black holes necessarily radiate gravitational waves. We thus emphasize that it would be important, albeit possibly out of present reach, to have a better understanding of the hydrodynamic description of gravitational waves and of the gravitational interaction between two bodies. We also argue that it might well be that a non-axisymmetric m-lobed instability is also present in Myers-Perry black holes for rotations below the recently found ultraspinning instability.Comment: 1+22 pages, 3 figures. v2: minor corrections and improvements, matches published versio