The quantum angular Calogero-Moser model

The rational Calogero-Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of R^n to the `angular Calogero-Moser model' on the sphere S^{n-1}. We discuss the energy spectrum of this quantum system, its degeneracies and the eigenstates. The spectral flow with the coupling parameter yields isospectrality for integer increments. Decoupling the center of mass before effecting the spherical reduction produces a `relative angular Calogero-Moser model', which is analyzed in parallel. We generalize our considerations to the Calogero-Moser models associated with Coxeter groups. Finally, we attach spin degrees of freedom to our particles and extend the results to the spin-Calogero system.Comment: 1+19 pages, v2: minor corrections, 4 refs. added, version published in JHE

The aerodynamic effects of wing–wing interaction in flapping insect wings

We employed a dynamically scaled mechanical model of the small fruit fly Drosophila melanogaster (Reynolds number 100–200) to investigate force enhancement due to contralateral wing interactions during stroke reversal (the 'clap-and-fling'). The results suggest that lift enhancement during clap-and-fling requires an angular separation between the two wings of no more than 10–12°. Within the limitations of the robotic apparatus, the clap-and-fling augmented total lift production by up to 17%, but depended strongly on stroke kinematics. The time course of the interaction between the wings was quite complex. For example, wing interaction attenuated total force during the initial part of the wing clap, but slightly enhanced force at the end of the clap phase. We measured two temporally transient peaks of both lift and drag enhancement during the fling phase: a prominent peak during the initial phase of the fling motion, which accounts for most of the benefit in lift production, and a smaller peak of force enhancement at the end fling when the wings started to move apart. A detailed digital particle image velocimetry (DPIV) analysis during clap-and-fling showed that the most obvious effect of the bilateral 'image' wing on flow occurs during the early phase of the fling, due to a strong fluid influx between the wings as they separate. The DPIV analysis revealed, moreover, that circulation induced by a leading edge vortex (LEV) during the early fling phase was smaller than predicted by inviscid two-dimensional analytical models, whereas circulation of LEV nearly matched the predictions of Weis-Fogh's inviscid model at late fling phase. In addition, the presence of the image wing presumably causes subtle modifications in both the wake capture and viscous forces. Collectively, these effects explain some of the changes in total force and lift production during the fling. Quite surprisingly, the effect of clap-and-fling is not restricted to the dorsal part of the stroke cycle but extends to the beginning of upstroke, suggesting that the presence of the image wing distorts the gross wake structure throughout the stroke cycle

On Three-Dimensional Space Groups

An entirely new and independent enumeration of the crystallographic space groups is given, based on obtaining the groups as fibrations over the plane crystallographic groups, when this is possible. For the 35 ``irreducible'' groups for which it is not, an independent method is used that has the advantage of elucidating their subgroup relationships. Each space group is given a short ``fibrifold name'' which, much like the orbifold names for two-dimensional groups, while being only specified up to isotopy, contains enough information to allow the construction of the group from the name.Comment: 26 pages, 8 figure

Confirmation of the Dietary Background of Beef from its Stable Isotope Signature

End of project reportConsumers are increasingly demanding information on the authenticity and source of the food they purchase. Molecular DNA-based technology allows animal identification, but without certification or a “paper-trail” but does not provide information about feed history or the production system under which the animal was reared. The stable isotopes of chemical elements (e.g.13C/12C, 15N/14N) are naturally present in animal tissue and reflect the isotopic composition of the diet. The overall aim of this project was to determine the feasibility of using the stable isotopic composition as an intrinsic, biochemical marker to gain information about feed components used in the production of beef. Factors likely to affect the isotopic signature such as source of tissue, duration of feeding and production systems were examined. It is expected that this highly innovative and original technique will permit the identification of country of origin and dietary history of beef and so greatly assist efforts to market Irish beef, particularly in lucrative European markets. Sequential sampling and stable isotope analysis of bovine tail hair and hoof revealed that the two tissues can provide a detailed and continuous record of animal dietary history. Because hair can be sampled repeatedly and noninvasively, we anticipate that this approach will also prove useful for the investigation of short-term wildlife movements and changes in dietary preferences

On large-scale diagonalization techniques for the Anderson model of localization

We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for large-scale sparse real and symmetric indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation by Cullum and Willoughby with the shift-and-invert techniques in the implicitly restarted Lanczos method and in the Jacobi–Davidson method. Our preconditioning approaches for the shift-and-invert symmetric indefinite linear system are based on maximum weighted matchings and algebraic multilevel incomplete LDLT factorizations. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques for the highly ill-conditioned symmetric indefinite Anderson matrices. We demonstrate the effectiveness and the numerical accuracy of these algorithms. Our numerical examples reveal that recent algebraic multilevel preconditioning solvers can accelerate the computation of a large-scale eigenvalue problem corresponding to the Anderson model of localization by several orders of magnitude

Fast Genes and Slow Clades: Comparative Rates of Molecular Evolution in Mammals

Although interest in the rate of molecular evolution and the molecular clock remains high, our knowledge for most groups in these areas is derived largely from a patchwork of studies limited in both their taxon coverage and the number of genes examined. Using a comprehensive molecular data set of 44 genes (18 nDNA, 11 tRNA and 15 additional mtDNA genes) together with a virtually complete and dated phylogeny of extant mammals, I 1) describe differences in the rate of molecular evolution (i.e. substitution rate) within this group in an explicit phylogenetic and quantitative framework and 2) present the first attempt to localize the phylogenetic positions of any rate shifts. Significant rate differences were few and confirmed several long-held trends, including a progressive rate slowdown within hominids and a reduced substitution rate within Cetacea. However, many new patterns were also uncovered, including the mammalian orders being characterized generally by basal rate slowdowns. A link between substitution rate and the size of a clade (which derives from its net speciation rate) is also suggested, with the species-poor major clades (“orders”) showing more decreased rates that often extend throughout the entire clade. Significant rate increases were rare, with the rates within (murid) rodents being fast, but not significantly so with respect to other mammals as a whole. Despite clear lineage-specific differences, rates generally change gradually along these lineages, supporting the potential existence of a local molecular clock in mammals. Together, these results will lay the foundation for a broad-scale analysis to establish the correlates and causes of the rate of molecular evolution in mammals

Local Equation of State and Velocity Distributions of a Driven Granular Gas

We present event-driven simulations of a granular gas of inelastic hard disks with incomplete normal restitution in two dimensions between vibrating walls (without gravity). We measure hydrodynamic quantities such as the stress tensor, density and temperature profiles, as well as velocity distributions. Relating the local pressure to the local temperature and local density, we construct a local constitutive equation. For strong inelasticities the local constitutive relation depends on global system parameters, like the volume fraction and the aspect ratio. For moderate inelasticities the constitutive relation is approximately independent of the system parameters and can hence be regarded as a local equation of state, even though the system is highly inhomogeneous with heterogeneous temperature and density profiles arising as a consequence of the energy injection. Concerning the local velocity distributions we find that they do not scale with the square root of the local granular temperature. Moreover the high-velocity tails are different for the distribution of the x- and the y-component of the velocity, and even depend on the position in the sample, the global volume fraction, and the coefficient of restitution.Comment: 14 pages, 14 figures of which Figs. 13a-f and Fig. 14 are archived as separate .gif files due to upload-size limitations. A version of the paper including all figures in better quality can be downloaded at http://www.theorie.physik.uni-goettingen.de/~herbst/download/LocEqSt.ps.gz (3.8 MB, ps.gz) or at http://www.theorie.physik.uni-goettingen.de/~herbst/download/LocEqSt.pdf (4.9 MB, pdf

Numerical Solution of Dynamic Equilibrium Models Under Poisson Uncertainty

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households

A Topologically Massive Gauge Theory with 32 Supercharges

We construct a novel topologically massive abelian Chern-Simons gauge theory with 32 global supersymmetries in three spacetime dimensions. In spite of the 32 supercharges, the theory exhibits massive excitations only up to spin 1. The possibility of such a multiplet shortening is due to the presence of non-central R-symmetry generators in the Poincare superalgebra, whose supermultiplets are determined.Comment: 20 pages; v2: minor changes, ref. added, to appear in Phys. Rev.