Lattice Point Generating Functions and Symmetric Cones

We show that a recent identity of Beck-Gessel-Lee-Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex polyhedral cones that are invariant under the action of a finite reflection group. We obtain general expressions for the multivariate generating functions of such cones, and work out the specific cases of a symmetry group of type A (previously known) and types B and D (new). We obtain several applications of the special cases in type B, including identities involving permutation statistics and lecture hall partitions.Comment: 19 page

Meson exchange in the weak decay of Lambda hypernuclei and the Gamma_n/Gamma_p ratio

We take an approach to the Lambda non-mesonic weak decay in nuclei based on the exchange of mesons. The one pion and one kaon exchange are considered, together with the exchange of two pions, either correlated, leading to an important scalar-isoscalar exchange (sigma-like exchange), or uncorrelated (box diagrams). Extra effects of omega exchange in the scalar-isoscalar channel are also considered. Constraints of chiral dynamics are used to generate these exchanges. A drastic reduction of the OPE results for the Gamma_n/Gamma_p ratio is obtained and the new results are compatible with all present experiments within errors. The absolute rates obtained for different nuclei are also in good agreement with experiment.Comment: 30 pages, 16 figures, 8 tables, to be published in Nucl. Phys.

A fast single server private information retrieval protocol with low communication cost

Existing single server Private Information Retrieval (PIR) protocols are far from practical. To be practical, a single server PIR protocol has to be both communicationally and computationally efficient. In this paper, we present a single server PIR protocol that has low communication cost and is much faster than existing protocols. A major building block of the PIR protocol in this paper is a tree-based compression scheme, which we call folding/unfolding. This compression scheme enables us to lower the communication complexity to O(loglogn). The other major building block is the BGV fully homomorphic encryption scheme. We show how we design the protocol to exploit the internal parallelism of the BGV scheme. This significantly reduces the server side computational overhead and makes our protocol much faster than the existing protocols. Our protocol can be further accelerated by utilising hardware parallelism. We have built a prototype of the protocol. We report on the performance of our protocol based on the prototype and compare it with the current most efficient protocols

Abundances of the elements in the solar system

A review of the abundances and condensation temperatures of the elements and their nuclides in the solar nebula and in chondritic meteorites. Abundances of the elements in some neighboring stars are also discussed.Comment: 42 pages, 11 tables, 8 figures, chapter, In Landolt- B\"ornstein, New Series, Vol. VI/4B, Chap. 4.4, J.E. Tr\"umper (ed.), Berlin, Heidelberg, New York: Springer-Verlag, p. 560-63

The influence of localised size reorganisation on short-duration bidispersed granular flows

We investigate experimentally the runout resulting from the collapse of a granular column containing two particle species that differ in size only. The experimental configuration is strictly twodimensional (only one particle per width of the experimental tank) and we explore both the role of the initial arrangement and proportion of the two particle sizes in the column, using high-speed videography, and by determining the centres of mass of the big and small particles in the initial column and the final deposit. The duration of the experiment is sufficiently short that large-scale segregation does not occur, however, we find a clear dependence of runout on both initial mixture arrangement and proportion for all conditions. We investigated this observation through detailed analysis of the flow front motion, and identify a characteristic "stopping" phase when dissipation dominates, and we apply a shallow layer model at the flow front to show how the initial mixture arrangement and proportion influence the effective coefficient of friction during emplacement. We find that a bidispersed mixture can induce a larger friction on emplacement than a monodispersed mixture, and the highest coefficient of friction was found for a well-mixed initial arrangement of particles at the proportion that shows maximum horizontal spreading of the flow. These observations suggest that downwards percolation of fine particles takes place at the front of the collapsing column, and so localised size segregation processes at the flow front can control flow mobility. This effect is likely to be important in controlling the mobility of large geophysical flows that occur on finite time scales, and whose deposits typically show granular segregation at the front and edges but not throughout the entire deposit

Limits on spin-dependent WIMP-nucleon cross-sections from the first ZEPLIN-II data

The first underground data run of the ZEPLIN-II experiment has set a limit on the nuclear recoil rate in the two-phase xenon detector for direct dark matter searches. In this paper the results from this run are converted into the limits on spin-dependent WIMP-proton and WIMP-neutron cross-sections. The minimum of the curve for WIMP-neutron cross-section corresponds to 0.07 pb at a WIMP mass of around 65 GeV.Comment: 12 pages, 2 figures, to be published in Physics Letters

Numerical Modeling of Evanescent-Wave Atom Optics

We numerically solve the time-dependent Schrodinger equation for a two-level atom interacting with an evanescent light field. The atom may be reflected or diffracted. Using the experimental parameter values we quantitatively model the evanescent field dopplerons (velocity-tuned resonances) observed by Stenlake et al. [Phys. Rev. A 49, 16 (1994)]. Besides successfully modeling the experiment, our approach provides complementary insights to the usual solution of the time-independent Schrodinger equation. We neglect spontaneous emission