Prodsimplicial-Neighborly Polytopes

Simultaneously generalizing both neighborly and neighborly cubical polytopes, we introduce PSN polytopes: their k-skeleton is combinatorially equivalent to that of a product of r simplices. We construct PSN polytopes by three different methods, the most versatile of which is an extension of Sanyal and Ziegler's "projecting deformed products" construction to products of arbitrary simple polytopes. For general r and k, the lowest dimension we achieve is 2k+r+1. Using topological obstructions similar to those introduced by Sanyal to bound the number of vertices of Minkowski sums, we show that this dimension is minimal if we additionally require that the PSN polytope is obtained as a projection of a polytope that is combinatorially equivalent to the product of r simplices, when the dimensions of these simplices are all large compared to k.Comment: 28 pages, 9 figures; minor correction

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Background study for the pn-CCD detector of CERN Axion Solar Telescope

The CERN Axion Solar Telescope (CAST) experiment searches for axions from the Sun converted into photons with energies up to around 10 keV via the inverse Primakoff effect in the high magnetic field of a superconducting Large Hadron Collider (LHC) prototype magnet. A backside illuminated pn-CCD detector in conjunction with an X-ray mirror optics is one of the three detectors used in CAST to register the expected photon signal. Since this signal is very rare and different background components (environmental gamma radiation, cosmic rays, intrinsic radioactive impurities in the set-up, ...) entangle it, a detailed study of the detector background has been undertaken with the aim to understand and further reduce the background level of the detector. The analysis is based on measured data taken during the Phase I of CAST and on Monte Carlo simulations of different background components. This study will show that the observed background level (at a rate of (8.00+-0.07)10^-5 counts/cm^2/s/keV between 1 and 7 keV) seems to be dominated by the external gamma background due to usual activities at the experimental site, while radioactive impurities in the detector itself and cosmic neutrons could make just smaller contribution.Comment: Comments: 10 pages, 9 figures and images, submitted to Astroparticle Physic

Background reduction and sensitivity for germanium double beta decay experiments

Germanium detectors have very good capabilities for the investigation of rare phenomena like the neutrinoless double beta decay. Rejection of the background entangling the expected signal is one primary goal in this kind of experiments. Here, the attainable background reduction in the energy region where the neutrinoless double beta decay signal of 76Ge is expected to appear has been evaluated for experiments using germanium detectors, taking into consideration different strategies like the granularity of the detector system, the segmentation of each individual germanium detector and the application of Pulse Shape Analysis techniques to discriminate signal from background events. Detection efficiency to the signal is affected by background rejection techniques, and therefore it has been estimated for each of the background rejection scenarios considered. Finally, conditions regarding crystal mass, radiopurity, exposure to cosmic rays, shielding and rejection capabilities are discussed with the aim to achieve a background level of 10-3 c keV-1 kg-1 y-1 in the region of interest, which would allow to explore neutrino effective masses around 40 meV.Comment: 13 pages, 19 figures. Accepted by Astroparticle Physic

A Generating Function for all Semi-Magic Squares and the Volume of the Birkhoff Polytope

We present a multivariate generating function for all n x n nonnegative integral matrices with all row and column sums equal to a positive integer t, the so called semi-magic squares. As a consequence we obtain formulas for all coefficients of the Ehrhart polynomial of the polytope B_n of n x n doubly-stochastic matrices, also known as the Birkhoff polytope. In particular we derive formulas for the volumes of B_n and any of its faces.Comment: 24 pages, 1 figure. To appear in Journal of Algebraic Combinatoric

Helium bubble formation in ultrafine and nanocrystalline tungsten under different extreme conditions

We have investigated the effects of helium ion irradiation energy and sample temperature on the performance of grain boundaries as helium sinks in ultrafine grained and nanocrystalline tungsten. Irradiations were performed at displacement and non-displacement energies and at temperatures above and below that required for vacancy migration. Microstructural investigations were performed using Transmission Electron Microscopy (TEM) combined with either in-situ or ex-situ ion irradiation. Under helium irradiation at an energy which does not cause atomic displacements in tungsten (70 eV), regardless of temperature and thus vacancy migration conditions, bubbles were uniformly distributed with no preferential bubble formation on grain boundaries. At energies that can cause displacements, bubbles were observed to be preferentially formed on the grain boundaries only at high temperatures where vacancy migration occurs. Under these conditions, the decoration of grain boundaries with large facetted bubbles occurred on nanocrystalline grains with dimensions less than 60 nm. We discuss the importance of vacancy supply and the formation and migration of radiation-induced defects on the performance of grain boundaries as helium sinks and the resulting irradiation tolerance of ultrafine grained and nanocrystalline tungsten to bubble formatio

Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

We derive efficient algorithms for coarse approximation of algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe in an elementary way, come from tropical geometry. We thus reduce a hard algebraic problem to high-precision linear optimization, proving new upper and lower complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding

An in situ transmission electron microscopy study of the ion irradiation induced amorphisation of silicon by He and Xe

Transmission electron microscopy with in situ ion irradiation has been used to examine the ionbeam-induced amorphisation of crystalline silicon under irradiation with light (He) and heavy (Xe) ions at room temperature. Analysis of the electron diffraction data reveal the heterogeneous amorphisation mechanism to be dominant in both cases. The differences in the amorphisation curves are discussed in terms of intra-cascade dynamic recovery, and the role of electronic and nuclear loss mechanisms

Charge and current-sensitive preamplifiers for pulse shape discrimination techniques with silicon detectors

New charge and current-sensitive preamplifiers coupled to silicon detectors and devoted to studies in nuclear structure and dynamics have been developed and tested. For the first time shapes of current pulses from light charged particles and carbon ions are presented. Capabilities for pulse shape discrimination techniques are demonstrated.Comment: 14 pages, 12 figures, to be published in Nucl. Inst. Meth.