Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs

We define 2-decompositions of ribbon graphs, which generalise 2-sums and tensor products of graphs. We give formulae for the Bollobas-Riordan polynomial of such a 2-decomposition, and derive the classical Brylawski formula for the Tutte polynomial of a tensor product as a (very) special case. This study was initially motivated from knot theory, and we include an application of our formulae to mutation in knot diagrams.Comment: Version 2 has minor changes. To appear in Annals of Combinatoric

Low noise amplication of an optically carried microwave signal: application to atom interferometry

In this paper, we report a new scheme to amplify a microwave signal carried on a laser light at $\lambda$=852nm. The amplification is done via a semiconductor tapered amplifier and this scheme is used to drive stimulated Raman transitions in an atom interferometer. Sideband generation in the amplifier, due to self-phase and amplitude modulation, is investigated and characterized. We also demonstrate that the amplifier does not induce any significant phase-noise on the beating signal. Finally, the degradation of the performances of the interferometer due to the amplification process is shown to be negligible

Anisotropy at the end of the cosmic ray spectrum?

The starburst galaxies M82 and NGC253 have been proposed as the primary sources of cosmic rays with energies above $10^{18.7}$ eV. For energies \agt 10^{20.3} eV the model predicts strong anisotropies. We calculate the probabilities that the latter can be due to chance occurrence. For the highest energy cosmic ray events in this energy region, we find that the observed directionality has less than 1% probability of occurring due to random fluctuations. Moreover, during the first 5 years of operation at Auger, the observation of even half the predicted anisotropy has a probability of less than $10^{-5}$ to occur by chance fluctuation. Thus, this model can be subject to test at very small cost to the Auger priors budget and, whatever the outcome of that test, valuable information on the Galactic magnetic field will be obtained.Comment: Final version to be published in Physical Review

Supersymmetric Benchmarks with Non-Universal Scalar Masses or Gravitino Dark Matter

We propose and examine a new set of benchmark supersymmetric scenarios, some of which have non-universal Higgs scalar masses (NUHM) and others have gravitino dark matter (GDM). The scalar masses in these models are either considerably larger or smaller than the narrow range allowed for the same gaugino mass m_{1/2} in the constrained MSSM (CMSSM) with universal scalar masses m_0 and neutralino dark matter. The NUHM and GDM models with larger m_0 may have large branching ratios for Higgs and/or $Z$ production in the cascade decays of heavier sparticles, whose detection we discuss. The phenomenology of the GDM models depends on the nature of the next-to-lightest supersymmetric particle (NLSP), which has a lifetime exceeding 10^4 seconds in the proposed benchmark scenarios. In one GDM scenario the NLSP is the lightest neutralino \chi, and the supersymmetric collider signatures are similar to those in previous CMSSM benchmarks, but with a distinctive spectrum. In the other GDM scenarios based on minimal supergravity (mSUGRA), the NLSP is the lighter stau slepton {\tilde \tau}_1, with a lifetime between ~ 10^4 and 3 X 10^6 seconds. Every supersymmetric cascade would end in a {\tilde \tau}_1, which would have a distinctive time-of-flight signature. Slow-moving {\tilde \tau}_1's might be trapped in a collider detector or outside it, and the preferred detection strategy would depend on the {\tilde \tau}_1 lifetime. We discuss the extent to which these mSUGRA GDM scenarios could be distinguished from gauge-mediated models.Comment: 52 pages LaTeX, 13 figure

Black Holes from Cosmic Rays: Probes of Extra Dimensions and New Limits on TeV-Scale Gravity

If extra spacetime dimensions and low-scale gravity exist, black holes will be produced in observable collisions of elementary particles. For the next several years, ultra-high energy cosmic rays provide the most promising window on this phenomenon. In particular, cosmic neutrinos can produce black holes deep in the Earth's atmosphere, leading to quasi-horizontal giant air showers. We determine the sensitivity of cosmic ray detectors to black hole production and compare the results to other probes of extra dimensions. With n \ge 4 extra dimensions, current bounds on deeply penetrating showers from AGASA already provide the most stringent bound on low-scale gravity, requiring a fundamental Planck scale M_D > 1.3 - 1.8 TeV. The Auger Observatory will probe M_D as large as 4 TeV and may observe on the order of a hundred black holes in 5 years. We also consider the implications of angular momentum and possible exponentially suppressed parton cross sections; including these effects, large black hole rates are still possible. Finally, we demonstrate that even if only a few black hole events are observed, a standard model interpretation may be excluded by comparison with Earth-skimming neutrino rates.Comment: 30 pages, 18 figures; v2: discussion of gravitational infall, AGASA and Fly's Eye comparison added; v3: Earth-skimming results modified and strengthened, published versio

SuperWIMP Dark Matter Signals from the Early Universe

Cold dark matter may be made of superweakly-interacting massive particles, superWIMPs, that naturally inherit the desired relic density from late decays of metastable WIMPs. Well-motivated examples are weak-scale gravitinos in supergravity and Kaluza-Klein gravitons from extra dimensions. These particles are impossible to detect in all dark matter experiments. We find, however, that superWIMP dark matter may be discovered through cosmological signatures from the early universe. In particular, superWIMP dark matter has observable consequences for Big Bang nucleosynthesis and the cosmic microwave background (CMB), and may explain the observed underabundance of 7Li without upsetting the concordance between deuterium and CMB baryometers. We discuss implications for future probes of CMB black body distortions and collider searches for new particles. In the course of this study, we also present a model-independent analysis of entropy production from late-decaying particles in light of WMAP data.Comment: 19 pages, 5 figures, typos correcte

Evaluation of Hungarian Wines for Resveratrol by Overpressured Layer Chromatography

A method, including solid phase extraction sample preparation, overpressured layer chromatographic separation and subsequent densitometric evaluation, was developed for measurement of total resveratrol (cis- and trans-isomers) content of wine. The amount of resveratrol was determined in wine samples from different winemaking regions of Hungary. The total resveratrol was high in Hungarian red wines (3.6–11 mg/L), and much lower in white ones (0.04–1.5 mg/L)

Analytic models of plausible gravitational lens potentials

Gravitational lenses on galaxy scales are plausibly modelled as having ellipsoidal symmetry and a universal dark matter density profile, with a Sersic profile to describe the distribution of baryonic matter. Predicting all lensing effects requires knowledge of the total lens potential: in this work we give analytic forms for that of the above hybrid model. Emphasising that complex lens potentials can be constructed from simpler components in linear combination, we provide a recipe for attaining elliptical symmetry in either projected mass or lens potential. We also provide analytic formulae for the lens potentials of Sersic profiles for integer and half-integer index. We then present formulae describing the gravitational lensing effects due to smoothly-truncated universal density profiles in cold dark matter model. For our isolated haloes the density profile falls off as radius to the minus fifth or seventh power beyond the tidal radius, functional forms that allow all orders of lens potential derivatives to be calculated analytically, while ensuring a non-divergent total mass. We show how the observables predicted by this profile differ from that of the original infinite-mass NFW profile. Expressions for the gravitational flexion are highlighted. We show how decreasing the tidal radius allows stripped haloes to be modelled, providing a framework for a fuller investigation of dark matter substructure in galaxies and clusters. Finally we remark on the need for finite mass halo profiles when doing cosmological ray-tracing simulations, and the need for readily-calculable higher order derivatives of the lens potential when studying catastrophes in strong lenses.Comment: 24 pages, 10 figures, matches published versio

Percolation in three-dimensional random field Ising magnets

The structure of the three-dimensional random field Ising magnet is studied by ground state calculations. We investigate the percolation of the minority spin orientation in the paramagnetic phase above the bulk phase transition, located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the Gaussian random fields (J=1). With an external field H there is a disorder strength dependent critical field +/- H_c(Delta) for the down (or up) spin spanning. The percolation transition is in the standard percolation universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/- 0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <= Delta_p. When, with zero external field, Delta is decreased from a large value there is a transition from the simultaneous up and down spin spanning, with probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta). We provide evidence that this is asymptotically true even at H=0 for Delta_c < Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is approached from above. Percolation implies extra finite size effects in the ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review

A Quantum-Mechanical Equivalent-Photon Spectrum for Heavy-Ion Physics

In a previous paper, we calculated the fully quantum-mechanical cross section for electromagnetic excitation during peripheral heavy-ion collisions. Here, we examine the sensitivity of that cross section to the detailed structure of the projectile and target nuclei. At the transition energies relevant to nuclear physics, we find the cross section to be weakly dependent on the projectile charge radius, and to be sensitive to only the leading momentum-transfer dependence of the target transition form factors. We exploit these facts to derive a quantum-mechanical ``equivalent-photon spectrum'' valid in the long-wavelength limit. This improved spectrum includes the effects of projectile size, the finite longitudinal momentum transfer required by kinematics, and the response of the target nucleus to the off-shell photon.Comment: 19 pages, 5 figure