Estimates on Green functions of second order differential operators with singular coefficients

We investigate the Green functions G(x,x^{\prime}) of some second order differential operators on R^{d+1} with singular coefficients depending only on one coordinate x_{0}. We express the Green functions by means of the Brownian motion. Applying probabilistic methods we prove that when x=(0,{\bf x}) and x^{\prime}=(0,{\bf x}^{\prime}) (here x_{0}=0) lie on the singular hyperplanes then G(0,{\bf x};0,{\bf x}^{\prime}) is more regular than the Green function of operators with regular coefficients.Comment: 16 page

Galactic secondary positron flux at the Earth

Secondary positrons are produced by spallation of cosmic rays within the interstellar gas. Measurements have been typically expressed in terms of the positron fraction, which exhibits an increase above 10 GeV. Many scenarios have been proposed to explain this feature, among them some additional primary positrons originating from dark matter annihilation in the Galaxy. The PAMELA satellite has provided high quality data that has enabled high accuracy statistical analyses to be made, showing that the increase in the positron fraction extends up to about 100 GeV. It is therefore of paramount importance to constrain theoretically the expected secondary positron flux to interpret the observations in an accurate way. We find the secondary positron flux to be reproduced well by the available observations, and to have theoretical uncertainties that we quantify to be as large as about one order of magnitude. We also discuss the positron fraction issue and find that our predictions may be consistent with the data taken before PAMELA. For PAMELA data, we find that an excess is probably present after considering uncertainties in the positron flux, although its amplitude depends strongly on the assumptions made in relation to the electron flux. By fitting the current electron data, we show that when considering a soft electron spectrum, the amplitude of the excess might be far lower than usually claimed. We provide fresh insights that may help to explain the positron data with or without new physical model ingredients. PAMELA observations and the forthcoming AMS-02 mission will allow stronger constraints to be aplaced on the cosmic--ray transport parameters, and are likely to reduce drastically the theoretical uncertainties.Comment: 15 pages, 12 figures. The recent PAMELA data on the positron fraction (arXiv:0810.4995) have been included and the ensuing discussion has been extended. Accepted version in A&

Infinite barbarians

This paper discusses an infinite regress that looms behind a certain kind of historical explanation. The movement of one barbarian group is often explained by the movement of others, but those movements in turn call for an explanation. While their explanation can again be the movement of yet another group of barbarians, if this sort of explanation does not stop somewhere we are left with an infinite regress of barbarians. While that regress would be vicious, it cannot be accommodated by several general views about what viciousness in infinite regresses amounts to. This example is additional evidence that we should prefer a pluralist approach to infinite regresses

Improved sensitivity of H.E.S.S.-II through the fifth telescope focus system

The Imaging Atmospheric Cherenkov Telescope (IACT) works by imaging the very short flash of Cherenkov radiation generated by the cascade of relativistic charged particles produced when a TeV gamma ray strikes the atmosphere. This energetic air shower is initiated at an altitude of 10-30 km depending on the energy and the arrival direction of the primary gamma ray. Whether the best image of the shower is obtained by focusing the telescope at infinity and measuring the Cherenkov photon angles or focusing on the central region of the shower is a not obvious question. This is particularly true for large size IACT for which the depth of the field is much smaller. We address this issue in particular with the fifth telescope (CT5) of the High Energy Stereoscopic System (H.E.S.S.); a 28 m dish large size telescope recently entered in operation and sensitive to an energy threshold of tens of GeVs. CT5 is equipped with a focus system, its working principle and the expected effect of focusing depth on the telescope sensitivity at low energies (50-200 GeV) is discussed.Comment: In Proceedings of the 33rd International Cosmic Ray Conference (ICRC2013), Rio de Janeiro (Brazil

New Constraints from PAMELA anti-proton data on Annihilating and Decaying Dark Matter

Recently the PAMELA experiment has released its updated anti-proton flux and anti-proton to proton flux ratio data up to energies of ~200GeV. With no clear excess of cosmic ray anti-protons at high energies, one can extend constraints on the production of anti-protons from dark matter. In this letter, we consider both the cases of dark matter annihilating and decaying into standard model particles that produce significant numbers of anti-protons. We provide two sets of constraints on the annihilation cross-sections/decay lifetimes. In the one set of constraints we ignore any source of anti-protons other than dark matter, which give the highest allowed cross-sections/inverse lifetimes. In the other set we include also anti-protons produced in collisions of cosmic rays with interstellar medium nuclei, getting tighter but more realistic constraints on the annihilation cross-sections/decay lifetimes.Comment: 7 pages, 3 figures, 3 table

Micro-Capsules in Shear Flow

This paper deals with flow-induced shape transitions of elastic capsules. The state of the art concerning both theory and experiments is briefly reviewed starting with dynamically induced small deformation of initially spherical capsules and the formation of wrinkles on polymerized membranes. Initially non-spherical capsules show tumbling and tank-treading motion in shear flow. Theoretical descriptions of the transition between these two types of motion assuming a fixed shape are at variance with the full capsule dynamics obtained numerically. To resolve the discrepancy, we expand the exact equations of motion for small deformations and find that shape changes play a dominant role. We classify the dynamical phase transitions and obtain numerical and analytical results for the phase boundaries as a function of viscosity contrast, shear and elongational flow rate. We conclude with perspectives on timedependent flow, on shear-induced unbinding from surfaces, on the role of thermal fluctuations, and on applying the concepts of stochastic thermodynamics to these systems.Comment: 34 pages, 15 figure

Hyb-Seq for flowering plant systematics

High-throughput DNA sequencing (HTS) presents great opportunities for plant systematics, yet genomic complexity needs to be reduced for HTS to be effectively applied. We highlight Hyb-Seq as a promising approach, especially in light of the recent development of probes enriching 353 low-copy nuclear genes from any flowering plant taxon

Automorphism covariant representations of the holonomy-flux *-algebra

We continue an analysis of representations of cylindrical functions and fluxes which are commonly used as elementary variables of Loop Quantum Gravity. We consider an arbitrary principal bundle of a compact connected structure group and following Sahlmann's ideas define a holonomy-flux *-algebra whose elements correspond to the elementary variables. There exists a natural action of automorphisms of the bundle on the algebra; the action generalizes the action of analytic diffeomorphisms and gauge transformations on the algebra considered in earlier works. We define the automorphism covariance of a *-representation of the algebra on a Hilbert space and prove that the only Hilbert space admitting such a representation is a direct sum of spaces L^2 given by a unique measure on the space of generalized connections. This result is a generalization of our previous work (Class. Quantum. Grav. 20 (2003) 3543-3567, gr-qc/0302059) where we assumed that the principal bundle is trivial, and its base manifold is R^d.Comment: 34 pages, 1 figure, LaTeX2e, minor clarifying remark

Antimatter signals of singlet scalar dark matter

We consider the singlet scalar model of dark matter and study the expected antiproton and positron signals from dark matter annihilations. The regions of the viable parameter space of the model that are excluded by present data are determined, as well as those regions that will be probed by the forthcoming experiment AMS-02. In all cases, different propagation models are investigated, and the possible enhancement due to dark matter substructures is analyzed. We find that the antiproton signal is more easily detectable than the positron one over the whole parameter space. For a typical propagation model and without any boost factor, AMS-02 will be able to probe --via antiprotons-- the singlet model of dark matter up to masses of 600 GeV. Antiprotons constitute, therefore, a promising signal to constraint or detect the singlet scalar model.Comment: 24 pages, 8 figures. v2: minor improvements. Accepted for publication in JCA