The Dynamical Mordell-Lang problem

Let X be a Noetherian space, let f be a continuous self-map on X, let Y be a closed subset of X, and let x be a point on X. We show that the set S consisting of all nonnegative integers n such that f^n(x) is in Y is a union of at most finitely many arithmetic progressions along with a set of Banach density zero. In particular, we obtain that given any quasi-projective variety X, any rational self-map map f on X, any subvariety Y of X, and any point x in X whose orbit under f is in the domain of definition for f, the set S is a finite union of arithmetic progressions together with a set of Banach density zero. We prove a similar result for the backward orbit of a point

Dark Matter Annihilation Signatures from Electroweak Bremsstrahlung

We examine observational signatures of dark matter annihilation in the Milky Way arising from electroweak bremsstrahlung contributions to the annihilation cross section. It has been known for some time that photon bremsstrahlung may significantly boost DM annihilation yields. Recently, we have shown that electroweak bremsstrahlung of W and Z gauge bosons can be the dominant annihilation channel in some popular models with helicity-suppressed 2 --> 2 annihilation. W/Z-bremsstrahlung is particularly interesting because the gauge bosons produced via annihilation subsequently decay to produce large correlated fluxes of electrons, positrons, neutrinos, hadrons (including antiprotons) and gamma rays, which are all of importance in indirect dark matter searches. Here we calculate the spectra of stable annihilation products produced via gamma/W/Z-bremsstrahlung. After modifying the fluxes to account for the propagation through the Galaxy, we set upper bounds on the annihilation cross section via a comparison with observational data. We show that stringent cosmic ray antiproton limits preclude a sizable dark matter contribution to observed cosmic ray positron fluxes in the class of models for which the bremsstrahlung processes dominate.Comment: 11 pages, 6 figures. Updated to match PRD versio

Electroweak Bremsstrahlung in Dark Matter Annihilation

A conservative upper bound on the total dark matter (DM) annihilation rate can be obtained by constraining the appearance rate of the annihilation products which are hardest to detect. The production of neutrinos, via the process $\chi \chi \to \bar\nu \nu$, has thus been used to set a strong general bound on the dark matter annihilation rate. However, Standard Model radiative corrections to this process will inevitably produce photons which may be easier to detect. We present an explicit calculation of the branching ratios for the electroweak bremsstrahlung processes $\chi \chi \to \bar\nu \nu Z$ and $\chi \chi \to \bar\nu e W$. These modes inevitably lead to electromagnetic showers and further constraints on the DM annihilation cross-section. In addition to annihilation, our calculations are also applicable to the case of dark matter decay.Comment: 7 pages, 4 figures. New appendix with an extensive discussion of Majorana fermions and helicity suppression

Conservatism implications of shock test tailoring for multiple design environments

A method for analyzing shock conservation in test specifications that have been tailored to qualify a structure for multiple design environments is discussed. Shock test conservation is qualified for shock response spectra, shock intensity spectra and ranked peak acceleration data in terms of an Index of Conservation (IOC) and an Overtest Factor (OTF). The multi-environment conservation analysis addresses the issue of both absolute and average conservation. The method is demonstrated in a case where four laboratory tests have been specified to qualify a component which must survive seven different field environments. Final judgment of the tailored test specification is shown to require an understanding of the predominant failure modes of the test item

Searching for Dark Matter at the LHC with a Mono-Z

We investigate a mono-Z process as a potential dark matter search strategy at the LHC. In this channel a single Z boson recoils against missing transverse momentum, attributed to dark matter particles, $\chi$, which escape the detector. This search strategy is related, and complementary to, monojet and monophoton searches. For illustrative purposes we consider the process $q\bar{q} -> \chi\chi Z$ in a toy dark matter model, where the Z boson is emitted from either the initial state quarks, or from the internal propagator. Among the signatures of this process will be a pair of muons with high pT that reconstruct to the invariant mass of the Z, and large amounts of missing transverse energy. Being a purely electroweak signal, QCD and other Standard Model backgrounds are relatively easily removed with modest selection cuts. We compare the signal to Standard Model backgrounds and demonstrate that, even for conservative cuts, there exist regions of parameter space where the signal may be clearly visible above background in future LHC data, allowing either new discovery potential or the possibility of supplementing information about the dark sector beyond that available from other observable channels.Comment: 11 pages, 13 figure

Macroscopic modelling of the surface tension of polymer-surfactant systems

Polymer-surfactant mixtures are increasingly being used in a wide range of applications. Weakly-interacting systems, such as SDS/PEO and SDS/PVP, comprise ionic surfactants and neutral polymers, while strongly-interacting systems, such as SDS/POLYDMDAAC and C12TAB/NaPSS, comprise ionic surfactants and oppositely charged ionic polymers. The complex nature of interactions in the mixtures leads to interesting and surprising surface tension profiles as the concentrations of polymer and surfactant are varied. The purpose of our research has been to develop a model to explain these surface tension profiles and to understand how they relate to the formation of different complexes in the bulk solution. In this paper we shouw how an existing model based on the law of mass action can be extended to model the surface tension of weakly-interacting systems, and we also extend it further to produce a model for the surface tension of strongly interacting systems. Applying the model to a variety of strongly-interacting systems gives remarkable agreement with the experimental results. The model provides a sound theoretical basis for comparing and contrasting the behaviour of different systems and greatly enhances our understanding of the features observed

Coherent states and the classical-quantum limit considered from the point of view of entanglement

Three paradigms commonly used in classical, pre-quantum physics to describe particles (that is: the material point, the test-particle and the diluted particle (droplet model)) can be identified as limit-cases of a quantum regime in which pairs of particles interact without getting entangled with each other. This entanglement-free regime also provides a simplified model of what is called in the decoherence approach "islands of classicality", that is, preferred bases that would be selected through evolution by a Darwinist mechanism that aims at optimising information. We show how, under very general conditions, coherent states are natural candidates for classical pointer states. This occurs essentially because, when a (supposedly bosonic) system coherently exchanges only one quantum at a time with the (supposedly bosonic) environment, coherent states of the system do not get entangled with the environment, due to the bosonic symmetry.Comment: This is the definitive version of a paper entitled The classical-quantum limit considered from the point of view of entanglement: a survey (author T. Durt). The older version has been replaced by the definitive on