75,722 research outputs found

    Annihilation Signals from Asymmetric Dark Matter

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    In the simplest models of asymmetric dark matter (ADM) annihilation signals are not expected, since the DM is non-self-conjugate and the relic density of anti-DM is negligible. We investigate a new class of models in which a symmetric DM component, in the `low-mass' 1-10 GeV regime favoured for linking the DM and baryon asymmetries, is repopulated through decays. We find that, in models without significant velocity dependence of the annihilation cross section, observational constraints generally force these decays to be (cosmologically) slow. These late decays can give rise to gamma-ray signal morphologies differing from usual annihilation profiles. A distinctive feature of such models is that signals may be absent from dwarf spheroidal galaxies.Comment: 31 pages, 9 figures, v3; minor corrections, and reference added - matches version published in JHE

    Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

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    In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem

    Mixed Hodge structures and formality of symmetric monoidal functors

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    We use mixed Hodge theory to show that the functor of singular chains with rational coefficients is formal as a lax symmetric monoidal functor, when restricted to complex schemes whose weight filtration in cohomology satisfies a certain purity property. This has direct applications to the formality of operads or, more generally, of algebraic structures encoded by a colored operad. We also prove a dual statement, with applications to formality in the context of rational homotopy theory. In the general case of complex schemes with non-pure weight filtration, we relate the singular chains functor to a functor defined via the first term of the weight spectral sequence.Comment: 26 page

    Phenomenology of left-right symmetric dark matter

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    We present a detailed study of dark matter phenomenology in low-scale left-right symmetric models. Stability of new fermion or scalar multiplets is ensured by an accidental matter parity that survives the spontaneous symmetry breaking of the gauge group by scalar triplets. The relic abundance of these particles is set by gauge interactions and gives rise to dark matter candidates with masses above the electroweak scale. Dark matter annihilations are thus modified by the Sommerfeld effect, not only in the early Universe, but also today, for instance, in the Center of the Galaxy. Majorana candidates - triplet, quintuplet, bi-doublet, and bi-triplet - bring only one new parameter to the model, their mass, and are hence highly testable at colliders and through astrophysical observations. Scalar candidates - doublet and 7-plet, the latter being only stable at the renormalizable level - have additional scalar-scalar interactions that give rise to rich phenomenology. The particles under discussion share many features with the well-known candidates wino, Higgsino, inert doublet scalar, sneutrino, and Minimal Dark Matter. In particular, they all predict a large gamma-ray flux from dark matter annihilations, which can be searched for with Cherenkov telescopes. We furthermore discuss models with unequal left-right gauge couplings, gR≠gLg_R \neq g_L, taking the recent experimental hints for a charged gauge boson with 2 TeV mass as a benchmark point. In this case, the dark matter mass is determined by the observed relic density.Comment: 32 + 23 pages, 4.5 MB; Minor changes and additional comments. Matches published versio

    Discrete models of force chain networks

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    A fundamental property of any material is its response to a localized stress applied at a boundary. For granular materials consisting of hard, cohesionless particles, not even the general form of the stress response is known. Directed force chain networks (DFCNs) provide a theoretical framework for addressing this issue, and analysis of simplified DFCN models reveal both rich mathematical structure and surprising properties. We review some basic elements of DFCN models and present a class of homogeneous solutions for cases in which force chains are restricted to lie on a discrete set of directions.Comment: 17 pages, 6 figures, dcds-B.cls; Minor corrections to version 2, but including an important factor of 2; Submitted to Discrete and Continuous Dynamical Systems B for special issue honoring David Schaeffe
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