75,722 research outputs found
Annihilation Signals from Asymmetric Dark Matter
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
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
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
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, , 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
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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