Pulse propagation in discrete systems of coupled excitable cells

Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or the recovery is too fast. We give an asymptotic construction of pulses for spatially discrete FitzHugh-Nagumo systems which agrees well with numerical simulations and discuss evolution of initial data into pulses and pulse generation at a boundary. Formulas for the speed and length of pulses are also obtained.Comment: 16 pages, 10 figures, to appear in SIAM J. Appl. Mat

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

The Migdal Effect and Photon Bremsstrahlung in effective field theories of dark matter direct detection and coherent elastic neutrino-nucleus scattering

Dark matter direct detection experiments have limited sensitivity to light dark matter (below a few GeV), due to the challenges of lowering energy thresholds for the detection of nuclear recoil to below $\mathcal{O}(\mathrm{keV})$. While impressive progress has been made on this front, light dark matter remains the least constrained region of dark-matter parameter space. It has been shown that both ionization and excitation due to the Migdal effect and coherently-emitted photon bremsstrahlung from the recoiling atom can provide observable channels for light dark matter that would otherwise have been missed owing to the resulting nuclear recoil falling below the detector threshold. In this paper we extend previous work by calculating the Migdal effect and photon bremmstrahlung rates for a general set of interaction types, including those that are momentum-independent or -dependent, spin-independent or -dependent, as well as examining the rates for a variety of target materials, allowing us to place new experimental limits on some of these interaction types. Additionally, we include a calculation of these effects induced by the coherent scattering on nuclei of solar or atmospheric neutrinos. We demonstrate that the Migdal effect dominates over the bremsstrahlung effect for all targets considered for interactions induced by either dark matter or neutrinos. This reduces photon bremsstrahlung to irrelevancy for future direct detection experiments.Comment: 17 pages, 6 figure

New general formulation and experimental verification of harmonic clipping contours in high-frequency power devices

This paper presents a novel closed form solution for the theoretical calculation of harmonic clipping contours when an arbitrary number of harmonics is considered. The clipping contours can be used to design the loads of a high frequency power device in order to avoid drain current clipping, hence preventing strong non-linear effects. For the first time the predicted second harmonic contours are validated thoroughly by means of experimental characterization of GaN HEMT devices. The measured contours result in good agreement with the theory. Moreover, the effect of third harmonic load tuning is also assessed, and verified for the first time. These results prove that the clipping contours can be used as a tool for the systematic design of low distortion power amplifiers