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Breaking Kelvin: Circulation conservation and vortex breakup in MHD at low Magnetic Prandtl Number

In this paper we examine the role of weak magnetic fields in breaking Kelvin's circulation theorem and in vortex breakup in two-dimensional magnetohydrodynamics for the physically important case of a low magnetic Prandtl number (low $Pm$) fluid. We consider three canonical inviscid solutions for the purely hydrodynamical problem, namely a Gaussian vortex, a circular vortex patch and an elliptical vortex patch. We examine how magnetic fields lead to an initial loss of circulation $\Gamma$ and attempt to derive scaling laws for the loss of circulation as a function of field strength and diffusion as measured by two non-dimensional parameters. We show that for all cases the loss of circulation depends on the integrated effects of the Lorentz force, with the patch cases leading to significantly greater circulation loss. For the case of the elliptical vortex the loss of circulation depends on the total area swept out by the rotating vortex and so this leads to more efficient circulation loss than for a circular vortex.Comment: 21 pages, 12 figure

Stability analysis of collective neutrino oscillations in the supernova accretion phase with realistic energy and angle distributions

We revisit our previous results on the matter suppression of self-induced neutrino flavor conversions during a supernova (SN) accretion phase, performing a linearized stability analysis of the neutrino equations of motion, in the presence of realistic SN density profiles. In our previous numerical study, we used a simplified model based on an isotropic neutrino emission with a single typical energy. Here, we take into account realistic neutrino energy and angle distributions. We find that multi-energy effects have a sub-leading impact in the flavor stability of the SN neutrino fluxes with respect to our previous single-energy results. Conversely, realistic forward-peaked neutrino angular distributions would enhance the matter suppression of the self-induced oscillations with respect to an isotropic neutrino emission. As a result, in our models for iron-core SNe, collective flavor conversions have a negligible impact on the characterization of the observable neutrino signal during the accretion phase. Instead, for a low-mass O-Ne-Mg core SN model, with lower matter density profile and less forward-peaked angular distributions, collective conversions are possible also at early times.Comment: v2: 8 pages, 3 eps figures. Revised version. Minor changes. References updated. Matches the version published on PR

Impact of elasticity on the piezoresponse of adjacent ferroelectric domains investigated by scanning force microscopy

As a consequence of elasticity, mechanical deformations of crystals occur on a length scale comparable to their thickness. This is exemplified by applying a homogeneous electric field to a multi-domain ferroelectric crystal: as one domain is expanding the adjacent ones are contracting, leading to clamping at the domain boundaries. The piezomechanically driven surface corrugation of micron-sized domain patterns in thick crystals using large-area top electrodes is thus drastically suppressed, barely accessible by means of piezoresponse force microscopy

No collective neutrino flavor conversions during the supernova accretion phase

The large neutrino fluxes emitted with a distinct flavor hierarchy from core-collapse supernovae (SNe) during the post-bounce accretion phase, offer the best opportunity to detect effects from neutrino flavor oscillations. We perform a dedicated study of the SN neutrino flavor evolution during the accretion phase, using results from recent neutrino radiation hydrodynamics simulations. In contrast to what expected in the presence of only neutrino-neutrino interactions, we find that the multi-angle effects associated with the dense ordinary matter suppress collective oscillations. This is related to the high matter densities during the accretion phase in core-collapse SNe of massive iron-core progenitors. The matter suppression implies that neutrino oscillations will start outside the neutrino transport region and therefore will have a negligible impact on the neutrino heating and the explosion dynamics. Furthermore, the possible detection of the next galactic SN neutrino signal from the accretion phase, based on the usual Mikheyev- Smirnov-Wolfenstein effect in the SN mantle and Earth matter effects, can reveal the neutrino mass hierarchy in the case that the mixing angle $\theta_{13}$ is not very small.Comment: (4 pages, 4 eps figures, v2 revised version. Discussion clarified. Matches the version published on PRL

Equation of motion method for Full Counting Statistics: Steady state superradiance

For the multi-mode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant generating function. Approximating the exact system of equations at the level of cumulant generating function and system operators at lowest order, allows us to recover master equation results of the Full Counting Statistics for certain parameter regimes at very low cost of computation. The thermodynamic limit, that is not accessible with the master equation approach, can be derived analytically for different approximations.Comment: 7 pages, 3 figures, revised version, accepted by PR

Analysis of matter suppression in collective neutrino oscillations during the supernova accretion phase

The usual description of self-induced neutrino flavor conversions in core collapse supernovae (SNe) is based on the dominance of the neutrino density n_nu over the net electron density n_e. However, this condition is not met during the post-bounce accretion phase, when the dense matter in a SN is piled up above the neutrinosphere. As recently pointed-out, a dominant matter term in the anisotropic SN environment would dephase the flavor evolution for neutrinos traveling on different trajectories, challenging the occurrence of the collective behavior in the dense neutrino gas. Using the results from recent long term simulations of core-collapse SN explosions, based on three flavor Boltzmann neutrino transport in spherical symmetry, we find that both the situations of complete matter suppression (when n_e >> n_nu) and matter-induced decoherence (when n_e \gtrsim n_nu) of flavor conversions are realized during the accretion phase. The matter suppression at high densities prevents any possible impact of the neutrino oscillations on the neutrino heating and hence on the dynamics of the explosion. Furthermore, it changes the interpretation of the Earth matter effect on the SN neutrino signal during the accretion phase, allowing the possibility of the neutrino mass hierarchy discrimination at not too small values of the leptonic mixing angle \theta_{13} (i.e. \sin^2{\theta}_{13} \gtrsim 10^{-3}).Comment: Revised version (15 pages, 13 eps figures) published on Physical Review D. Discussion enlarged, references update

On Predicting the Solar Cycle using Mean-Field Models

We discuss the difficulties of predicting the solar cycle using mean-field models. Here we argue that these difficulties arise owing to the significant modulation of the solar activity cycle, and that this modulation arises owing to either stochastic or deterministic processes. We analyse the implications for predictability in both of these situations by considering two separate solar dynamo models. The first model represents a stochastically-perturbed flux transport dynamo. Here even very weak stochastic perturbations can give rise to significant modulation in the activity cycle. This modulation leads to a loss of predictability. In the second model, we neglect stochastic effects and assume that generation of magnetic field in the Sun can be described by a fully deterministic nonlinear mean-field model -- this is a best case scenario for prediction. We designate the output from this deterministic model (with parameters chosen to produce chaotically modulated cycles) as a target timeseries that subsequent deterministic mean-field models are required to predict. Long-term prediction is impossible even if a model that is correct in all details is utilised in the prediction. Furthermore, we show that even short-term prediction is impossible if there is a small discrepancy in the input parameters from the fiducial model. This is the case even if the predicting model has been tuned to reproduce the output of previous cycles. Given the inherent uncertainties in determining the transport coefficients and nonlinear responses for mean-field models, we argue that this makes predicting the solar cycle using the output from such models impossible.Comment: 22 Pages, 5 Figures, Preprint accepted for publication in Ap

Androgen-responsive non-coding small RNAs extend the potential of HCG stimulation to act as a bioassay of androgen sufficiency

Background: It is unclear whether a short-term change in circulating androgens is associated with changes in the transcriptome of the peripheral blood mononuclear cells (PBMC). Aims & Methods: To explore the effect of hCG-stimulation on the PBMC-transcriptome, 12 boys with a median age (range) of 0.7yrs (0.3, 11.2) who received intramuscular hCG 1500u on 3 consecutive days as part of their investigations underwent transcriptomic array analysis on RNA extracted from peripheral blood mononuclear cells before and after hCG stimulation. Results: Median pre and post hCG testosterone for the overall group was 0.7nmol/l (<0.5,6) and 7.9nmol/l (<0.5, 31.5), respectively. Of the 12 boys, 3 (25%) did not respond to hCG stimulation with a pre and post median serum testosterone of <0.5nmol/l and <0.5nmol/l, respectively. When corrected for gene expression changes in the non-responders to exclude hCG effects, all 9 of the hCG responders consistently demonstrated a 20% or greater increase in the expression of piR-37153 and piR-39248, non-coding PIWI-interacting RNAs (piRNAs). In addition, of the 9 responders, 8, 6 and 4 demonstrated a 30%, 40% and 50% rise, respectively in a total of 2 further piRNAs. In addition, 3 of the responders showed a 50% or greater rise in the expression of another small RNA, SNORD5. On comparing fold change in serum testosterone with fold change in the above transcripts, a positive correlation was detected for SNORD5 (p=0.01). Conclusions: The identification of a dynamic and androgen-responsive PBMC-transcriptome extends the potential value of the hCG test for assessment of androgen sufficiency