On the stability of travelling waves with vorticity obtained by minimisation

We modify the approach of Burton and Toland [Comm. Pure Appl. Math. (2011)] to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the function space to a class of stream functions that do not correspond necessarily to travelling profiles. In particular, for smooth profiles and smooth stream functions, the normal component of the velocity field at the free boundary is not required a priori to vanish in some Galilean coordinate system. Travelling periodic waves are obtained by a direct minimisation of a functional that corresponds to the total energy and that is therefore preserved by the time-dependent evolutionary problem (this minimisation appears in Burton and Toland after a first maximisation). In addition, we not only use the circulation along the upper boundary as a constraint, but also the total horizontal impulse (the velocity becoming a Lagrange multiplier). This allows us to preclude parallel flows by choosing appropriately the values of these two constraints and the sign of the vorticity. By stability, we mean conditional energetic stability of the set of minimizers as a whole, the perturbations being spatially periodic of given period.Comment: NoDEA Nonlinear Differential Equations and Applications, to appea

Non-invasive laminar inference with MEG: comparison of methods and source inversion algorithms

Magnetoencephalography (MEG) is a direct measure of neuronal current flow; its anatomical resolution is therefore not constrained by physiology but rather by data quality and the models used to explain these data. Recent simulation work has shown that it is possible to distinguish between signals arising in the deep and superficial cortical laminae given accurate knowledge of these surfaces with respect to the MEG sensors. This previous work has focused around a single inversion scheme (multiple sparse priors) and a single global parametric fit metric (free energy). In this paper we use several different source inversion algorithms and both local and global, as well as parametric and non-parametric fit metrics in order to demonstrate the robustness of the discrimination between layers. We find that only algorithms with some sparsity constraint can successfully be used to make laminar discrimination. Importantly, local t-statistics, global cross-validation and free energy all provide robust and mutually corroborating metrics of fit. We show that discrimination accuracy is affected by patch size estimates, cortical surface features, and lead field strength, which suggests several possible future improvements to this technique. This study demonstrates the possibility of determining the laminar origin of MEG sensor activity, and thus directly testing theories of human cognition that involve laminar- and frequency-specific mechanisms. This possibility can now be achieved using recent developments in high precision MEG, most notably the use of subject-specific head-casts, which allow for significant increases in data quality and therefore anatomically precise MEG recordings

Testing Lorentz invariance of dark matter

We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.Comment: 42 pages, 9 figure

Recurrent measurement of frailty is important for mortality prediction: findings from the North West Adelaide Health Study

OBJECTIVES:Frailty places individuals at greater risk of adverse health outcomes. However, it is a dynamic condition and may not always lead to decline. Our objective was to determine the relationship between frailty status (at baseline and follow-up) and mortality using both the frailty phenotype (FP) and frailty index (FI). DESIGN:Population-based cohort. SETTING:Community-dwelling older adults. PARTICIPANTS:A total of 909 individuals aged 65 years or older (55% female), mean age 74.4 (SD 6.2) years, had frailty measurement at baseline. Overall, 549 participants had frailty measurement at two time points. MEASUREMENTS:Frailty was measured using the FP and FI, with a mean 4.5 years between baseline and follow-up. Mortality was matched to official death records with a minimum of 10 years of follow-up. RESULTS:For both measures, baseline frailty was a significant predictor of mortality up to 10 years, with initially good predictive ability (area under the curve [AUC] = .8-.9) decreasing over time. Repeated measurement at follow-up resulted in good prediction compared with lower (AUC = .6-.7) discrimination of equivalent baseline frailty status. In a multivariable model, frailty measurement at follow-up was a stronger predictor of mortality compared with baseline. Frailty change for the Continuous FI was a significant predictor of decreased or increased mortality risk based on corresponding improvement or worsening of score (hazard ratio = 1.04; 95% confidence interval = 1.02-1.07; P = .001). CONCLUSIONS:Frailty measurement is a good predictor of mortality up to 10 years; however, recency of frailty measurement is important for improved prediction. A regular review of frailty status is required in older adults.Mark Q. Thompson, Olga Theou, Graeme R. Tucker, Robert J. Adams, and Renuka Visvanatha

Prevention is better than cure, but...: Preventive medication as a risk to ordinariness?

Preventive health remains at the forefront of public health concerns; recent initiatives, such as the NHS health check, may lead to recommendations for medication in response to the identification of 'at risk' individuals. Little is known about lay views of preventive medication. This paper uses the case of aspirin as a prophylactic against heart disease to explore views among people invited to screening for a trial investigating the efficacy of such an approach. Qualitative interviews (N=46) and focus groups (N=5, participants 31) revealed dilemmas about preventive medication in the form of clashes between norms: first, in general terms, assumptions about the benefit of prevention were complicated by dislike of medication; second, the individual duty to engage in prevention was complicated by the need not to be over involved with one's own health; third, the potential appeal of this alternative approach to health promotion was complicated by unease about the implications of encouraging irresponsible behaviour among others. Though respondents made different decisions about using the drug, they reported very similar ways of trying to resolve these conflicts, drawing upon concepts of necessity and legitimisation and the special ordinariness of the particular dru

Non-paraxial Split-step Finite-difference Method for Beam Propagation

A method based on symmetrized splitting of the propagation operator in the finite difference scheme for non-paraxial beam propagation is presented. The formulation allows the solution of the second order scalar wave equation without having to make the slowly varying envelope and one-way propagation approximations. The method is highly accurate and numerically efficient. Unlike most Padé approximant based methods, it is non-iterative in nature and requires less computation. The method can be used for bi-directional propagation as well

Precision Measurement of the Proton and Deuteron Spin Structure Functions g2 and Asymmetries A2

We have measured the spin structure functions g2p and g2d and the virtual photon asymmetries A2p and A2d over the kinematic range 0.02 < x < 0.8 and 0.7 < Q^2 < 20 GeV^2 by scattering 29.1 and 32.3 GeV longitudinally polarized electrons from transversely polarized NH3 and 6LiD targets. Our measured g2 approximately follows the twist-2 Wandzura-Wilczek calculation. The twist-3 reduced matrix elements d2p and d2n are less than two standard deviations from zero. The data are inconsistent with the Burkhardt-Cottingham sum rule if there is no pathological behavior as x->0. The Efremov-Leader-Teryaev integral is consistent with zero within our measured kinematic range. The absolute value of A2 is significantly smaller than the sqrt[R(1+A1)/2] limit.Comment: 12 pages, 4 figures, 2 table

Standard Model baryogenesis through four-fermion operators in braneworlds

We study a new baryogenesis scenario in a class of braneworld models with low fundamental scale, which typically have difficulty with baryogenesis. The scenario is characterized by its minimal nature: the field content is that of the Standard Model and all interactions consistent with the gauge symmetry are admitted. Baryon number is violated via a dimension-6 proton decay operator, suppressed today by the mechanism of quark-lepton separation in extra dimensions; we assume that this operator was unsuppressed in the early Universe due to a time-dependent quark-lepton separation. The source of CP violation is the CKM matrix, in combination with the dimension-6 operators. We find that almost independently of cosmology, sufficient baryogenesis is nearly impossible in such a scenario if the fundamental scale is above 100 TeV, as required by an unsuppressed neutron-antineutron oscillation operator. The only exception producing sufficient baryon asymmetry is a scenario involving out-of-equilibrium c quarks interacting with equilibrium b quarks.Comment: 39 pages, 5 figures v2: typos, presentational changes, references and acknowledgments adde

What Can WMAP Tell Us About The Very Early Universe? New Physics as an Explanation of Suppressed Large Scale Power and Running Spectral Index

The Wilkinson Microwave Anisotropy Probe microwave background data may be giving us clues about new physics at the transition from a ``stringy'' epoch of the universe to the standard Friedmann Robertson Walker description. Deviations on large angular scales of the data, as compared to theoretical expectations, as well as running of the spectral index of density perturbations, can be explained by new physics whose scale is set by the height of an inflationary potential. As examples of possible signatures for this new physics, we study the cosmic microwave background spectrum for two string inspired models: 1) modifications to the Friedmann equations and 2) velocity dependent potentials. The suppression of low ``l'' modes in the microwave background data arises due to the new physics. In addition, the spectral index is red (n<1) on small scales and blue (n>1) on large scales, in agreement with data.Comment: 18 pages, 2 figures, submitted for publication in Physical Review D, references added in this versio