Refraction of dispersive shock waves

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of defocusing nonlinear Schr\"odinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.Comment: 45 pages, 23 figures, minor revisio

Comparison of coherent and weakly incoherent transport models for the interlayer magnetoresistance of layered Fermi liquids

The interlayer magnetoresistance of layered metals in a tilted magnetic field is calculated for two distinct models for the interlayer transport. The first model involves coherent interlayer transport and makes use of results of semi-classical or Bloch-Boltzmann transport theory. The second model involves weakly incoherent interlayer transport where the electron is scattered many times within a layer before tunneling into the next layer. The results are relevant to the interpretation of experiments on angular-dependent magnetoresistance oscillations (AMRO) in quasi-one- and quasi-two-dimensional metals. We find that the dependence of the magnetoresistance on the direction of the magnetic field is identical for both models except when the field is almost parallel to the layers. An important implication of this result is that a three-dimensional Fermi surface is not necessary for the observation of the Yamaji and Danner oscillations seen in quasi-two- and quasi-one-dimensional metals, respectively. A universal expression is given for the dependence of the resistance at AMRO maxima and minima on the magnetic field and scattering time (and thus the temperature). We point out three distinctive features of coherent interlayer transport: (i) a beat frequency in the magnetic oscillations of quasi-two-dimensional systems, (ii) a peak in the angular-dependent magnetoresistance when the field is sufficiently large and parallel to the layers, and (iii) a crossover from a linear to a quadratic field dependence for the magnetoresistance when the field is parallel to the layers. Properties (i) and (ii) are compared with published experimental data for a range of quasi-two-dimensional organic metals and for Sr2RuO4.Comment: 21 pages, RevTeX + epsf, 4 figures. Published version. Subsection added. References update

Development and initial validation of a measure of metacognitive beliefs in health anxiety: The MCQ-HA

Metacognitive beliefs have been shown to correlate with emotional disorders and more recently have been implicated in health anxiety. Research exploring these beliefs have tended to use the Metacognition Questionnaire (MCQ), which is a general measure. To facilitate research on the metacognitive model applied to health anxiety the present study reports on the development and initial evaluation of a new specific metacognitive measure of health anxiety, the Metacognitions Questionnaire-Health Anxiety (MCQ-HA). Principal components analysis identified 14 suitable items to be explored. Subsequent exploratory factor analysis of the MCQ-HA identified three factors: “Beliefs that Thoughts can cause Illness”, “Beliefs about Biased thinking”, and “Beliefs that Thoughts are Uncontrollable”. Confirmatory factor analysis supported the three factor model with all selected goodness-of-fit statistics equivalent to or better than recommended values. Preliminary evidence suggests good internal-consistency, incremental, convergent and discriminant validity in relation to associated measures. The MCQ-HA appears to be a potentially useful predictor of health anxiet

Synoptic-to-planetary scale wind variability enhances phytoplankton biomass at ocean fronts

In nutrient-limited conditions, phytoplankton growth at fronts is enhanced by winds, which drive upward nutrient fluxes via enhanced turbulent mixing and upwelling. Hence, depth-integrated phytoplankton biomass can be 10 times greater at isolated fronts. Using theory and two-dimensional simulations with a coupled physical-biogeochemical ocean model, this paper builds conceptual understanding of the physical processes driving upward nutrient fluxes at fronts forced by unsteady winds with timescales of 4–16 days. The largest vertical nutrient fluxes occur when the surface mixing layer penetrates the nutricline, which fuels phytoplankton in the mixed layer. At a front, mixed layer deepening depends on the magnitude and direction of the wind stress, cross-front variations in buoyancy and velocity at the surface, and potential vorticity at the base of the mixed layer, which itself depends on past wind events. Consequently, mixing layers are deeper and more intermittent in time at fronts than outside fronts. Moreover, mixing can decouple in time from the wind stress, even without other sources of physical variability. Wind-driven upwelling also enhances depth-integrated phytoplankton biomass at fronts; when the mixed layer remains shallower than the nutricline, this results in enhanced subsurface phytoplankton. Oscillatory along-front winds induce both oscillatory and mean upwelling. The mean effect of oscillatory vertical motion is to transiently increase subsurface phytoplankton over days to weeks, whereas slower mean upwelling sustains this increase over weeks to months. Taken together, these results emphasize that wind-driven phytoplankton growth is both spatially and temporally intermittent and depends on a diverse combination of physical processes.DBW was supported by the National Science Foundation postdoctoral research fellowship program, award number 1421125. J.R.T. was supported by the Natural Environment Research Council, award NE/J010472/1