Apparent suppression of turbulent magnetic dynamo action by a dc magnetic field

Numerical studies of the effect of a dc magnetic field on dynamo action (development of magnetic fields with large spatial scales), due to helically-driven magnetohydrodynamic turbulence, are reported. The apparent effect of the dc magnetic field is to suppress the dynamo action, above a relatively low threshold. However, the possibility that the suppression results from an improper combination of rectangular triply spatially-periodic boundary conditions and a uniform dc magnetic field is addressed: heretofore a common and convenient computational convention in turbulence investigations. Physical reasons for the observed suppression are suggested. Other geometries and boundary conditions are offered for which the dynamo action is expected not to be suppressed by the presence of a dc magnetic field component.Comment: To appear in Physics of Plasma

A Self-Consistent Marginally Stable State for Parallel Ion Cyclotron Waves

We derive an equation whose solutions describe self-consistent states of marginal stability for a proton-electron plasma interacting with parallel-propagating ion cyclotron waves. Ion cyclotron waves propagating through this marginally stable plasma will neither grow nor damp. The dispersion relation of these waves, {\omega} (k), smoothly rises from the usual MHD behavior at small |k| to reach {\omega} = {\Omega}p as k \rightarrow \pm\infty. The proton distribution function has constant phase-space density along the characteristic resonant surfaces defined by this dispersion relation. Our equation contains a free function describing the variation of the proton phase-space density across these surfaces. Taking this free function to be a simple "box function", we obtain specific solutions of the marginally stable state for a range of proton parallel betas. The phase speeds of these waves are larger than those given by the cold plasma dispersion relation, and the characteristic surfaces are more sharply peaked in the v\bot direction. The threshold anisotropy for generation of ion cyclotron waves is also larger than that given by estimates which assume bi-Maxwellian proton distributions.Comment: in press in Physics of Plasma

Velocity field distributions due to ideal line vortices

We evaluate numerically the velocity field distributions produced by a bounded, two-dimensional fluid model consisting of a collection of parallel ideal line vortices. We sample at many spatial points inside a rigid circular boundary. We focus on ``nearest neighbor'' contributions that result from vortices that fall (randomly) very close to the spatial points where the velocity is being sampled. We confirm that these events lead to a non-Gaussian high-velocity ``tail'' on an otherwise Gaussian distribution function for the Eulerian velocity field. We also investigate the behavior of distributions that do not have equilibrium mean-field probability distributions that are uniform inside the circle, but instead correspond to both higher and lower mean-field energies than those associated with the uniform vorticity distribution. We find substantial differences between these and the uniform case.Comment: 21 pages, 9 figures. To be published in Physical Review E (http://pre.aps.org/) in May 200

Low magnetic Prandtl number dynamos with helical forcing

We present direct numerical simulations of dynamo action in a forced Roberts flow. The behavior of the dynamo is followed as the mechanical Reynolds number is increased, starting from the laminar case until a turbulent regime is reached. The critical magnetic Reynolds for dynamo action is found, and in the turbulent flow it is observed to be nearly independent on the magnetic Prandtl number in the range from 0.3 to 0.1. Also the dependence of this threshold with the amount of mechanical helicity in the flow is studied. For the different regimes found, the configuration of the magnetic and velocity fields in the saturated steady state are discussed.Comment: 9 pages, 14 figure

Numerical study of dynamo action at low magnetic Prandtl numbers

We present a three--pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers $P_M$. The difficulty of resolving a large range of scales is circumvented by combining Direct Numerical Simulations, a Lagrangian-averaged model, and Large-Eddy Simulations (LES). The flow is generated by the Taylor-Green forcing; it combines a well defined structure at large scales and turbulent fluctuations at small scales. Our main findings are: (i) dynamos are observed from $P_M=1$ down to $P_M=10^{-2}$; (ii) the critical magnetic Reynolds number increases sharply with $P_M^{-1}$ as turbulence sets in and then saturates; (iii) in the linear growth phase, the most unstable magnetic modes move to small scales as $P_M$ is decreased and a Kazantsev $k^{3/2}$ spectrum develops; then the dynamo grows at large scales and modifies the turbulent velocity fluctuations.Comment: 4 pages, 4 figure

A central limit theorem for the zeroes of the zeta function

On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic interval. The result mirrors results of Soshnikov and others in random matrix theory. In an appendix we put forward some general theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.Comment: 22 pages. Incorporates referees suggestions. Contains minor corrections to published versio

Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function

We argue that the freezing transition scenario, previously explored in the statistical mechanics of 1/f-noise random energy models, also determines the value distribution of the maximum of the modulus of the characteristic polynomials of large N x N random unitary (CUE) matrices. We postulate that our results extend to the extreme values taken by the Riemann zeta-function zeta(s) over sections of the critical line s=1/2+it of constant length and present the results of numerical computations in support. Our main purpose is to draw attention to possible connections between the statistical mechanics of random energy landscapes, random matrix theory, and the theory of the Riemann zeta function.Comment: published version with a few misprints corrected and references adde

ERP evidence suggests executive dysfunction in ecstasy polydrug users

Background: Deficits in executive functions such as access to semantic/long-term memory have been shown in ecstasy users in previous research. Equally, there have been many reports of equivocal findings in this area. The current study sought to further investigate behavioural and electro-physiological measures of this executive function in ecstasy users. Method: Twenty ecstasy–polydrug users, 20 non-ecstasy–polydrug users and 20 drug-naïve controls were recruited. Participants completed background questionnaires about their drug use, sleep quality, fluid intelligence and mood state. Each individual also completed a semantic retrieval task whilst 64 channel Electroencephalography (EEG) measures were recorded. Results: Analysis of Variance (ANOVA) revealed no between-group differences in behavioural performance on the task. Mixed ANOVA on event-related potential (ERP) components P2, N2 and P3 revealed significant between-group differences in the N2 component. Subsequent exploratory univariate ANOVAs on the N2 component revealed marginally significant between-group differences, generally showing greater negativity at occipito-parietal electrodes in ecstasy users compared to drug-naïve controls. Despite absence of behavioural differences, differences in N2 magnitude are evidence of abnormal executive functioning in ecstasy–polydrug users

Recent Studies of the Cosmic-Ray Latitude Effect at High Altitudes

With an improved Geiger counter telescope, having an angular aperture of about ±15° from its axis, a series of balloon flights was made in August and September, 1947, at seven stations extending from San Antonio, Texas, to Saskatoon, Canada. The axis of the telescope in all cases was oriented in a vertical direction. All sets of equipment were compared with a standard to reduce all results to a common basis. The standard sets, in turn, were compared with an accurately constructed telescope which had been used to make an absolute determination of cosmic-ray intensity at the vertical in Pasadena. Two flights were made from each of the seven stations. The agreement between flights made within a few hours of each other at a given station is very good. Results from two flights made at a given station several days apart are not in general as consistent. Likewise, no monotonic increase of the radiation with increase of latitude was observed. Evidence is presented for rather large fluctuations at high altitudes of the lower energy components of cosmic rays. Some of the reasons for these fluctuations are discussed