Diffusion of passive scalar in a finite-scale random flow

We consider a solvable model of the decay of scalar variance in a single-scale random velocity field. We show that if there is a separation between the flow scale k_flow^{-1} and the box size k_box^{-1}, the decay rate lambda ~ (k_box/k_flow)^2 is determined by the turbulent diffusion of the box-scale mode. Exponential decay at the rate lambda is preceded by a transient powerlike decay (the total scalar variance ~ t^{-5/2} if the Corrsin invariant is zero, t^{-3/2} otherwise) that lasts a time t~1/\lambda. Spectra are sharply peaked at k=k_box. The box-scale peak acts as a slowly decaying source to a secondary peak at the flow scale. The variance spectrum at scales intermediate between the two peaks (k_box0). The mixing of the flow-scale modes by the random flow produces, for the case of large Peclet number, a k^{-1+delta} spectrum at k>>k_flow, where delta ~ lambda is a small correction. Our solution thus elucidates the spectral make up of the ``strange mode,'' combining small-scale structure and a decay law set by the largest scales.Comment: revtex4, 8 pages, 4 figures; final published versio

Dissipation-Scale Turbulence in the Solar Wind

We present a cascade model for turbulence in weakly collisional plasmas that follows the nonlinear cascade of energy from the large scales of driving in the MHD regime to the small scales of the kinetic Alfven wave regime where the turbulence is dissipated by kinetic processes. Steady-state solutions of the model for the slow solar wind yield three conclusions: (1) beyond the observed break in the magnetic energy spectrum, one expects an exponential cut-off; (2) the widely held interpretation that this dissipation range obeys power-law behavior is an artifact of instrumental sensitivity limitations; and, (3) over the range of parameters relevant to the solar wind, the observed variation of dissipation range spectral indices from -2 to -4 is naturally explained by the varying effectiveness of Landau damping, from an undamped prediction of -7/3 to a strongly damped index around -4.Comment: 6 pages, 2 figures, accepted for publication in AIP Conference Proceedings on "Turbulence and Nonlinear Processes in Astrophysical Plasmas

Kinetic stability of Chapman-Enskog plasmas

In this paper, we investigate the kinetic stability of classical, collisional plasma - that is, plasma in which the mean-free-path $\lambda$ of constituent particles is short compared to the length scale $L$ over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared to the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman-Enskog (CE) expansion in $\lambda/L \ll 1$, and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma $\beta$, the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in magnetised plasma, we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the 'whisper instability') whose growth rate in some parameter regimes is large compared to other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of $\lambda$, the electron inertial scale $d_e$ and $\beta$. This work is of general consequence in emphasising the fact that high-$\beta$ collisional plasmas can be kinetically unstable; for strongly magnetised CE plasmas, the condition for instability is $\beta > L/\lambda$. In this situation, the determination of transport coefficients via the standard CE approach is not valid.Comment: 182 pages total (99 main text, remaining appendices), 31 figure

Self-similar turbulent dynamo

The amplification of magnetic fields in a highly conducting fluid is studied numerically. During growth, the magnetic field is spatially intermittent: it does not uniformly fill the volume, but is concentrated in long thin folded structures. Contrary to a commonly held view, intermittency of the folded field does not increase indefinitely throughout the growth stage if diffusion is present. Instead, as we show, the probability-density function (PDF) of the field strength becomes self-similar. The normalized moments increase with magnetic Prandtl number in a powerlike fashion. We argue that the self-similarity is to be expected with a finite flow scale and system size. In the nonlinear saturated state, intermittency is reduced and the PDF is exponential. Parallels are noted with self-similar behavior recently observed for passive-scalar mixing and for map dynamos.Comment: revtex, 4 pages, 5 figures; minor changes to match published versio

Astrophysical Gyrokinetics: Basic Equations and Linear Theory

Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of astrophysical plasmas, including accretion disks, the solar wind, and the interstellar and intracluster medium. On small scales, this turbulence is often expected to consist of highly anisotropic fluctuations with frequencies small compared to the ion cyclotron frequency. For a number of applications, the small scales are also collisionless, so a kinetic treatment of the turbulence is necessary. We show that this anisotropic turbulence is well described by a low frequency expansion of the kinetic theory called gyrokinetics. This paper is the first in a series to examine turbulent astrophysical plasmas in the gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations and explore the linear properties of gyrokinetics as a prelude to nonlinear simulations. The linear dispersion relation for gyrokinetics is obtained and its solutions are compared to those of hot-plasma kinetic theory. These results are used to validate the performance of the gyrokinetic simulation code {\tt GS2} in the parameter regimes relevant for astrophysical plasmas. New results on global energy conservation in gyrokinetics are also derived. We briefly outline several of the problems to be addressed by future nonlinear simulations, including particle heating by turbulence in hot accretion flows and in the solar wind, the magnetic and electric field power spectra in the solar wind, and the origin of small-scale density fluctuations in the interstellar medium.Comment: emulateapj, 24 pages, 10 figures, revised submission to ApJ: references added, typos corrected, reorganized and streamline

Mice Expressing Low Levels of CalDAG-GEFI Exhibit Markedly Impaired Platelet Activation With Minor Impact on HemostasisHighlights

OBJECTIVE: The tight regulation of platelet adhesiveness, mediated by the αIIbβ3 integrin, is critical for hemostasis and prevention of thrombosis. We recently demonstrated that integrin affinity in platelets is controlled by the guanine nucleotide exchange factor, CalDAG-GEFI (CD-GEFI), and its target, RAP1. In this study, we investigated whether low-level expression of CD-GEFI leads to protection from thrombosis without pathological bleeding in mice. APPROACH AND RESULTS: Cdg1(low) mice were generated by knockin of human CD-GEFI cDNA into the mouse Cdg1 locus. CD-GEFI expression in platelets from Cdg1(low) mice was reduced by ≈90% when compared with controls. Activation of RAP1 and αIIbβ3 was abolished at low agonist concentrations and partially inhibited at high agonist concentrations in Cdg1(low) platelets. Consistently, the aggregation response of Cdg1(low) platelets was weaker than that of wild-type platelets, but more efficient than that observed in Cdg1(-/-) platelets. Importantly, Cdg1(low) mice were strongly protected from arterial and immune complex-mediated thrombosis, with only minimal impact on primary hemostasis. CONCLUSIONS: Together, our studies suggest the partial inhibition of CD-GEFI function as a powerful new approach to safely prevent thrombotic complications

Resting pastures to improve land condition in northern Australia: guidelines based on the literature and simulation modelling

Pasture rest is a possible strategy for improving land condition in the extensive grazing lands of northern Australia. If pastures currently in poor condition could be improved, then overall animal productivity and the sustainability of grazing could be increased. The scientific literature is examined to assess the strength of the experimental information to support and guide the use of pasture rest, and simulation modelling is undertaken to extend this information to a broader range of resting practices, growing conditions and initial pasture condition. From this, guidelines are developed that can be applied in the management of northern Australia’s grazing lands and also serve as hypotheses for further field experiments. The literature on pasture rest is diverse but there is a paucity of data from much of northern Australia as most experiments have been conducted in southern and central parts of Queensland. Despite this, the limited experimental information and the results from modelling were used to formulate the following guidelines. Rest during the growing season gives the most rapid improvement in the proportion of perennial grasses in pastures; rest during the dormant winter period is ineffective in increasing perennial grasses in a pasture but may have other benefits. Appropriate stocking rates are essential to gain the greatest benefit from rest: if stocking rates are too high, then pasture rest will not lead to improvement; if stocking rates are low, pastures will tend to improve without rest. The lower the initial percentage of perennial grasses, the more frequent the rests should be to give a major improvement within a reasonable management timeframe. Conditions during the growing season also have an impact on responses with the greatest improvement likely to be in years of good growing conditions. The duration and frequency of rest periods can be combined into a single value expressed as the proportion of time during which resting occurs; when this is done the modelling suggests the greater the proportion of time that a pasture is rested, the greater is the improvement but this needs to be tested experimentally. These guidelines should assist land managers to use pasture resting but the challenge remains to integrate pasture rest with other pasture and animal management practices at the whole-property scale

Resting pastures to improve land condition in northern Australia: guidelines based on the literature and simulation modelling

Pasture rest is a possible strategy for improving land condition in the extensive grazing lands of northern Australia. If pastures currently in poor condition could be improved, then overall animal productivity and the sustainability of grazing could be increased. The scientific literature is examined to assess the strength of the experimental information to support and guide the use of pasture rest, and simulation modelling is undertaken to extend this information to a broader range of resting practices, growing conditions and initial pasture condition. From this, guidelines are developed that can be applied in the management of northern Australia’s grazing lands and also serve as hypotheses for further field experiments. The literature on pasture rest is diverse but there is a paucity of data from much of northern Australia as most experiments have been conducted in southern and central parts of Queensland. Despite this, the limited experimental information and the results from modelling were used to formulate the following guidelines. Rest during the growing season gives the most rapid improvement in the proportion of perennial grasses in pastures; rest during the dormant winter period is ineffective in increasing perennial grasses in a pasture but may have other benefits. Appropriate stocking rates are essential to gain the greatest benefit from rest: if stocking rates are too high, then pasture rest will not lead to improvement; if stocking rates are low, pastures will tend to improve without rest. The lower the initial percentage of perennial grasses, the more frequent the rests should be to give a major improvement within a reasonable management timeframe. Conditions during the growing season also have an impact on responses with the greatest improvement likely to be in years of good growing conditions. The duration and frequency of rest periods can be combined into a single value expressed as the proportion of time during which resting occurs; when this is done the modelling suggests the greater the proportion of time that a pasture is rested, the greater is the improvement but this needs to be tested experimentally. These guidelines should assist land managers to use pasture resting but the challenge remains to integrate pasture rest with other pasture and animal management practices at the whole-property scale

Density matrix algorithm for the calculation of dynamical properties of low dimensional systems

I extend the scope of the density matrix renormalization group technique developed by White to the calculation of dynamical correlation functions. As an application and performance evaluation I calculate the spin dynamics of the 1D Heisenberg chain.Comment: 4 pages + 4 figures in one Latex + 4 postscript file