Test particle propagation in magnetostatic turbulence. 1. Failure of the diffusion approximation

The equation which governs the quasi-linear approximation to the ensemble and gyro-phase averaged one-body probability distribution function is constructed from first principles. This derived equation is subjected to a thorough investigation in order to calculate the possible limitations of the quasi-linear approximation. It is shown that the reduction of this equation to a standard diffusion equation in the Markovian limit can be accomplished through the application of the adiabatic approximation. A numerical solution of the standard diffusion equation in the Markovian limit is obtained for the narrow parallel beam injection. Comparison of the diabatic and adiabatic results explicitly demonstrates the failure of the Markovian description of the probability distribution function. Through the use of a linear time-scale extension the failure of the adiabatic approximation, which leads to the Markovian limit, is shown to be due to mixing of the relaxation and interaction time scales in the presence of the strong mean field

Detection of bump-on-tail reduced electron velocity distributions at the electron foreshock boundary

Reduced velocity distributions are derived from three-dimensional measurements of the velocity distribution of electrons in the 7 to 500 eV range in the electron foreshock. Bump-on-tail reduced distributions are presented for the first time at the foreshock boundary consistent with Filbert and Kellogg's proposed time-of-flight mechanism for generating the electron beams. In a significant number of boundary crossings, bump-on-tail reduced distributions were found in consecutive 3 sec measurements made 9 sec apart. It is concluded that, although the beams are linearly unstable to plasma waves according to the Penrose criterion, they persist on a time scale of 3 to 15 sec

Test particle propagation in magnetostatic turbulence. 3: The approach to equilibrium

The asymptotic behavior, for large time, of the quasi-linear diabatic solutions and their local approximations is considered. A time averaging procedure is introduced which yields the averages of these solutions over time intervals which contain only large time values. A discussion of the quasi-linear diabatic solutions which is limited to those solutions that are bounded from below as functions of time is given. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity the time averaged quasi-linear diabatic solutions must approach isotropy (mu-independence). The first derivative with respect to mu of these solutions is also considered. This discussion is limited to first derivatives which are bounded functions of time. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity, the time averaged first derivative must approach zero everywhere in mu except at mu = 0 where it must approach a large value which is calculated. The impact of this large derivative on the quasi-linear expansion scheme is discussed. An H-theorem for the first local approximation to the quasi-linear diabatic solutions is constructed. Without time averaging, the H-theorem is used to determine sufficient conditions for the first local approximate solutions to asymptote, with increasing time, to exactly the same final state which the time averaged quasi-linear diabatic solutions must approach as discussed above

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained

On the theory of large amplitude Alfven waves

Large amplitude Alfvenic disturbances of arbitrary spatial shape and polarization are described by MHD equations, without resort to the usual assumption of planarity. However, because of their nonplanar nature, the direction of propagation of these disturbances cannot, in general, be determined by looking for minima in a variance matrix constructed from observed field fluctuations. When such minima exist, one is observing that subset of interplanetary Alfven waves that is essentially planar

Compact oscillons in the signum-Gordon model

We present explicit solutions of the signum-Gordon scalar field equation which have finite energy and are periodic in time. Such oscillons have a strictly finite size. They do not emit radiation.Comment: 12 pages, 4 figure

P424Short-term ACE Inhibition upregulates cardiac expression of SERCA2a and protects against ventricular arrhythmias in healthy rats

Introduction: Chronic angiotensin converting enzyme inhibitor (ACEIs) treatment can suppress arrhythmogenesis. To examine whether the effect is more immediate and independent of suppression of pathological remodelling, we tested the antiarrhythmic effect of short-term ACE inhibition in healthy normotensive rats. Methods and results: Wistar rats were administered with enalaprilat (ENA, i.p., 5 mg/kg every 12 h) or vehicle (CON) for two weeks. Cellular shortening was measured in isolated, electrically paced cardiomyocytes. Standard 12-lead electrocardiography was performed and, hearts of anesthetized open-chest rats were subjected to 6-min ischemia followed by 10-minute reperfusion to examine susceptibility to ventricular arrhythmias. Expressions of calcium regulating proteins (SERCA2a, cardiac sarco/endoplasmic reticulum Ca2+-ATPase; CSQ, calsequestrin; TRD, triadin; PLB, phospholamban; FKBP12.6, FK506-binding protein) were measured by Western blot and mRNA levels of L-type calcium channel (Cacna1c), ryanodine receptor (Ryr2) and potassium channels Kcnh2 and Kcnq1 were measured by qRT-PCR. ENA decreased systolic as well as diastolic blood pressure (by 20%, and by 31%, respectively, for both P<0.05) but enhanced shortening of cardiomyocytes at basal conditions (by 34%, P<0.05) and under beta-adrenergic stimulation (by 73%, P<0.05). Enalaprilat shortened QTc interval duration (CON: 78±1 ms vs. ENA: 72±2 ms; P<0.05) and significantly decreased the total duration of ventricular fibrillations (VF) and the number of VF episodes (P<0.05). Reduction in arrhythmogenesis was associated with a pronounced upregulation of SERCA2a and increased Cacna1c mRNA levels. Conclusion: Short-term ACEI treatment can provide protection against I/R injury-induced ventricular arrhythmias in healthy myocardium and this effect is associated with increased SERCA2a expression. CON ENA Calcium regulating proteins SERCA2a 100±20 304±13* CSQ 100±6 105±7 TRD 100±16 117±10 PLB 100±9 109±16 FKBP12 100±12 93±

Test your surrogate data before you test for nonlinearity

The schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis. In particular, we pinpoint some important caveats of the prominent algorithm of amplitude adjusted Fourier transform surrogates (AAFT) and compare it to the iterated AAFT (IAAFT), which is more consistent in representing the null hypothesis. It turns out that in many applications with real data the inferences of nonlinearity after marginal rejection of the null hypothesis were premature and have to be re-investigated taken into account the inaccuracies in the AAFT algorithm, mainly concerning the mismatching of the linear correlations. In order to deal with such inaccuracies we propose the use of linear together with nonlinear polynomials as discriminating statistics. The application of this setup to some well-known real data sets cautions against the use of the AAFT algorithm.Comment: 14 pages, 15 figures, submitted to Physical Review

Longitudinal study on nerve ultrasound and corneal confocal microscopy in NF155 paranodopathy

We report the case of a 27-year-old patient with subacute anti-neurofascin-155 neuropathy with bifacial palsy, who showed excellent response to rituximab. We provide longitudinal data of established clinical scores, nerve conduction studies, antibody titers, and novel imaging methods (nerve ultrasonography and corneal confocal microscopy). Clinical and electrophysiological improvement followed the reduction of serum antibody titer and correlated with a reduction of corneal inflammatory cellular infiltrates whereas the increase in the cross-sectional area of the peripheral nerves remained 12 months after first manifestation. Our findings suggest that novel techniques provide useful follow-up parameters in paranodopathies