Reconnection current sheet structure in a turbulent medium

In the presence of turbulence, magnetic field lines lose their dynamical identity and particles entrained on field lines diffuse through space at a rate determined by the amplitude of the turbulence. In previous work (Lazarian and Vishniac, 1999; Kowal et al., 2009; Eyink et al., 2011) we showed that this leads to reconnection speeds which are independent of resistivity. In particular, in Kowal et al. (2009) we showed that numerical simulations were consistent with the predictions of this model. Here we examine the structure of the current sheet in simulations of turbulent reconnection. Laminar flows consistent with the Sweet-Parker reconnection model produce very thin and well ordered currents sheets. On the other hand, the simulations of Kowal et al. (2009) show a strongly disordered state even for relatively low levels of turbulence. Comparing data cubes with and without reconnection, we find that large scale field reversals are the cumulative effect of many individual eddies, each of which has magnetic properties which are not very different from turbulent eddies in a homogeneous background. This implies that the properties of stationary and homogeneous MHD turbulence are a reasonable guide to understanding turbulence during large scale magnetic reconnection events. In addition, dissipation and high energy particle acceleration during reconnection events take place over a macroscopic volume, rather than being confined to a narrow zone whose properties depend on microscopic transport coefficients.

Reconnection studies under different types of turbulence driving

We study a model of fast magnetic reconnection in the presence of weak turbulence proposed by Lazarian and Vishniac (1999) using three-dimensional direct numerical simulations. The model has been already successfully tested in Kowal et al. (2009) confirming the dependencies of the reconnection speed V-rec on the turbulence injection power P-inj and the injection scale l(inj) expressed by a constraint V-rec similar to P(inj)(1/2)l(inj)(3/4)and no observed dependency on Ohmic resistivity. In Kowal et al. (2009), in order to drive turbulence, we injected velocity fluctuations in Fourier space with frequencies concentrated around k(inj) = 1/l(inj), as described in Alvelius (1999). In this paper, we extend our previous studies by comparing fast magnetic reconnection under different mechanisms of turbulence injection by introducing a new way of turbulence driving. The new method injects velocity or magnetic eddies with a specified amplitude and scale in random locations directly in real space. We provide exact relations between the eddy parameters and turbulent power and injection scale. We performed simulations with new forcing in order to study turbulent power and injection scale dependencies. The results show no discrepancy between models with two different methods of turbulence driving exposing the same scalings in both cases. This is in agreement with the Lazarian and Vishniac (1999) predictions. In addition, we performed a series of models with varying viscosity nu. Although Lazarian and Vishniac (1999) do not provide any prediction for this dependence, we report a weak relation between the reconnection speed with viscosity, V-rec similar to nu(-1/4).

First report on the kinetics of the uncatalyzed esterification of cellulose under homogeneous reaction conditions: a rationale for the effect of carboxylic acid anhydride chain-length on the degree of biopolymer substitution

The kinetics of the homogeneous acylation of microcrystalline cellulose, MCC, with carboxylic acid anhydrides with different acyl chain-length (Nc; ethanoic to hexanoic) in LiCl/N,N-dimethylacetamide have been studied by conductivity measurements from 65 to 85 A degrees C. We have employed cyclohexylmethanol, CHM, and trans-1,2-cyclohexanediol, CHD, as model compounds for the hydroxyl groups of the anhydroglucose unit of cellulose. The ratios of rate constants of acylation of primary (CHM; Prim-OH) and secondary (CHD; Sec-OH) groups have been employed, after correction, in order to split the overall rate constants of the reaction of MCC into contributions from the discrete OH groups. For the model compounds, we have found that k((Prim-OH))/k((Sec-OH)) > 1, akin to reactions of cellulose under heterogeneous conditions; this ratio increases as a function of increasing Nc. The overall, and partial rate constants of the acylation of MCC decrease from ethanoic- to butanoic-anhydride and then increase for pentanoic- and hexanoic anhydride, due to subtle changes in- and compensations of the enthalpy and entropy of activation.

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are computed using only their weights and degree of homogeneity. A key point of the main theorem is to find the number called polar ratio of this polynomial class. An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneity. The constancy of the L numbers in families formed by such arrangements is shown, with the deformed terms having weighted degree greater than the weighted degree of the initial germ. Moreover, using the results of Massey applied to families of function germs, we obtain the constancy of the homology of the Milnor fibre in this family of semi-weighted homogeneous arrangements.

Further results in J and CTOD estimation procedures for SE(T) fracture specimens - Part I: Homogeneous materials

This study provides further developments of the evaluation procedure for J and CTOD in SE(T) fracture specimens based on plastic eta-factors and load separation analysis. Non-linear finite element analyses for plane-strain and 3-D models provide the relationship between plastic work and crack driving forces which define the eta-values. Further analyses based on the load separation method define alternative eta-values for the analyzed specimen configurations. Overall, the present results provide improved estimation equations for J and CTOD as a function of loading condition (pin load vs. clamp ends), crack geometry and strain hardening properties. (C) 2011 Elsevier Ltd. All rights reserved.

Dynamical analysis of turbulence in fusion plasmas and nonlinear waves

Turbulence is one of the key problems of classical physics, and it has been the object of intense research in the last decades in a large spectrum of problems involving fluids, plasmas, and waves. In order to review some advances in theoretical and experimental investigations on turbulence a mini-symposium on this subject was organized in the Dynamics Days South America 2010 Conference. The main goal of this mini-symposium was to present recent developments in both fundamental aspects and dynamical analysis of turbulence in nonlinear waves and fusion plasmas. In this paper we present a summary of the works presented at this mini-symposium. Among the questions to be addressed were the onset and control of turbulence and spatio-temporal chaos. (C) 2011 Elsevier B. V. All rights reserved.

Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

Identification and characterization of drought/wet events homogeneous environments based on regional climate simulations

The objective of this study was to identify and characterize homogeneous environments based on the probability of drought/wet occurrence in the central-northern Brazil, considering Rondonia, Mato Grosso, Goias and Tocantins States. The drought index denominated the moisture anomaly Z-index (Z-index) was used. The input climate data for the drought index was generated by the regional climate model RegCM3 for the period from 1975 to 1989. As result of cluster analysis, it was identified 13 homogeneous environments. These environments were characterized based on the probability of drought/wet, relative density of drought/wet occurrence, annual rainfall variability and probability of drought occurrence during the rainy season (October to March). The Mato Grosso State had the highest number of homogeneous environments and the environment 11, located at southwest of this State had the highest probability of drought occurrence, 9%. The environment 10, located at the extreme east of Goias State, showed the lowest median for the total annual rainfall. The climatic event with the highest probability of occurrence in the study area is close to normal or normality moisture.

Turbulence driven particle transport in Texas Helimak

We analyze the turbulence driven particle transport in Texas Helimak [K. W. Gentle and H. He, Plasma Sci. Technol. 10, 284 (2008)], a toroidal plasma device with a one-dimensional equilibrium with magnetic curvature and shear. Alterations on the radial electric field, through an external voltage bias, change the spectral plasma characteristics inducing a dominant frequency for negative bias values and a broad band frequency spectrum for positive bias values. When applying a negative bias, the transport is high where the waves propagate with phase velocities near the plasma flow velocity, an indication that the transport is strongly affected by a wave particle resonant interaction. On the other hand, for positive bias values, the plasma has a reversed shear flow, and we observe that the transport is almost zero in the shearless radial region, an evidence of a transport barrier in this region. (c) 2012 American Institute of Physics. [doi:10.1063/1.3676607]

EQUIVALENCE OF REAL MILNOR FIBRATIONS FOR QUASI-HOMOGENEOUS SINGULARITIES

We show that for real quasi-homogeneous singularities f : (R-m, 0) -> (R-2, 0) with isolated singular point at the origin, the projection map of the Milnor fibration S-epsilon(m-1) \ K-epsilon -> S-1 is given by f/parallel to f parallel to. Moreover, for these singularities the two versions of the Milnor fibration, on the sphere and on a Milnor tube, are equivalent. In order to prove this, we show that the flow of the Euler vector field plays and important role. In addition, we present, in an easy way, a characterization of the critical points of the projection (f/parallel to f parallel to) : S-epsilon(m-1) \ K-epsilon -> S-1.

Homogeneous metallicities and radial velocities for Galactic globular clusters

Well determined radial velocities and abundances are essential for analyzing the properties of the globular cluster system of the Milky Way. However more than 50% of these clusters have no spectroscopic measure of their metallicity. In this context, this work provides new radial velocities and abundances for twenty Milky Way globular clusters which lack or have poorly known values for these quantities. The radial velocities and abundances are derived from spectra obtained at the Ca II triplet using the FORS2 imager and spectrograph at the VLT, calibrated with spectra of red giants in a number of clusters with well determined abundances. For about half of the clusters in our sample we present significant revisions of the existing velocities or abundances, or both. We also confirm the existence of a sizable abundance spread in the globular cluster M 54, which lies at the center of the Sagittarius dwarf galaxy. In addition evidence is provided for the existence of a small intrinsic internal abundance spread (sigma[Fe/H](int) approximate to 0.11-0.14 dex, similar to that of M 54) in the luminous distant globular cluster NGC 5824. This cluster thus joins the small number of Galactic globular clusters known to possess internal metallicity ([Fe/H]) spreads.

Self-organized criticality in MHD driven plasma edge turbulence

We analyze long-range time correlations and self-similar characteristics of the electrostatic turbulence at the plasma edge and scrape-off layer in the Tokamak Chauffage Alfven Bresillien (TCABR), with low and high Magnetohydrodynamics (MHD) activity. We find evidence of self-organized criticality (SOC), mainly in the region near the tokamak limiter. Comparative analyses of data before and during the MHD activity reveals that during the high mHD activity the Hurst parameter decreases. Finally, we present a cellular automaton whose parameters are adjusted to simulate the analyzed turbulence SOC change with the MHD activity variation. (C) 2011 Published by Elsevier B.V.

Particle Acceleration in Turbulence and Weakly Stochastic Reconnection

In this Letter we analyze the energy distribution evolution of test particles injected in three dimensional (3D) magnetohydrodynamic (MHD) simulations of different magnetic reconnection configurations. When considering a single Sweet-Parker topology, the particles accelerate predominantly through a first-order Fermi process, as predicted in [3] and demonstrated numerically in [8]. When turbulence is included within the current sheet, the acceleration rate is highly enhanced, because reconnection becomes fast and independent of resistivity [4,11] and allows the formation of a thick volume filled with multiple simultaneously reconnecting magnetic fluxes. Charged particles trapped within this volume suffer several head-on scatterings with the contracting magnetic fluctuations, which significantly increase the acceleration rate and results in a first-order Fermi process. For comparison, we also tested acceleration in MHD turbulence, where particles suffer collisions with approaching and receding magnetic irregularities, resulting in a reduced acceleration rate. We argue that the dominant acceleration mechanism approaches a second order Fermi process in this case.

Figures of equilibrium for tidally deformed non-homogeneous celestial bodies

Abstract (2,250 Maximum Characters): Several theories of tidal evolution, since the theory developed by Darwin in the XIX century, are based on the figure of equilibrium of the tidally deformed body. Frequently the adopted figure is a Jeans prolate spheroid. In some case, however, the rotation is important and Roche ellipsoids are used. The main limitations of these models are (a) they refer to homogeneous bodies; (b) the rotation axis is perpendicular to the plane of the orbit. This communication aims at presenting several results in which these hypotheses are not done. In what concerns the non-homogeneity, the presented results concerns initially bodies formed by N homogeneous layers and we study the non sphericity of each layer and relate them to the density distribution. The result is similar to the Clairaut figure of equilibrium, often used in planetary sciences, but taking into full account the tidal deformation. The case of the rotation axis non perpendicular to the orbital plane is much more complex and the study has been restricted for the moment to the case of homogeneous bodies.

Analysis of Electrostatic Turbulence Drive in Texas Helimak.

Plasma turbulence and particle transport in Texas Helimak change with the radial electric field profile modified by an external voltage bias. When the bias is positive, the turbulence shows enhanced level and broadband spectra with extreme events, similar to the turbulence in tokamak scrape-‐off layer. However, negative bias reduces the turbulence level and decreases the spectrum widths. Moreover, for negative biased shots, the particle transport is strongly affected by a wave particle resonant interaction. On the other hand, for positive bias values, the plasma presents a transport barrier in the reversed shear flow region.