Helicity and alpha-effect by current-driven instabilities of helical magnetic fields

Helical magnetic background fields with adjustable pitch angle are imposed on a conducting fluid in a differentially rotating cylindrical container. The small-scale kinetic and current helicities are calculated for various field geometries, and shown to have the opposite sign as the helicity of the large-scale field. These helicities and also the corresponding $\alpha$-effect scale with the current helicity of the background field. The $\alpha$-tensor is highly anisotropic as the components $\alpha_{\phi\phi}$ and $\alpha_{zz}$ have opposite signs. The amplitudes of the azimuthal $\alpha$-effect computed with the cylindrical 3D MHD code are so small that the operation of an $\alpha\Omega$ dynamo on the basis of the current-driven, kink-type instabilities of toroidal fields is highly questionable. In any case the low value of the $\alpha$-effect would lead to very long growth times of a dynamo in the radiation zone of the Sun and early-type stars of the order of mega-years.Comment: 6 pages, 7 figures, submitted to MNRA

Design aspects of a solar array drive for spot, with a high platform stability objective

A solar array drive mechanism (MEGS) for the SPOT platform, which is a prototype of a multimission platform, is described. High-resolution cameras and other optical instruments are carried by the platform, requiring excellent platform stability in order to obtain high-quality pictures. Therefore, a severe requirement for the MEGS is the low level of disturbing torques it may generate considering the 0.6 times 10 to the minus 3 power deg/sec stability required. The mechanical design aspects aiming at reducing the mean friction torque, and therefore its fluctuations, are described as well as the method of compensation of the motor imperfections. It was concluded, however, that this is not sufficient to reach the stability requirement

Determination of the interactions in confined macroscopic Wigner islands: theory and experiments

Macroscopic Wigner islands present an interesting complementary approach to explore the properties of two-dimensional confined particles systems. In this work, we characterize theoretically and experimentally the interaction between their basic components, viz., conducting spheres lying on the bottom electrode of a plane condenser. We show that the interaction energy can be approximately described by a decaying exponential as well as by a modified Bessel function of the second kind. In particular, this implies that the interactions in this system, whose characteristics are easily controllable, are the same as those between vortices in type-II superconductors.Comment: 8 pages, 8 figure

Self-similar solutions with fat tails for Smoluchowski's coagulation equation with locally bounded kernels

The existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation has so far only been established for the solvable and the diagonal kernel. In this paper we prove the existence of such self-similar solutions for continuous kernels $K$ that are homogeneous of degree $\gamma \in [0,1)$ and satisfy $K(x,y) \leq C (x^{\gamma} + y^{\gamma})$. More precisely, for any $\rho \in (\gamma,1)$ we establish the existence of a continuous weak self-similar profile with decay $x^{-(1{+}\rho)}$ as $x \to \infty$

Fluctuations of the Casimir-like force between two membrane inclusions

Although Casimir forces are inseparable from their fluctuations, little is known about these fluctuations in soft matter systems. We use the membrane stress tensor to study the fluctuations of the membrane-mediated Casimir-like force. This method enables us to recover the Casimir force between two inclusions and to calculate its variance. We show that the Casimir force is dominated by its fluctuations. Furthermore, when the distance d between the inclusions is decreased from infinity, the variance of the Casimir force decreases as -1/d^2. This distance dependence shares a common physical origin with the Casimir force itself.Comment: 5 pages, 3 figure

Universal analytic properties of noise. Introducing the J-Matrix formalism

We propose a new method in the spectral analysis of noisy time-series data for damped oscillators. From the Jacobi three terms recursive relation for the denominators of the Pad\'e Approximations built on the well-known Z-transform of an infinite time-series, we build an Hilbert space operator, a J-Operator, where each bound state (inside the unit circle in the complex plane) is simply associated to one damped oscillator while the continuous spectrum of the J-Operator, which lies on the unit circle itself, is shown to represent the noise. Signal and noise are thus clearly separated in the complex plane. For a finite time series of length 2N, the J-operator is replaced by a finite order J-Matrix J_N, having N eigenvalues which are time reversal covariant. Different classes of input noise, such as blank (white and uniform), Gaussian and pink, are discussed in detail, the J-Matrix formalism allowing us to efficiently calculate hundreds of poles of the Z-transform. Evidence of a universal behaviour in the final statistical distribution of the associated poles and zeros of the Z-transform is shown. In particular the poles and zeros tend, when the length of the time series goes to infinity, to a uniform angular distribution on the unit circle. Therefore at finite order, the roots of unity in the complex plane appear to be noise attractors. We show that the Z-transform presents the exceptional feature of allowing lossless undersampling and how to make use of this property. A few basic examples are given to suggest the power of the proposed method.Comment: 14 pages, 8 figure

Long-range Ni/Mn structural order in epitaxial double perovskite La2NiMnO6 thin films

We report and compare the structural, magnetic, and optical properties of ordered La2NiMnO6 thin films and its disordered LaNi0.5Mn0.5O3 counterpart. An x-ray diffraction study reveals that the B-site Ni/Mn ordering induces additional XRD reflections as the crystal symmetry is transformed from a pseudocubic perovskite unit cell in the disordered phase to a monoclinic form with larger lattice parameters for the ordered phase. Polarized Raman spectroscopy studies reveal that the ordered samples are characterized by additional phonon excitations that are absent in the disordered phase. The appearance of these additional phonon excitations is interpreted as the clearest signature of Brillouin zone folding as a result of the long-range Ni/Mn ordering in La2NiMnO6. Both ordered and disordered materials display a single ferromagnetic-to-paramagnetic transition. The ordered films display also a saturation magnetization close to 4.8 mB/f.u. and a transition temperature (FM-TC) around 270 K, while the disordered ones have only a 3.7 mB/f.u. saturation magnetization and a FM-TC around 138 K. The differences in their magnetic behaviours are understood based on the distinct local electronic configurations of their Ni/Mn cations.Comment: 15 pages, 5 fig

Phase formation, phonon behavior, and magnetic properties of novel ferromagnetic La3BAlMnO9 (B = Co or Ni) triple perovskites

In the quest for novel magnetoelectric materials, we have grown, stabilized and explored the properties of La3BAlMnO9 (B = Co or Mn) thin films. In this paper, we report the influence of the growth parameters that promote B/Al/Mn ordering in the pseudo-cubic unit cell and their likely influence on the magnetic and multiferroic properties. The temperature dependence of the magnetization shows that La3CoAlMnO9 is ferromagnetic up to 190 K while La3NiAlMnO9 shows a TC of 130 K. The behavior of these films are compared and contrasted with related La2BMnO6 double perovskites. It is observed that the insertion of AlO6 octahedra between CoO6 and MnO6 suppresses significantly the strength of the superexchange interaction, spin-phonon and spin-polar coupling.Comment: 13 pages, 3 fig

Field theoretic calculation of scalar turbulence

The cascade rate of passive scalar and Bachelor's constant in scalar turbulence are calculated using the flux formula. This calculation is done to first order in perturbation series. Batchelor's constant in three dimension is found to be approximately 1.25. In higher dimension, the constant increases as $d^{1/3}$.Comment: RevTex4, publ. in Int. J. Mod. Phy. B, v.15, p.3419, 200

The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$ and $xy$. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here we add to this a complete description of the set of all limit points of solutions modulo scaling (the scaling attractor) and the dynamics on this limit set (the ultimate dynamics). The main tool is Bertoin's L\'{e}vy-Khintchine representation formula for eternal solutions of Smoluchowski's equation (Adv. Appl. Prob. 12 (2002) 547--64). This representation linearizes the dynamics on the scaling attractor, revealing these dynamics to be conjugate to a continuous dilation, and chaotic in a classical sense. Furthermore, our study of scaling limits explains how Smoluchowski dynamics ``compactifies'' in a natural way that accounts for clusters of zero and infinite size (dust and gel)