Analytic ranks of elliptic curves over number fields

Let $E$ be an elliptic curves over the rational numbers. Let $F$ be a cyclic extension of prime degree $l$. Then, we show that the average of analytic ranks of $E(F)$ over all cyclic extension of prime degree $l$ is at most $2+r_\mathbb{Q}(E)$, where $r_\mathbb{Q}(E)$ is the analytic rank of $E(\mathbb Q)$. This bound is independent of the degree of the cyclic extension. Also, we also obtain some average rank result over $S_d$-fields

Super Jackstraws and Super Waterwheels

We construct various new BPS states of D-branes preserving 8 supersymmetries. These include super Jackstraws (a bunch of scattered D- or (p,q)-strings preserving supersymmetries), and super waterwheels (a number of D2-branes intersecting at generic angles on parallel lines while preserving supersymmetries). Super D-Jackstraws are scattered in various dimensions but are dynamical with all their intersections following a common null direction. Meanwhile, super (p,q)-Jackstraws form a planar static configuration. We show that the SO(2) subgroup of SL(2,R), the group of classical S-duality transformations in IIB theory, can be used to generate this latter configuration of variously charged (p,q)-strings intersecting at various angles. The waterwheel configuration of D2-branes preserves 8 supersymmetries as long as the `critical' Born-Infeld electric fields are along the common direction.Comment: 23 pages, 10 figure

Velocity statistics from spectral line data: effects of density-velocity correlations, magnetic field, and shear

In a previous work Lazarian and Pogosyan suggested a technique to extract velocity and density statistics, of interstellar turbulence, by means of analysing statistics of spectral line data cubes. In this paper we test that technique, by studying the effect of correlation between velocity and density fields, providing a systematic analysis of the uncertainties arising from the numerics, and exploring the effect of a linear shear. We make use of both compressible MHD simulations and synthetic data to emulate spectroscopic observations and test the technique. With the same synthetic spectroscopic data, we also studied anisotropies of the two point statistics and related those anisotropies with the magnetic field direction. This presents a new technique for magnetic field studies. The results show that the velocity and density spectral indices measured are consistent with the analytical predictions. We identified the dominant source of error with the limited number of data points along a given line of sight. We decrease this type of noise by increasing the number of points and by introducing Gaussian smoothing. We argue that in real observations the number of emitting elements is essentially infinite and that source of noise vanishes.Comment: 12 pages, 10 figures. Accepted for publication in MNRA

Scaling, Intermittency and Decay of MHD Turbulence

We discuss a few recent developments that are important for understanding of MHD turbulence. First, MHD turbulence is not so messy as it is usually believed. In fact, the notion of strong non-linear coupling of compressible and incompressible motions along MHD cascade is not tenable. Alfven, slow and fast modes of MHD turbulence follow their own cascades and exhibit degrees of anisotropy consistent with theoretical expectations. Second, the fast decay of turbulence is not related to the compressibility of fluid. Rates of decay of compressible and incompressible motions are very similar. Third, viscosity by neutrals does not suppress MHD turbulence in a partially ionized gas. Instead, MHD turbulence develops magnetic cascade at scales below the scale at which neutrals damp ordinary hydrodynamic motions. Forth, density statistics does not exhibit the universality that the velocity and magnetic field do. For instance, at small Mach numbers the density is anisotropic, but it gets isotropic at high Mach numbers. Fifth, the intermittency of magnetic field and velocity are different. Both depend on whether the measurements are done in local system of reference oriented along the local magnetic field or in the global system of reference related to the mean magnetic field.Comment: 12 pages, Invited Review, Workshop on Theoretical Plasma Physics, Trieste, Italy, 5-16 Jul

Magnetic Reconnection and Turbulent Mixing: From ISM to Clusters of Galaxies

Magnetic reconnection, or the ability of the magnetic field lines that are frozen in plasma to change their topology, is a fundamental problem of magnetohydrodynamics (MHD). We briefly examine the problem starting with the well-known Sweet-Parker scheme, discuss effects of tearing modes, anomalous resistivity and the concept of hyperresistivity. We show that the field stochasticity by itself provides a way to enable fast reconnection even if, at the scale of individual turbulent wiggles, the reconnection happens at the slow Sweet-Parker rate. We show that fast reconnection allows efficient mixing of magnetic field in the direction perpendicular to the local direction of magnetic field. While the idea of stochastic reconnection still requires numerical confirmation, our numerical simulations testify that mixing motions perpendicular to the local magnetic field are up to high degree hydrodynamical. This suggests that the turbulent heat transport should be similar to that in non-magnetized turbulent fluid, namely, should have a diffusion coefficient \sim LV_L, where V_L is the amplitude of the turbulent velocity and L is the scale of the turbulent motions. We present numerical simulations which support this conclusion. The application of this idea to thermal conductivity in clusters of galaxies shows that this mechanism may dominate the diffusion of heat and may be efficient enough to prevent cooling flow formation.Comment: 12 pages, 2 figures, invited talk at JENAM2002 - The Unsolved Universe:Challenges for the Future (v2: minor changes

Schwinger Effect in Non-parallel D1-branes: A Path Integral Approach

We study the Schwinger effect in a system of non-parallel D1-branes for the bosonic strings using the path integral formalism. We drive the string pair creation rate by calculating the one loop vacuum amplitude of the setup in presence of the background electric filed defined along one of the D1-branes. We find an angle dependent minimum value for the background field and show that the decaying of vacuum into string pairs takes place for the field above this value. It is shown that in $\theta\rightarrow\frac{\pi}{2}$ limit the vacuum becomes stable and thus no pair creation occurs

Kinetically-controlled thin-film growth of layered β\beta- and γ−\gamma-Nax_{x}CoO2_{2} cobaltate

We report growth characteristics of epitaxial $\beta$-Na$_{0.6}$CoO$_{2}$ and $\gamma$-Na$_{0.7}$CoO$_{2}$ thin films on (001) sapphire substrates grown by pulsed-laser deposition. Reduction of deposition rate could change structure of Na$_{x}$CoO$_{2}$ thin film from $\beta$-phase with island growth mode to $\gamma$-phase with layer-by-layer growth mode. The $\gamma$-Na$_{0.7}$CoO$_{2}$ thin film exhibits spiral surface growth with multiterraced islands and highly crystallized texture compared to that of the $\beta$-Na$_{0.6}$CoO$_{2}$ thin film. This heterogeneous epitaxial film growth can give opportunity of strain effect of physical properties and growth dynamics of Na$_{x}$CoO$_{2}$ as well as subtle nature of structural change.Comment: accepted for publication in Applied Physics Letter