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

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

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

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

Dilaton as a Dark Matter Candidate and its Detection

Assuming that the dilaton is the dark matter of the universe, we propose an experiment to detect the relic dilaton using the electromagnetic resonant cavity, based on the dilaton-photon conversion in strong electromagnetic background. We calculate the density of the relic dilaton, and estimate the dilaton mass for which the dilaton becomes the dark matter of the universe. With this we calculate the dilaton detection power in the resonant cavity, and compare it with the axion detection power in similar resonant cavity experiment.Comment: 23 pages, 2 figure

Comment on Ds∗→Dsπ0D_s^* \to D_s \pi^0 Decay

We calculate the rate for $D_s^* \rightarrow D_s \pi^0$ decay using Chiral Perturbation Theory. This isospin violating process results from $\pi^0$ - $\eta$ mixing, and its amplitude is proportional to $(m_d - m_u)/\bigl(m_s-(m_u+m_d)/2 \bigr)$. Experimental information on the branching ratio for $D_s^* \rightarrow D_s \pi^0$ can provide insight into the pattern of $SU(3)$ violation in radiative $D^*$ decays.Comment: 7 pages with 2 figures not included but available upon request, CALT-68-191

Lineal Trails of D2-D2bar Superstrings

We study the superstrings suspended between a D2- and an anti-D2-brane. We quantize the string in the presence of some general configuration of gauge fields over the (anti-)D-brane world volumes. The interstring can move only in a specific direction that is normal to the difference of the electric fields of each (anti-)D-branes. Especially when the electric fields are the same, the interstring cannot move. We obtain the condition for the tachyons to disappear from the spectrum.Comment: 15 pages with 4 figures, referenced added, Sec. 5 on the spectrum made cleare