Moduli Space of Topological 2-form Gravity

We propose a topological version of four-dimensional (Euclidean) Einstein gravity, in which anti-self-dual 2-forms and an SU(2) connection are used as fundamental fields. The theory describes the moduli space of conformally self-dual Einstein manifolds. In the presence of a cosmological constant, we evaluate the index of the elliptic complex associated with the moduli space.Comment: 10pages, Latex (minor changes

Local virial relation and velocity anisotropy for collisionless self-gravitating systems

The collisionless quasi-equilibrium state realized after the cold collapse of self-gravitating systems has two remarkable characters. One of them is the linear temperature-mass (TM) relation, which yields a characteristic non-Gaussian velocity distribution. Another is the local virial (LV) relation, the virial relation which holds even locally in collisionless systems through phase mixing such as cold-collapse. A family of polytropes are examined from a view point of these two characters. The LV relation imposes a strong constraint on these models: only polytropes with index $n \sim 5$ with a flat boundary condition at the center are compatible with the numerical results, except for the outer region. Using the analytic solutions based on the static and spherical Jeans equation, we show that this incompatibility in the outer region implies the important effect of anisotropy of velocity dispersion. Furthermore, the velocity anisotropy is essential in explaining various numerical results under the condition of the local virial relation.Comment: 8 pages, 5 figures, Proceedings of CN-Kyoto International Workshop on Complexity and Nonextensivity; added a reference for section

A Measurement of the Quadrupole Power Spectrum in the Clustering of the 2dF QSO Survey

We report a measurement of the quadrupole power spectrum in the two degree field (2dF) QSO redshift (2QZ) survey. The analysis uses an algorithm parallel to that for the estimation of the standard monopole power spectrum without first requiring computation of the correlation function or the anisotropic power spectrum. The error on the quadrupole spectrum is rather large but the best fit value of the bias parameter from the quadrupole spectrum is consistent with that from previous investigations of the 2dF data.Comment: 12pages, accepted by PAS

Thermo-mechanical behavior of titanium beryllide pebble beds at elevated temperatures

The thermomechanical behavior of titanium beryllide pebble beds was investigated experimentally at temperatures between 200 and 500°C in helium atmosphere at atmospheric pressure. The pebbles consist of a mixture of TiBe12 and Ti2Be17 titanate beryllide phases and a small residual amount of Be phase, denominated as Be-7.7Ti. Like previous experiments at ambient temperature [1], the pebble beds were compressed uniaxially up to 4.5MPa and the effective thermal conductivity k was measured using the hot wire technique. Compared to ambient temperature, the stress-strain curves do not differ significantly in investigated temperature range. Because the thermal conductivity of solid TiBe12 is fairly constant in a wide temperature range [2], k increases moderately with increasing temperature because of the increasing thermal conductivity of helium. Compared to beryllium pebble beds, the k of the Be-7.7Ti pebble beds increases again much lesser because of the significantly smaller thermal conductivity of the solid material and the mechanically harder behavior resulting in smaller contact surfaces

Coupled spin models for magnetic variation of planets and stars

Geomagnetism is characterized by intermittent polarity reversals and rapid fluctuations. We have recently proposed a coupled macro-spin model to describe these dynamics based on the idea that the whole dynamo mechanism is described by the coherent interactions of many small dynamo elements. In this paper, we further develop this idea and construct a minimal model for magnetic variations. This simple model naturally yields many of the observed features of geomagnetism: its time evolution, the power spectrum, the frequency distribution of stable polarity periods, etc. This model has coexistent two phases; i.e. the cluster phase which determines the global dipole magnetic moment and the expanded phase which gives random perpetual perturbations that yield intermittent polarity flip of the dipole moment. This model can also describe the synchronization of the spin oscillation. This corresponds to the case of sun and the model well describes the quasi-regular cycles of the solar magnetism. Furthermore, by analyzing the relevant terms of MHD equation based on our model, we have obtained a scaling relation for the magnetism for planets, satellites, sun, and stars. Comparing it with various observations, we can estimate the scale of the macro-spins.Comment: 16 pages, 9 figure

Universal Non-Gaussian Velocity Distribution in Violent Gravitational Processes

We study the velocity distribution in spherical collapses and cluster-pair collisions by use of N-body simulations. Reflecting the violent gravitational processes, the velocity distribution of the resultant quasi-stationary state generally becomes non-Gaussian. Through the strong mixing of the violent process, there appears a universal non-Gaussian velocity distribution, which is a democratic (equal-weighted) superposition of many Gaussian distributions (DT distribution). This is deeply related with the local virial equilibrium and the linear mass-temperature relation which characterize the system. We show the robustness of this distribution function against various initial conditions which leads to the violent gravitational process. The DT distribution has a positive correlation with the energy fluctuation of the system. On the other hand, the coherent motion such as the radial motion in the spherical collapse and the rotation with the angular momentum suppress the appearance of the DT distribution.Comment: 11 pages, 19 eps figures, RevTex, submitted to PRE, Revised version, minor change