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

Thermo-Hysteresis Phenomenon of the Electrical Resistivity in Fe_2Ti Suggesting Its Martensitic Transformation

Some indirect evidence is found of the occurrence of a martensitic transformation below room temperature in the Laves phase compounds in the Fe-Ti alloy system. The detailed measurements of the electrical resistivity from 4.2 to 1200°K show a large thermo-hysteresis, suggesting that the low temperature transformation develops just below room temperature and the high temperature one begins at about 560°K in the stoichiometric compound. Although the X-ray powder photographs show no clear evidence of a new phase, it may be interpreted that the new phase consists of a very small volume with a fine structure

Thermomechanical controls on magma supply and volcanic deformation: application to Aira caldera, Japan

ArticleGround deformation often precedes volcanic eruptions, and results from complex interactions between source processes and the thermomechanical behaviour of surrounding rocks. Previous models aiming to constrain source processes were unable to include realistic mechanical and thermal rock properties, and the role of thermomechanical heterogeneity in magma accumulation was unclear. Here we show how spatio-temporal deformation and magma reservoir evolution are fundamentally controlled by three-dimensional thermomechanical heterogeneity. Using the example of continued inflation at Aira caldera, Japan, we demonstrate that magma is accumulating faster than it can be erupted, and the current uplift is approaching the level inferred prior to the violent 1914 Plinian eruption. Magma storage conditions coincide with estimates for the caldera-forming reservoir ~29,000 years ago, and the inferred magma supply rate indicates a ~130-year timeframe to amass enough magma to feed a future 1914-sized eruption. These new inferences are important for eruption forecasting and risk mitigation, and have significant implications for the interpretations of volcanic deformation worldwide.This work was supported by the European Commission, Framework Program 7 (grant 282759, “VUELCO”, and grant 308665, “MEDSUV”), the Natural Environmental Research Council (NE/G01843X/1, “STREVA”, and “COMET”), the Royal Society (UF090006), the University of Bristol International Strategic Fund, and the MEXT project (Ministry of Education, Culture, Sports, Science and Technology). We thank Paul Alanis for the seismic tomography data, Keigo Yamamoto for the levelling data, and Takeshi Tameguri for the VT data. We thank Jon Blundy and Kathy Cashman for feedback on an early version of the manuscript

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

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

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

Kondo Effect in the Transport Properties of the CsCl-Type Compounds Fe_<1-x>Ti_<1+x> : II. Magnetic Scattering Center due to Atomic Disordering(Physics)

Neutron diffraction measurements were made at room temperature for the CsCl-type compounds, Fe_Ti_, in order to confirm the origins of the anomalous transport phenomena in the titanium-rich compositions and the superparamagnetism near the stoichiometric one. On the basis of those results, it could be concluded that the former behaviour is due to the Kondo effect, originating in a magnetic cluster of nine iron atoms with a concentration of about 10^, produced by the atomic disorder. The composition dependence of the residual resistivity also seems to be explainable from this point of view

Gravitational Instantons and Moduli Spaces of Topological 2-form Gravity

A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual 2-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of conformally self-dual Einstein manifolds for the non-zero cosmological constant case and Einstein-Kahlerian manifold with the vanishing real first Chern class for the zero cosmological constant. In the non-zero cosmological constant case, we evaluate the index of the elliptic complex associated with the moduli space and calculate the partition function. We also clarify the moduli space and its dimension for the zero cosmological constant case which are related to the Plebansky's heavenly equations.Comment: 36pages, LaTex, TIT/HEP-247/COSMO-4