Core of the Magnetic Obstacle

Rich recirculation patterns have been recently discovered in the electrically conducting flow subject to a local external magnetic termed "the magnetic obstacle" [Phys. Rev. Lett. 98 (2007), 144504]. This paper continues the study of magnetic obstacles and sheds new light on the core of the magnetic obstacle that develops between magnetic poles when the intensity of the external field is very large. A series of both 3D and 2D numerical simulations have been carried out, through which it is shown that the core of the magnetic obstacle is streamlined both by the upstream flow and by the induced cross stream electric currents, like a foreign insulated insertion placed inside the ordinary hydrodynamic flow. The closed streamlines of the mass flow resemble contour lines of electric potential, while closed streamlines of the electric current resemble contour lines of pressure. New recirculation patterns not reported before are found in the series of 2D simulations. These are composed of many (even number) vortices aligned along the spanwise line crossing the magnetic gap. The intensities of these vortices are shown to vanish toward to the center of the magnetic gap, confirming the general conclusion of 3D simulations that the core of the magnetic obstacle is frozen. The implications of these findings for the case of turbulent flow are discussed briefly.Comment: 14 pages, 9 figures, submitted to Journal of Turbulenc

Collapses and explosions in self-gravitating systems

Collapse and reverse to collapse explosion transition in self-gravitating systems are studied by molecular dynamics simulations. A microcanonical ensemble of point particles confined to a spherical box is considered; the particles interact via an attractive soft Coulomb potential. It is observed that the collapse in the particle system indeed takes place when the energy of the uniform state is put near or below the metastability-instability threshold (collapse energy), predicted by the mean-field theory. Similarly, the explosion in the particle system occurs when the energy of the core-halo state is increased above the explosion energy, where according to the mean field predictions the core-halo state becomes unstable. For a system consisting of 125 -- 500 particles, the collapse takes about $10^5$ single particle crossing times to complete, while a typical explosion is by an order of magnitude faster. A finite lifetime of metastable states is observed. It is also found that the mean-field description of the uniform and the core-halo states is exact within the statistical uncertainty of the molecular dynamics data.Comment: 9 pages, 14 figure

Molar mass estimate of dark matter from the dark mass distribution measurements

We study the distribution of dark matter versus visible matter using a set of data obtained from strong gravitational lensing in the galaxy cluster CL0024+1654 and another set of data inferred from the universal rotation curves in spiral galaxies. The important feature of these two dramatically different observations is that the mass density profile of both visible and dark components can be estimated. From these measurements we deduce the mass of the dark matter particle and our estimate of the mass for the dark matter particle is $\mu_d \approx (200-800)$MeV. We contrast our estimates from CL0024+1654 data and the universal rotation curves of the spiral galaxies and discuss their consistency.Comment: 14 pages, 13 figure

Phase transitions in small systems

Traditionally, phase transitions are defined in the thermodynamic limit only. We discuss how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be seen and classified for small systems. "Small"systems are systems where the linear dimension is of the characteristic range of the interaction between the particles; i.e. also astrophysical systems are "small"in this sense. Boltzmann defines the entropy as the logarithm of the area $W(E,N)={\rm e}^{S(E,N)}$ of the surface in the mechanical N-body phase space at total energy E. The topology of S(E,N) or more precisely, of the curvature determinant $D(E,N)=\partial^2S/\partial E^2 \times \partial^2S/\partial N^2-(\partial^2S/\partial E\partial N)^2$ allows the classification of phase transitions without taking the thermodynamic limit. Micro-canonical thermo-statistics and phase transitions will be discussed here for a system coupled by short range forces in another situation where entropy is not extensive. The first calculation of the entire entropy surface S(E,N) for the diluted Potts model (ordinary (q=3)-Potts model plus vacancies) on a $50 \times 50$ square lattice is shown. The regions in {E,N}where D> 0 correspond to pure phases, ordered resp. disordered, and D< 0 represent transitions of first order with phase separation and "surface tension". These regions are bordered by a line with D=0. A line of continuous transitions starts at the critical point of the ordinary (q=3)-Potts model and runs down to a branching point Pm. Along this line $\mathbf{\nabla}D$ vanishes in the direction of the eigenvector $\mathbf{v_1}$ of D with the largest eigen-value $\lambda_1\approx 0$. It characterizes a maximum of the largest eigenvalue $\lambda_1$. This corresponds to a critical line where the transition is continuous and the surface tension disappears. Here the neighboring phases are indistinguishable. The region where two or more lines with D=0 cross is the region of the (multi)-critical point. The micro-canonical ensemble allows to put these phenomena entirely on the level of mechanics

The Antonov problem for rotating systems

We study the classical Antonov problem (of retrieving the statistical equilibrium properties of a self-gravitating gas of classical particles obeying Boltzmann statistics in space and confined in a spherical box) for a rotating system. It is shown that a critical angular momentum $\lambda_c$ (or, in the canonical language, a critical angular velocity $\omega_c$) exists, such that for $\lambda<\lambda_c$ the system's behaviour is qualitatively similar to that of a non-rotating gas, with a high energy disordered phase and a low energy collapsed phase ending with Antonov's limit, below which there is no equilibrium state. For $\lambda>\lambda_c$, instead, the low-energy phase is characterized by the formation of two dense clusters (a ``binary star''). Remarkably, no Antonov limit is found for $\lambda>\lambda_c$. The thermodynamics of the system (phase diagram, caloric curves, local stability) is analyzed and compared with the recently-obtained picture emerging from a different type of statistics which forbids particle overlapping.Comment: 21 pages, 5 figures, minor revisions, to appear in Nucl. Phys.