Homogeneous cooling of rough, dissipative particles: Theory and simulations

We investigate freely cooling systems of rough spheres in two and three dimensions. Simulations using an event driven algorithm are compared with results of an approximate kinetic theory, based on the assumption of a generalized homogeneous cooling state. For short times $t$, translational and rotational energy are found to change linearly with $t$. For large times both energies decay like $t^{-2}$ with a ratio independent of time, but not corresponding to equipartition. Good agreement is found between theory and simulations, as long as no clustering instability is observed. System parameters, i.e. density, particle size, and particle mass can be absorbed in a rescaled time, so that the decay of translational and rotational energy is solely determined by normal restitution and surface roughness.Comment: 10 pages, 10 eps-figure

Active galactic nucleus feedback in clusters of galaxies

Observations made during the last ten years with the Chandra X-ray Observatory have shed much light on the cooling gas in the centers of clusters of galaxies and the role of active galactic nucleus (AGN) heating. Cooling of the hot intracluster medium in cluster centers can feed the supermassive black holes found in the nuclei of the dominant cluster galaxies leading to AGN outbursts which can reheat the gas, suppressing cooling and large amounts of star formation. AGN heating can come in the form of shocks, buoyantly rising bubbles that have been inflated by radio lobes, and the dissipation of sound waves.Comment: Refereed review article published in Chandra's First Decade of Discovery Special Feature edition of the Proceedings of the National Academy of Science

The Insignificance of Global Reheating in the Abell 1068 Cluster: X-Ray Analysis

We report on a Chandra observation of the massive, medium redshift (z=0.1386) cooling flow cluster Abell 1068. We detect a clear temperature gradient in the X-ray emitting gas from kT ~ 5 keV in the outer part of the cluster down to roughly 2 keV in the core, and a striking increase in the metallicity of the gas toward the cluster center. The total spectrum from the cluster can be fit by a cooling flow model with a total mass deposition rate of 150 solar masses/yr. Within the core (r < 30 kpc), the mass depositon rate of 40 solar masses/yr is comparable to estimates for the star formation rate from optical data. We find an apparent correlation between the cD galaxy's optical isophotes and enhanced metallicity isocontours in the central ~100 kpc of the cluster. We show that the approximate doubling of the metallicity associated with the cD can be plausibly explained by supernova explosions associated with the cD's ambient stellar population and the recent starburst. Finally, we calculate the amount of heating due to thermal conduction and show that this process is unlikely to offset cooling in Abell 1068.Comment: Accepted for publication in ApJ, 26 pages, 12 b+w figures, 3 color figure

Microscopic origin of granular ratcheting

Numerical simulations of assemblies of grains under cyclic loading exhibit ``granular ratcheting'': a small net deformation occurs with each cycle, leading to a linear accumulation of deformation with cycle number. We show that this is due to a curious property of the most frequently used models of the particle-particle interaction: namely, that the potential energy stored in contacts is path-dependent. There exist closed paths that change the stored energy, even if the particles remain in contact and do not slide. An alternative method for calculating the tangential force removes granular ratcheting.Comment: 13 pages, 18 figure

Semi-classical geometry of charged black holes

At the classical level, two-dimensional dilaton gravity coupled to an abelian gauge field has charged black hole solutions, which have much in common with four-dimensional Reissner-Nordstrom black holes, including multiple asymptotic regions, timelike curvature singularities, and Cauchy horizons. The black hole spacetime is, however, significantly modified by quantum effects, which can be systematically studied in this two-dimensional context. In particular, the back-reaction on the geometry due to pair-creation of charged fermions destabilizes the inner horizon and replaces it with a spacelike curvature singularity. The semi-classical geometry has the same global topology as an electrically neutral black hole.Comment: REVTeX, 4 pages, 2 figures; references adde

Bifurcation Diagram for Compartmentalized Granular Gases

The bifurcation diagram for a vibro-fluidized granular gas in N connected compartments is constructed and discussed. At vigorous driving, the uniform distribution (in which the gas is equi-partitioned over the compartments) is stable. But when the driving intensity is decreased this uniform distribution becomes unstable and gives way to a clustered state. For the simplest case, N=2, this transition takes place via a pitchfork bifurcation but for all N>2 the transition involves saddle-node bifurcations. The associated hysteresis becomes more and more pronounced for growing N. In the bifurcation diagram, apart from the uniform and the one-peaked distributions, also a number of multi-peaked solutions occur. These are transient states. Their physical relevance is discussed in the context of a stability analysis.Comment: Phys. Rev. E, in press. Figure quality has been reduced in order to decrease file-siz

On Time-dependent Collapsing Branes and Fuzzy Odd-dimensional Spheres

We study the time-dependent dynamics of a collection of N collapsing/expanding D0-branes in type IIA String Theory. We show that the fuzzy-S^3 and S^5 provide time-dependent solutions to the Matrix Model of D0-branes and its DBI generalisation. Some intriguing cancellations in the calculation of the non-abelian DBI Matrix actions result in the fuzzy-S^3 and S^5 having the same dynamics at large-N. For the Matrix model, we find analytic solutions describing the time-dependent radius, in terms of Jacobi elliptic functions. Investigation of the physical properties of these configurations shows that there are no bounces for the trajectory of the collapse at large-N. We also write down a set of useful identities for fuzzy-S^3, fuzzy-S^5 and general fuzzy odd-spheres.Comment: 35 pages, latex; v2: discussion in Appendix B on the large-N limit of the associator is modified, main results of paper unchange