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

Biodiversity, distribution and patterns of extinction of the last odontopleurid tilobites during the Devonian (Givetian, Frasnian)

Biostratigraphical ranges and palaeogeographical distribution of mid-Givetian to end-Frasnian odontopleurids are investigated. The discovery of Leonaspis rhenohercynica sp. nov. in mid-Givetian strata extends this genus unexpectedly up to the late Middle Devonian. New material of Radiaspis radiata (Goldfuss, 1843) and the first koneprusiine in Britain, Koneprusia? sp., are described from the famous Lummaton shell-bed, Torquay, Devon. New taxa of Koneprusia, K. serrensis, K. aboussalamae, K. brevispina, and K. sp. A and K. sp. B are defined. Ceratocephala (Leonaspis) harborti Richter & Richter, 1926, is revised and reassigned to Gondwanaspis Feist, 2002. Two new species of Gondwanaspis, G. dracula and G. spinosa, plus three others left in open nomenclature, are described from the late Frasnian of Western Australia. A further species of Gondwanaspis, G. prisca, is described from the early Frasnian of Montagne Noire. Species of Gondwanaspis are shown to possess a number of paedomorphic features. A functional analysis suggests that, unlike other odontopleurids, Gondwanaspis actively fed and rested with the same cephalic orientation. The sole odontopleurid survivors of the severe terminal mid-Givetian biocrisis (‘Taghanic Event’) belong to the koneprusiine Koneprusia in the late Givetian and Frasnian, and, of cryptogenic origin, the acidaspidine Gondwanaspis in the Frasnian. Whereas the former became extinct in the late Frasnian at the Lower Kellwasser Event, the latter disappeared, and with it the entire Odontopleuroidea, at the terminal Frasnian Upper Kellwasser global biocrisis

X-ray Polarization Signatures of Compton Scattering in Magnetic Cataclysmic Variables

Compton scattering within the accretion column of magnetic cataclysmic variables (mCVs) can induce a net polarization in the X-ray emission. We investigate this process using Monte Carlo simulations and find that significant polarization can arise as a result of the stratified flow structure in the shock-ionized column. We find that the degree of linear polarization can reach levels up to ~8% for systems with high accretion rates and low white-dwarf masses, when viewed at large inclination angles with respect to the accretion column axis. These levels are substantially higher than previously predicted estimates using an accretion column model with uniform density and temperature. We also find that for systems with a relatively low-mass white dwarf accreting at a high accretion rate, the polarization properties may be insensitive to the magnetic field, since most of the scattering occurs at the base of the accretion column where the density structure is determined mainly by bremsstrahlung cooling instead of cyclotron cooling.Comment: 7 pages, 8 figures, accepted by MNRA

A 15-Kiloparsec X-Ray Disk in the Elliptical Galaxy NGC 1700

We present Chandra observations of the young elliptical galaxy NGC 1700. The X-ray isophotes are highly flattened between semimajor axes of 30 and 80 arcseconds, reaching a maximum ellipticity of approximately 0.65 at 60 arcsec (15 kpc). The surface brightness profile in the spectrally soft, flattened region is shallower than that of the starlight, indicating that the emission comes from hot gas rather than stellar sources. The flattening is so extreme that the gas cannot be in hydrostatic equilibrium in any plausible potential. A likely alternative is that the gas has significant rotational support. A simple model, representing isothermal gas distributed about a particular angular momentum, can reproduce the X-ray morphology while staying consistent with stellar kinematics. The specific angular momentum of the gas matches that of the stars in the most isophotally distorted outer part of the galaxy, and its cooling time matches the time since the last major merger. We infer that the gas was acquired in that merger, which involved a pre-existing elliptical galaxy with a hot ISM. The hot gas carried the angular momentum of the encounter, and has since gradually settled into a rotationally flattened, cooling disk.Comment: 11 pages, 2 figures, AASTeX 5.0. Accepted for publication in The Astrophysical Journa

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

Energy non-equipartition in systems of inelastic, rough spheres

We calculate and verify with simulations the ratio between the average translational and rotational energies of systems with rough, inelastic particles, either forced or freely cooling. The ratio shows non-equipartition of energy. In stationary flows, this ratio depends mainly on the particle roughness, but in nonstationary flows, such as freely cooling granular media, it also depends strongly on the normal dissipation. The approach presented here unifies and simplifies different results obtained by more elaborate kinetic theories. We observe that the boundary induced energy flux plays an important role.Comment: 4 pages latex, 4 embedded eps figures, accepted by Phys Rev

Two-dimensional Burgers Cellular Automaton

A two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform dependent variables into discrete ones. Some exact solutions of the CA, such as shock wave solutions, are studied in detail.Comment: Latex2.09, 17 pages including 7 figure