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

Energy flows in vibrated granular media

We study vibrated granular media, investigating each of the three components of the energy flow: particle-particle dissipation, energy input at the vibrating wall, and particle-wall dissipation. Energy dissipated by interparticle collisions is well estimated by existing theories when the granular material is dilute, and these theories are extended to include rotational kinetic energy. When the granular material is dense, the observed particle-particle dissipation rate decreases to as little as 2/5 of the theoretical prediction. We observe that the rate of energy input is the weight of the granular material times an average vibration velocity times a function of the ratio of particle to vibration velocity. `Particle-wall' dissipation has been neglected in all theories up to now, but can play an important role when the granular material is dilute. The ratio between gravitational potential energy and kinetic energy can vary by as much as a factor of 3. Previous simulations and experiments have shown that E ~ V^delta, with delta=2 for dilute granular material, and delta ~ 1.5 for dense granular material. We relate this change in exponent to the departure of particle-particle dissipation from its theoretical value.Comment: 19 pages revtex, 10 embedded eps figures, accepted by PR

Quasi-rigidity: some uniqueness issues

Quasi-rigidity means that one builds a theory for assemblies of grains under a slowly changing external load by using the deformation of those grains as a small parameter. Is quasi-rigidity a complete theory for these granular assemblies? Does it provide unique predictions of the assembly's behavior, or must some other process be invoked to decide between several possibilities? We provide evidence that quasi-rigidity is a complete theory by showing that two possible sources of indeterminacy do not exist for the case of disk shaped grains. One possible source of indeterminacy arises from zero-frequency modes present in the packing. This problem can be solved by considering the conditions required to obtain force equilibrium. A second possible source of indeterminacy is the necessity to choose the status (sliding or non-sliding) at each contact. We show that only one choice is permitted, if contacts slide only when required by Coulomb friction.Comment: 14 pages, 3 figures, submitted to Phys Rev E (introduction and conclusion revised

The Management of Classical Hodgkin's Lymphoma: Past, Present, and Future

The management of classical Hodgkin's lymphoma (CHL) is a success story of modern multi-agent haemato-oncology. Prior to the middle of the twentieth century CHL was fatal in the majority of cases. Introduction of single agent radiotherapy (RT) demonstrated for the first time that these patients could be cured. Developments in chemotherapy including the mechlorethamine, vincristine, procarbazine and prednisolone (MOPP) and Adriamycin, bleomycin, vinblastine and dacarbazine (ABVD) regimens have resulted in cure rates of over 80%. Even in relapse, CHL patients can be salvaged with high dose chemotherapy and autologous haematopoietic stem cell transplantation (ASCT). Challenges remain, however, in finding new strategies to manage the small number of patients who continue to relapse or progress. In addition, the young age of many Hodgkin's patients forces difficult decisions in balancing the benefit of early disease control against the survival disadvantage of late toxicity. In this article we aim to summarise past trials, define the current standard of care and appraise future developments in the management of CHL

Background heatflow on hotspot planets: Io and Venus

On planets where most of the heat is transported to the surface by igneous activity (extrusive volcanism or near-surface intrusions), the surface heatflow at localities well away from regions of current igneous activity need not be even approximately the conductive heatflow through the entire lithosphere but may instead be dominated by the residual heat leaking out from the last igneous event in that locality. On Io, it is likely that (κτ)^(1/2) « lithosphere thickness ( κ = thermal diffusivity, τ = typical time between “resurfacing” events) and the background heatflow may be very large, comparable or even larger than the current observational heatflow, which is associated with the hotspots alone. This upward revision of Io's heatflow is compatible with observations and with recent indications of a non-steady tidal and thermal evolution. On Venus, (κτ)^(1/2) is probably comparable to the lithosphere thickness and the resulting upward revision of heatflow may be only marginally significant, unless magmatic activity is enormously greater than on Earth

Dynamics of inelastically colliding rough spheres: Relaxation of translational and rotational energy

We study the exchange of kinetic energy between translational and rotational degrees of freedom for inelastic collisions of rough spheres. Even if equipartition holds in the initial state it is immediately destroyed by collisions. The simplest generalisation of the homogeneous cooling state allows for two temperatures, characterizing translational and rotational degrees of freedom separately. For times larger than a crossover frequency, which is determined by the Enskog frequency and the initial temperature, both energies decay algebraically like $t^{-2}$ with a fixed ratio of amplitudes, different from one.Comment: 5 pages, RevTeX, 2 eps figures, slightly expanded discussion, new figures with dimensionless units, added references, accepted for publication in PRE as a Rapid Com

Effects of Velocity Correlation on Early Stage of Free Cooling Process of Inelastic Hard Sphere System

The free cooling process in the inelastic hard sphere system is studied by analysing the data from large scale molecular dynamics simulations on a three dimensional system. The initial energy decay, the velocity distribution function, and the velocity correlation functions are calculated to be compared with theoretical predictions. The energy decay rate in the homogeneous cooling state is slightly but distinctively smaller than that expected from the independent collision assumption. The form of the one particle velocity distribution is found not to be stationary. These contradict to the predictions of the kinetic theory based on the Enskog-Boltzmann equation and suggest that the velocity correlation is already important in the early stage of homogeneous cooling state. The energy decay rate is analysed in terms of the velocity correlation.Comment: 9 pages (figures included). To be published in J. Phys. Soc. Jpn. Vol. 73 No. 1 (2004) Added two references and removed one. Changed the name of T_{L}. Added unit constants in Sec. 5 and

Spatial Correlations in Compressible Granular Flows

For a freely evolving granular fluid, the buildup of spatial correlations in density and flow field is described using fluctuating hydrodynamics. The theory for incompressible flows is extended to the general, compressible case, including longitudinal velocity and density fluctuations, and yields qualitatively different results for long range correlations. The structure factor of density fluctuations shows a maximum at finite wavenumber, shifting in time to smaller wavenumbers and corresponding to a growing correlation length. It agrees well with two-dimensional molecular dynamics simulations.Comment: 12 pages, Latex, 3 figure