Gravothermal Catastrophe, an Example

This work discusses gravothermal catastrophe in astrophysical systems and provides an analytic collapse solution which exhibits many of the catastrophe properties. The system collapses into a trapped surface with outgoing energy radiated to a future boundary, and provides an example of catastrophic collapse.Comment: To appear in Phys. Rev.

Granular Pressure In A Liquid Fluidized Bed

The granular temperature and pressure underpins the kinetic theory of granular flows while they also playing an increasing role in other context such as modeling heat transfer, segregation, erosion, attrition and aggregation in various granular processing technologies. The validation of these theories demands experimental determination of these quantities. Diffusing wave spectroscopy (DWS) is a well established technique for measurement of granular temperature in dense granular systems. Using the dense kinetic theory expression, we derive the granular pressure from DWS data for the first time. The determined mean granular pressure variation with solid volume fraction in a liquid fluidized bed is compared with theoretical and simulation models as well as with previous experimental results. Additionally, we report axial granular pressure profiles at several solid volume fractions.Vladimir Zivkovic, Mark Biggs, Don Glasshttp://www.chemeca2010.com/abstract/341.as

Scaling of Granular Temperature in a Dense Vibrated Granular Bed

The granular temperature underpins the kinetic theory of granular flows as well as theories for heat transfer, segregation, erosion, attrition and aggregation in various granular systems. We report granular temperature data of mono-disperse glass particles in a three-dimensional dense granular bed subject to vertical sinusoidal vibrations over a wide range of vibrational conditions as measured by diffusing wave spectroscopy (DWS). The granular temperature was found to scale with the square of the peak vibrational velocity inline with a number of theoretical models and experiments, but a significant correlation was observed between the granular temperature and the acceleration at constant peak velocity. Therefore, a map of granular temperature as a function of the peak vibrational velocity (range of 30 to 55 mm/s) and acceleration (1.8 to 3.4 Γ) is presented for the first time and discussed.Vladimir Zivkovic, Mark Biggs, Don Glasshttp://www.chemeca2010.com/abstract/342.as

Topological constraints on spiral wave dynamics in spherical geometries with inhomogeneous excitability

We analyze the way topological constraints and inhomogeneity in the excitability influence the dynamics of spiral waves on spheres and punctured spheres of excitable media. We generalize the definition of an index such that it characterizes not only each spiral but also each hole in punctured, oriented, compact, two-dimensional differentiable manifolds and show that the sum of the indices is conserved and zero. We also show that heterogeneity and geometry are responsible for the formation of various spiral wave attractors, in particular, pairs of spirals in which one spiral acts as a source and a second as a sink -- the latter similar to an antispiral. The results provide a basis for the analysis of the propagation of waves in heterogeneous excitable media in physical and biological systems.Comment: 5 pages, 6 Figures, major revisions, accepted for publication in Phys. Rev.

The Aggregation Kinetics of a Simulated Telechelic Polymer

We investigate the aggregation kinetics of a simulated telechelic polymer gel. In the hybrid Molecular Dynamics (MD) / Monte Carlo (MC) algorithm, aggregates of associating end groups form and break according to MC rules, while the position of the polymers in space is dictated by MD. As a result, the aggregate sizes change every time step. In order to describe this aggregation process, we employ master equations. They define changes in the number of aggregates of a certain size in terms of reaction rates. These reaction rates indicate the likelihood that two aggregates combine to form a large one, or that a large aggregate splits into two smaller parts. The reaction rates are obtained from the simulations for a range of temperatures. Our results indicate that the rates are not only temperature dependent, but also a function of the sizes of the aggregates involved in the reaction. Using the measured rates, solutions to the master equations are shown to be stable and in agreement with the aggregate size distribution, as obtained directly from simulation data. Furthermore, we show how temperature induced variations in these rates give rise to the observed changes in the aggregate distribution that characterizes the sol-gel transition.Comment: 9 pages, 10 figure

Ideal MHD theory of low-frequency Alfven waves in the H-1 Heliac

A part analytical, part numerical ideal MHD analysis of low-frequency Alfven wave physics in the H-1 stellarator is given. The three-dimensional, compressible ideal spectrum for H-1 is presented and it is found that despite the low beta (approx. 10^-4) of H-1 plasmas, significant Alfven-acoustic interactions occur at low frequencies. Several quasi-discrete modes are found with the three-dimensional linearised ideal MHD eigenmode solver CAS3D, including beta-induced Alfven eigenmode (BAE)- type modes in beta-induced gaps. The strongly shaped, low-aspect ratio magnetic geometry of H-1 causes CAS3D convergence difficulties requiring the inclusion of many Fourier harmonics for the parallel component of the fluid displacement eigenvector even for shear wave motions. The highest beta-induced gap reproduces large parts of the observed configurational frequency dependencies in the presence of hollow temperature profiles

Effect of periodic parametric excitation on an ensemble of force-coupled self-oscillators

We report the synchronization behavior in a one-dimensional chain of identical limit cycle oscillators coupled to a mass-spring load via a force relation. We consider the effect of periodic parametric modulation on the final synchronization states of the system. Two types of external parametric excitations are investigated numerically: periodic modulation of the stiffness of the inertial oscillator and periodic excitation of the frequency of the self-oscillatory element. We show that the synchronization scenarios are ruled not only by the choice of parameters of the excitation force but depend on the initial collective state in the ensemble. We give detailed analysis of entrainment behavior for initially homogeneous and inhomogeneous states. Among other results, we describe a regime of partial synchronization. This regime is characterized by the frequency of collective oscillation being entrained to the stimulation frequency but different from the average individual oscillators frequency.Comment: Comments and suggestions are welcom

Diverse routes to oscillation death in a coupled-oscillator system.

We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact analytic results enable us to generalize OD as a multiparameter-sensitive phenomenon. It can be induced, not only by changes in couplings, but also by changes in the oscillator frequencies or amplitudes. We observe synchronization transitions as a function of coupling and confirm the robustness of the phenomena in the presence of noise. Numerical and analogue simulations are in good agreement with the theory

Fractal Scales in a Schwarzschild Atmosphere

Recently, Glass and Krisch have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid [1999 Class. Quantum Grav. vol 16, 1175]. Mass diffusion in the extended Schwarzschild atmosphere was studied. The continuous solutions of classical diffusive transport are believed to describe the envelope of underlying fractal behavior. In this work we examine the classical picture at scales on which fractal behavior might be evident.Comment: to appear in Class. Quantum Gra