Schwarzschild Atmospheric Processes: A Classical Path to the Quantum

We develop some classical descriptions for processes in the Schwarzschild string atmosphere. These processes suggest relationships between macroscopic and microscopic scales. The classical descriptions developed in this essay highlight the fundamental quantum nature of the Schwarzschild atmospheric processes.Comment: to appear in Gen. Rel. Gra

Spatio-temporal patterns in the Hantavirus infection

We present a model of the infection of Hantavirus in deer mouse, Peromyscus maniculatus, based on biological observations of the system in the North American Southwest. The results of the analysis shed light on relevant observations of the biological system, such as the sporadical disappearance of the infection, and the existence of foci or ``refugia'' that perform as reservoirs of the virus when environmental conditions are less than optimal.Comment: 6 pages, 5 inlined figures, RevTeX 4 forma

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

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

Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies

In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Fast switching, fast on the time-scale of the coupled oscillators, overcomes the descychnronizing decoherence suggested by disconnected instantaneous networks. This result agrees in spirit with that of where empirical evidence suggested that a moving averaged graph Laplacian could be used in the master-stability function analysis. A new fast switching stability criterion here-in gives sufficiency of a fast-switching network leading to synchronization. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD

Debris disks around Sun-like stars

We have observed nearly 200 FGK stars at 24 and 70 microns with the Spitzer Space Telescope. We identify excess infrared emission, including a number of cases where the observed flux is more than 10 times brighter than the predicted photospheric flux, and interpret these signatures as evidence of debris disks in those systems. We combine this sample of FGK stars with similar published results to produce a sample of more than 350 main sequence AFGKM stars. The incidence of debris disks is 4.2% (+2.0/-1.1) at 24 microns for a sample of 213 Sun-like (FG) stars and 16.4% (+2.8/-2.9) at 70 microns for 225 Sun-like (FG) stars. We find that the excess rates for A, F, G, and K stars are statistically indistinguishable, but with a suggestion of decreasing excess rate toward the later spectral types; this may be an age effect. The lack of strong trend among FGK stars of comparable ages is surprising, given the factor of 50 change in stellar luminosity across this spectral range. We also find that the incidence of debris disks declines very slowly beyond ages of 1 billion years.Comment: ApJ, in pres

Dimension in a Radiative Stellar Atmosphere

Dimensional scales are examined in an extended 3+1 Vaidya atmosphere surrounding a Schwarzschild source. At one scale, the Vaidya null fluid vanishes and the spacetime contains only a single spherical 2-surface. Both of these behaviors can be addressed by including higher dimensions in the spacetime metric.Comment: to appear in Gen. Rel. Gra

Dynamics of lattice spins as a model of arrhythmia

We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the medium) disturbances and construct lattice models for description of not-so-smooth disturbances, in particular, topological defects; these models are modifications of the diffusive XY model. We find that when the activity on each lattice site is very rigid in maintaining its form, the topological defects - vortices or spirals - nucleate a transition to a disordered, turbulent state.Comment: 17 pages, revtex, 3 figure