Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session Y39: Other Topics in Statistical Physics |
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Sponsoring Units: GSNP Chair: Harvey Gould, Clark University Room: Morial Convention Center 231 |
Friday, March 14, 2008 11:15AM - 11:27AM |
Y39.00001: Topology and the Transition to Spatiotemporal Chaos Nicholas Ouellette, J.P. Gollub Locations in a vector field where the field magnitude vanishes have special topological significance. For the case of the velocity field of a two-dimensional incompressible fluid, these points come in two types: elliptic (in vortex cores) and hyperbolic (non-rotating stagnation points). Here, we show a novel method for identifying these special points in experimental data sets by considering the local curvature of fluid element trajectories in a thin layer of conducting fluid driven by electromagnetic forcing. By constructing a curvature field, we show that regions of locally high curvature indicate the presence of hyperbolic and elliptic points. By then tracking the motion of these points in time, we show that their dynamics shed light on the transition of the flow to a spatiotemporally chaotic state. When the driving is weak, the hyperbolic and elliptic points are pinned to locations determined by the forcing geometry; when the driving is strong, they wander over the flow domain and interact pairwise. By comparing the behavior of several base flows, we show that our methods are robust even for complex flow situations. [Preview Abstract] |
Friday, March 14, 2008 11:27AM - 11:39AM |
Y39.00002: ABSTRACT HAS BEEN MOVED TO SESSION D9 |
Friday, March 14, 2008 11:39AM - 11:51AM |
Y39.00003: The dependence of vortex shedding on the aeroelastic response of a bluff body Marcel Ilie Airflow over a vertical flat plate is investigated as a function of Reynolds number, using Large Eddy Simulation. It is generally known that the structure of the wake, behind a bluff body, exhibits very complex turbulent flow patterns. In many practical applications the bluff bodies are flexible structures and this characteristic enables them to respond to the aerodynamic loads. The fluid-structure interaction phenomenon is of critical importance due to the inheriting danger associated with the vortex induced vibrations. The periodic shedding of vortices may result in significant fluctuating loading on the body. When the shedding frequency is close to one of the characteristic frequencies of the body, the resonant oscillations of the body can be excited, causing damaging instabilities. In the present analysis, the dependence of vortex shedding on the aeroelastic response of a vertical flat plate in cross-flow is investigated. A CFD based algorithm, using Large Eddy Simulation, is developed for the investigation of a strong (two-way) aeroelastic coupling between a subsonic flow and a flexible flat plate. The results of the present analysis indicate that there is a strong fluid-structure coupling. It was observed that the aeroelastic response of the flat plate is a function of Reynolds number. Also, the aeroelastic response of the flat plate influences the vortex shedding. [Preview Abstract] |
Friday, March 14, 2008 11:51AM - 12:03PM |
Y39.00004: VKS: a turbulent homogeneous dynamo with liquid sodium Michael Berhanu The magnetic field of the earth and of most astrophysical objects result from turbulent flows of electrically conducting fluids: the kinetic energy of the flow is converted into magnetic energy by dynamo effect. In September 2006 we observed this effect for the first time in a closed homogeneous turbulent flow of liquid sodium at very high Reynolds number in the Von-Karman Sodium (VKS). Despite the strong level of the fluctuations of the flow,we observed the growth and saturation of a stationary global mode of the magnetic field at the experiment's characteristic length. Does turbulence act as noise or does it participate in the magnetic generation process? If we modify the global properties of the flow, we observe transitions between different magnetic field modes, going from stationary to oscillatory, and, near the frontiers between these modes, interesting dynamical behaviours occur, such as bursts and relaxations cycles. In particular we found a state with reversals of the magnetic field similar to those of the Earth recorded on geological time scale. These evolutions present some features of low dimensional chaos, compatible with the interaction between few modes. Finally we observe for the first time bistability from a stationary dynamo to an oscillatory one. [Preview Abstract] |
Friday, March 14, 2008 12:03PM - 12:15PM |
Y39.00005: Dynamical Phase Transitions and Scaling Laws in the Response of a Rhythmically Perturbed Neuron Jan Engelbrecht, Renato Mirollo In order to explore how a local rhythm influences the timing of a neuron's spikes, we study the dynamics of an integrate-and-fire model neuron with an oscillatory stimulus. The frustration due to the competition between the neuron's natural firing period and that of the oscillatory rhythm leads to a rich structure of asymptotic phase locking patterns and ordering dynamics. The phase transitions between these states can be classified as either tangent or discontinuous bifurcations, each with its own characteristic scaling laws. The discontinuous bifurcations exhibit a new kind of phase transition that may be viewed as intermediate between continuous and first order, while tangent bifurcations behave like continuous transitions with a diverging coherence scale. [Preview Abstract] |
Friday, March 14, 2008 12:15PM - 12:27PM |
Y39.00006: Correlations, fluctuations and stability of a finite-size network of coupled oscillators Michael Buice, Carson Chow The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the population is not synchronous. This demonstration is facilitated by the construction of a non-equilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in 1/N, where N is the number of oscillators. The N $\rightarrow$ infinity limit of this theory is what is traditionally called mean field theory for the Kuramoto model. [Preview Abstract] |
Friday, March 14, 2008 12:27PM - 12:39PM |
Y39.00007: Time-Shifts and Correlations in Synchronized Chaos Jonathan Blakely, Ned Corron We introduce a new method for predicting characteristics of the synchronized state achieved by a wide class of uni-directional coupling schemes. Specifically, we derive a transfer function from the coupling model that provides estimates of the correlation between the drive and response waveforms, and of the time shift (i.e., lag or anticipation) of the synchronized state. Notably, this approach does not require modeling or simulation of the full coupled system. To demonstrate the method, we compare its predictions to simulations of a variety of different coupled oscillator systems as well as to an experimental system of coupled chaotic electronic circuits. Finally, we show that the transfer function can be exploited to design novel coupling schemes that significantly improve the correlation and increase the maximum achievable time shift. [Preview Abstract] |
Friday, March 14, 2008 12:39PM - 12:51PM |
Y39.00008: A linear reformulation of the Kuramoto model of self-synchronizing coupled oscillators David Roberts This talk will present a linear reformulation of the Kuramoto model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different intrinsic frequencies. The reformulated model provides an alternative coherent framework through which one can analytically tackle synchronization problems that are not amenable to the original Kuramoto analysis. It allows one to 1) find an analytic solution for a new class of continuum systems and 2) solve explicitly for the synchronization order parameter and the critical point of the phase-locking transition for a system with a finite number of oscillators (unlike the original Kuramoto model, which is solvable implicitly only in the mean-field limit). It also makes it possible to probe the system's dynamics as it moves towards a steady state. While this talk will cover only systems with global coupling, the new formalism introduced by the linear reformulation also lends itself to solving systems that exhibit local or asymmetric coupling. [Preview Abstract] |
Friday, March 14, 2008 12:51PM - 1:03PM |
Y39.00009: Constructing almost invariant sets for multi-stable systems Lora Billings, Ira Schwartz We consider the problem of noise driven dynamical systems possessing deterministic multiple stable invariant sets. Noise typically creates a single attractor by mixing the underlying deterministic basins of attraction. We show how to approximate the distributions of the almost invariant stochastic attractors probabilistically. We employ the tools from stochastic Markov operator theory to describe the dynamical evolution. Given a stochastic kernel with a known distribution, we approximate the almost invariant sets by translating the problem into a spectral problem. We illustrate the method on a model from epidemiology in a large population. This method distinguishes two almost invariant sets, having large and small outbreaks. [Preview Abstract] |
Friday, March 14, 2008 1:03PM - 1:15PM |
Y39.00010: The Critical Properties of Two-dimensional Oscillator Arrays Gabriele Migliorini We present a renormalization group study of two dimensional arrays of oscillators, with dissipative, short range interactions. We consider the case of non-identical oscillators, with distributed intrinsic frequencies within the array and study the steady-state properties of the system. In two dimensions no macroscopic mutual entrainment is found but, for identical oscillators, critical behavior of the Berezinskii-Kosterlitz-Thouless type is shown to be present. We then discuss the stability of (BKT) order in the physical case of distributed quenched random frequencies. In order to do that, we show how the steady-state dynamical properties of the two dimensional array of non-identical oscillators are related to the equilibrium properties of the XY model with quenched randomness, that has been already studied in the past. We propose a novel set of recursion relations to study this system within the Migdal Kadanoff renormalization group scheme, by mean of the discrete clock-state formulation. We compute the phase diagram in the presence of random dissipative coupling, at finite values of the clock state parameter. Possible experimental applications in two dimensional arrays of microelectromechanical oscillators are briefly suggested. [Preview Abstract] |
Friday, March 14, 2008 1:15PM - 1:27PM |
Y39.00011: Correlations of Coupled Logistic Maps John Harrison, Richard Taylor, Gus Hart Many systems in the world are non-linear and therefore often chaotic. Moreover, many systems influence or are influenced by other physical systems. That is, systems are often coupled to other systems. In an effort to uncover the fundamental issues of coupled systems, we have studied a system of coupled logistic maps. The logistic map, arguably the simplest chaotic system, shows unusual correlations when coupled to a second logistic map. We use a master--slave coupling, where the first map influences the second, but not the other way around. At low coupling strengths the correlations are complex but the two maps do not completely synchronize. At higher coupling strengths, the two maps ``lock'', becoming synchronized. The value of coupling that causes the two maps to lock can be determined analytically. Intriguingly, at intermediate couplings strengths, periodic forcing by the master can result in chaotic behavior in the slave. [Preview Abstract] |
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