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Edward Ott

Publications and source records attributed to Edward Ott.

At least 19 recordsLinked to original sources
PubMed2006

Universal properties of two-port scattering, impedance, and admittance matrices of wave-chaotic systems.

Statistical fluctuations in the eigenvalues of the scattering, impedance, and admittance matrices of two-port wave-chaotic systems are studied experimentally using a chaotic microwave cavity. These fluctuations are universal in that their properties are dependent only upon the degree of loss in the cavity. We remove the direct processes introduced by the nonideally coupled driving ports through a matrix normalization process that involves the radiation-impedance matrix of the two driving ports. We find good agreement between the experimentally obtained marginal probability density functions (PDFs) of the eigenvalues of the normalized impedance, admittance, and scattering matrix and those from random matrix theory (RMT). We also experimentally study the evolution of the joint PDF of the eigenphases of the normalized scattering matrix as a function of loss. Experimental agreement with the theory by Brouwer and Beenakker for the joint PDF of the magnitude of the eigenvalues of the normalized scattering matrix is also shown.

Journal Article↗
PubMed2006

Characterizing the dynamical importance of network nodes and links.

The largest eigenvalue of the adjacency matrix of networks is a key quantity determining several important dynamical processes on complex networks. Based on this fact, we present a quantitative, objective characterization of the dynamical importance of network nodes and links in terms of their effect on the largest eigenvalue. We show how our characterization of the dynamical importance of nodes can be affected by degree-degree correlations and network community structure. We discuss how our characterization can be used to optimize techniques for controlling certain network dynamical processes and apply our results to real networks.

Journal Article↗
PubMed2006

Emergence of coherence in complex networks of heterogeneous dynamical systems.

We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic, and applies generally to networks for which the number of connections per node is large. We find that the critical coupling strength at which a transition to synchrony takes place depends separately on the dynamics of the individual uncoupled systems and on the largest eigenvalue of the adjacency matrix of the coupling network. Our theory directly generalizes the Kuramoto model of equal strength all-to-all coupled phase oscillators to the case of oscillators with more realistic dynamics coupled via a large heterogeneous network.

Computer Communication Networks↗
PubMed2006

Characterization of fluctuations of impedance and scattering matrices in wave chaotic scattering.

In wave chaotic scattering, statistical fluctuations of the scattering matrix S and the impedance matrix Z depend both on universal properties and on nonuniversal details of how the scatterer is coupled to external channels. This paper considers the impedance and scattering variance ratios, Xi(z) and Xi(s), where Xi(z) = Var[Z(ij)]/{Var[Z(ii)]Var[Z(jj)]}1/2, Xi(s) = Var[S(ij)]/{Var[S(ii)]Var[S(jj)]}1/2, and Var[.] denotes variance. Xi(z) is shown to be a universal function of distributed losses within the scatterer. That is, Xi(z) is independent of nonuniversal coupling details. This contrasts with s for which universality applies only in the large loss limit. Explicit results are given for Xi(z) for time reversal symmetric and broken time reversal symmetric systems. Experimental tests of the theory are presented using data taken from scattering measurements on a chaotic microwave cavity.

Journal Article↗
PubMed2006

Scale dependence of branching in arterial and bronchial trees.

Although models of branching in arterial and bronchial trees often predict a dependence of bifurcation parameters on the scale of the bifurcating vessels, direct verification of this dependence by comparison with data is uncommon. We compare measurements of bifurcation parameters of airways and arterial trees of different mammals as a function of scale to general features predicted by theoretical models based on minimization of pumping power and network volume. We find that the size dependence is more complex than existing theories based solely on energy and volume minimization explain, and suggest additional factors that may govern the branching at different scales.

Animals↗
PubMed2006

Synchronization in large directed networks of coupled phase oscillators.

We study the emergence of collective synchronization in large directed networks of heterogeneous oscillators by generalizing the classical Kuramoto model of globally coupled phase oscillators to more realistic networks. We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider the case of networks with mixed positive-negative coupling strengths. We compare our theory with numerical simulations and find good agreement.

Action Potentials↗
PubMed2005

Theoretical mechanics: crowd synchrony on the Millennium Bridge.

Soon after the crowd streamed on to London's Millennium Bridge on the day it opened, the bridge started to sway from side to side: many pedestrians fell spontaneously into step with the bridge's vibrations, inadvertently amplifying them. Here we model this unexpected and now notorious phenomenon--which was not due to the bridge's innovative design as was first thought--by adapting ideas originally developed to describe the collective synchronization of biological oscillators such as neurons and fireflies. Our approach should help engineers to estimate the damping needed to stabilize other exceptionally crowded footbridges against synchronous lateral excitation by pedestrians.

Biological Clocks↗
PubMed2005

Formation of multifractal population patterns from reproductive growth and local resettlement.

We consider the general character of the spatial distribution of a population that grows through reproduction and subsequent local resettlement of new population members. We present several simple one- and two-dimensional point placement models to illustrate possible generic behavior of these distributions. We show, numerically and analytically, that these models all lead to multifractal spatial distributions of population. Additionally, we make qualitative links between our models and the example of the Earth at Night image, showing the Earth's nighttime man-made light as seen from space. The Earth at Night data suffer from saturation of the sensing photodetectors at high brightness ("clipping"), and we account for how this influences the determined dimension spectrum of the light intensity distribution.

Animals↗
PubMed2005

Intermittency in two-dimensional turbulence with drag.

We consider the enstrophy cascade in forced two-dimensional turbulence with a linear drag force. In the presence of linear drag, the energy wave-number spectrum drops with a power law faster than in the case without drag, and the vorticity field becomes intermittent, as shown by the anomalous scaling of the vorticity structure functions. Using previous theory, we compare numerical simulation results with predictions for the power law exponent of the energy wave-number spectrum and the scaling exponents of the vorticity structure functions zeta(2q). We also study, both by numerical experiment and theoretical analysis, the multifractal structure of the viscous enstrophy dissipation in terms of its Rényi dimension spectrum D(q). We derive a relation between D(q) and zeta(2q), and discuss its relevance to a version of the refined similarity hypothesis. In addition, we obtain and compare theoretically and numerically derived results for the dependence on separation r of the probability distribution of delta(r)omega, the difference between the vorticity at two points separated by a distance r. Our numerical simulations are done on a 4096 x 4096 grid.

Journal Article↗
PubMed2005

Exponential decay of chaotically advected passive scalars in the zero diffusivity limit.

The time asymptotic decay of the variance of a passive scalar in a chaotic flow is studied. Two mechanisms for this decay, which involve processes at short and long length scales, respectively, are considered. The validity of the short length scale mechanism, which is based on Lagrangian stretching theory, is discussed. We also investigate the regimes of applicability and observable signatures of the two mechanisms. Supporting evidence is provided by high resolution numerical experiments.

Journal Article↗
PubMed2005

Universal statistics of the scattering coefficient of chaotic microwave cavities.

We consider the statistics of the scattering coefficient S of a chaotic microwave cavity coupled to a single port. We remove the nonuniversal effects of the coupling from the experimental S data using the radiation impedance obtained directly from the experiments. We thus obtain the normalized scattering coefficient whose probability density function (PDF) is predicted to be universal in that it depends only on the loss (quality factor) of the cavity. We compare experimental PDFs of the normalized scattering coefficients with those obtained from random matrix theory (RMT), and find excellent agreement. The results apply to scattering measurements on any wave chaotic system.

Journal Article↗
PubMed2005

Onset of synchronization in large networks of coupled oscillators.

We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition and generalize recent results for the critical coupling strength. We find that, under appropriate conditions, the coupling strength at which the transition occurs is determined by the largest eigenvalue of the adjacency matrix. We show how, with an additional assumption, a mean-field approximation recently proposed is recovered from our results. We test our theory with numerical simulations and find that it describes the transition when our assumptions are satisfied. We find that our theory describes the transition well in situations in which the mean-field approximation fails. We study the finite-size effects caused by nodes with small degree and find that they cause the critical coupling strength to increase.

Journal Article↗
PubMed2005

Universal impedance fluctuations in wave chaotic systems.

We experimentally investigate theoretical predictions of universal impedance fluctuations in wave chaotic systems using a microwave analog of a quantum chaotic infinite square well potential. We emphasize the use of the radiation impedance to remove the nonuniversal effects of the particular coupling between the outside world and the scatterer. Specific predictions that we test include the probability density functions (PDFs) of the real and imaginary parts of the universal impedance, the equality of the variances of these PDFs, and the dependence of these PDFs on a single loss parameter.

Journal Article↗
PubMed2004

Segregation in a monolayer of magnetic spheres.

Segregation and pattern formation is investigated for binary mixtures of granular magnetic spheres in a vertically vibrated monolayer. The spheres, all of equal mass and size, have a maximum surface magnetic field B induced by encased cylindrical magnetic cores of length l. For binary mixtures of particles with equal l but different B, we find that the particles spontaneously segregate when driven. For fixed vibration frequency, the segregation rate increases roughly linearly with driving acceleration over the amplitudes investigated. For systems of fixed particle number density, the rate of segregation also decreases as the volume fraction of "strong" (high B) particles increases. We find that segregation also occurs in binary mixtures of particles with equal B, but different l. Finally, using a simple model of spheres with dipolar and higher magnetic moments, we show that the observed segregation phenomena occur in conjunction with a decrease in magnetic energy.

Journal Article↗
PubMed2004

Desynchronization waves and localized instabilities in oscillator arrays.

We consider a ring of identical or near-identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the desynchronization transition that occurs as the coupling strengths are increased. We demonstrate Anderson localization of the modes of instability and show that such localized instability generates waves of desynchronization that spread to the whole array. Similar results should apply to other networks with regular topology and heterogeneous connection strengths.

Journal Article↗
PubMed2004

Spatial patterns of desynchronization bursts in networks.

We adapt a previous model and analysis method (the master stability function), extensively used for studying the stability of the synchronous state of networks of identical chaotic oscillators, to the case of oscillators that are similar but not exactly identical. We find that bubbling induced desynchronization bursts occur for some parameter values. These bursts have spatial patterns, which can be predicted from the network connectivity matrix and the unstable periodic orbits embedded in the attractor. We test the analysis of bursts by comparison with numerical experiments. In the case that no bursting occurs, we discuss the deviations from the exactly synchronous state caused by the mismatch between oscillators.

Journal Article↗
PubMed2004

Onset of synchronization in systems of globally coupled chaotic maps.

We study the transition to coherence of an ensemble of globally coupled chaotic maps allowing for ensembles of nonidentical maps and for noise. The transition coupling strength is determined from a kind of transfer function of the perturbation evolution. We present analytical results, and we test these results using numerical experiments for several large systems consisting of ensembles of many coupled maps. The later includes ensembles of identical noiseless maps, identical maps subject to noise, and ensembles of nonidentical maps. One of our examples suggests that the validity of the perturbation theory approach can be problematic for an ensemble of noiseless identical maps if the maps are nonhyperbolic. However, for such a case, noise and/or parameter spread seems to have a regularizing effect restoring the validity of perturbation theory.

Journal Article↗