Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs.

The statistical properties of wave chaotic systems of varying dimensionalities and realizations have been studied extensively. These systems are commonly characterized by the statistics of the eigenmode spacings and the statistics of the eigenfunctions. Here, we propose photonic crystal (PC) defect waveguide graphs as a physical setting for chaotic graph studies.

Wireless power distributions in multi-cavity systems at high frequencies.

The next generations of wireless networks will work in frequency bands ranging from sub-6 GHz up to 100 GHz. Radio signal propagation differs here in several critical aspects from the behaviour in the microwave frequencies currently used. With wavelengths in the millimetre range (mmWave), both penetration loss and free-space path loss increase, while specular reflection will dominate over diffraction as an important propagation channel.

Wave scattering properties of multiple weakly coupled complex systems.

The statistics of the scattering of waves inside single ray-chaotic enclosures have been successfully described by the random coupling model (RCM). We expand the RCM to systems consisting of multiple complex ray-chaotic enclosures with various coupling scenarios. The statistical properties of the model-generated quantities are tested against measured data of electrically large multicavity systems of various designs.

Scattering statistics in nonlinear wave chaotic systems.

The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings, including both microwave and acoustic systems. It is of great interest to extend its use in nonlinear systems.

Revealing underlying universal wave fluctuations in a scaled ray-chaotic cavity with remote injection.

The Random Coupling Model (RCM) predicts the statistical properties of waves inside a ray-chaotic enclosure in the semiclassical regime by using Random Matrix Theory, combined with system-specific information. Experiments on single cavities are in general agreement with the predictions of the RCM. It is now desired to test the RCM on more complex structures, such as a cascade or network of coupled cavities, that represent realistic situations but that are difficult to test due to the large size of the structures of interest.

Nonlinear wave chaos: statistics of second harmonic fields.

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields.

Coherent oscillations of driven rf SQUID metamaterials.

Through experiments and numerical simulations we explore the behavior of rf SQUID (radio frequency superconducting quantum interference device) metamaterials, which show extreme tunability and nonlinearity. The emergent electromagnetic properties of this metamaterial are sensitive to the degree of coherent response of the driven interacting SQUIDs. Coherence suffers in the presence of disorder, which is experimentally found to be mainly due to a dc flux gradient.

Frequency and phase synchronization in large groups: Low dimensional description of synchronized clapping, firefly flashing, and cricket chirping.

A common observation is that large groups of oscillatory biological units often have the ability to synchronize. A paradigmatic model of such behavior is provided by the Kuramoto model, which achieves synchronization through coupling of the phase dynamics of individual oscillators, while each oscillator maintains a different constant inherent natural frequency. Here we consider the biologically likely possibility that the oscillatory units may be capable of enhancing their synchronization ability by adaptive frequency dynamics.

Modeling the network dynamics of pulse-coupled neurons.

We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions and degree correlations (assortativity). Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)], we obtain a reduced system of ordinary differential equations describing the mean-field dynamics, with significantly lower dimensionality compared with the complete set of dynamical equations for the system. We find that, for sufficiently large networks and degrees, the dynamical behavior of the reduced system agrees well with that of the full network.

Resynchronization of circadian oscillators and the east-west asymmetry of jet-lag.

Cells in the brain's Suprachiasmatic Nucleus (SCN) are known to regulate circadian rhythms in mammals. We model synchronization of SCN cells using the forced Kuramoto model, which consists of a large population of coupled phase oscillators (modeling individual SCN cells) with heterogeneous intrinsic frequencies and external periodic forcing. Here, the periodic forcing models diurnally varying external inputs such as sunrise, sunset, and alarm clocks.

Focusing waves at arbitrary locations in a ray-chaotic enclosure using time-reversed synthetic sonas.

Time-reversal methods are widely used to achieve wave focusing in acoustics and electromagnetics. Past time-reversal experiments typically require that a transmitter be initially present at the target focusing point, which limits the application of this technique. In this paper, we propose a method to focus waves at an arbitrary location inside a complex enclosure using a numerically calculated wave excitation signal.

Impact of imperfect information on network attack.

This paper explores the effectiveness of network attack when the attacker has imperfect information about the network. For Erdős-Rényi networks, we observe that dynamical importance and betweenness centrality-based attacks are surprisingly robust to the presence of a moderate amount of imperfect information and are more effective compared with simpler degree-based attacks even at moderate levels of network information error. In contrast, for scale-free networks the effectiveness of attack is much less degraded by a moderate level of information error.

Universal instability for wavelengths below the ion Larmor scale.

We demonstrate that the universal mode driven by the density gradient in a plasma slab can be absolutely unstable even in the presence of reasonable magnetic shear. Previous studies from the 1970s that reached the opposite conclusion used an eigenmode equation limited to L_{x}≫ρ_{i}, where L_{x} is the scale length of the mode in the radial direction, and ρ_{i} is the ion Larmor radius. Here we instead use a gyrokinetic approach which does not have this same limitation.

Spatially embedded growing small-world networks.

Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. Motivated by the growth and development of neuronal networks, we propose a class of spatially-based growing network models and investigate the resulting statistical network properties as a function of the dimension and topology of the space in which the networks are embedded. In particular, we consider two models in which nodes are placed one by one in random locations in space, with each such placement followed by configuration relaxation toward uniform node density, and connection of the new node with spatially nearby nodes.

Phase and amplitude dynamics in large systems of coupled oscillators: growth heterogeneity, nonlinear frequency shifts, and cluster states.

This paper addresses the behavior of large systems of heterogeneous, globally coupled oscillators each of which is described by the generic Landau-Stuart equation, which incorporates both phase and amplitude dynamics of individual oscillators. One goal of our paper is to investigate the effect of a spread in the amplitude growth parameter of the oscillators and of the effect of a homogeneous nonlinear frequency shift. Both of these effects are of potential relevance to recently reported experiments.

Statistical model of short wavelength transport through cavities with coexisting chaotic and regular ray trajectories.

We study the statistical properties of the impedance matrix (related to the scattering matrix) describing the input-output properties of waves in cavities in which ray trajectories that are regular and chaotic coexist (i.e., "mixed" systems).

Weakly explosive percolation in directed networks.

Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness of power grids and information networks, the spreading of epidemics and forest fires, and the stability of gene regulatory networks. Recent studies have shown that if network edges are added "competitively" in undirected networks, the onset of percolation is abrupt or "explosive.

Theory of chaos regularization of tunneling in chaotic quantum dots.

Recent numerical experiments of Pecora et al. [Phys. Rev.

Impedance and power fluctuations in linear chains of coupled wave chaotic cavities.

The flow of electromagnetic wave energy through a chain of coupled cavities is considered. The cavities are assumed to be of sufficiently irregular shape that their eigenmodes are described by random matrix theory. The cavities are coupled by electrically short single mode transmission lines.

Multiscale dynamics in communities of phase oscillators.

We investigate the dynamics of systems of many coupled phase oscillators with heterogeneous frequencies. We suppose that the oscillators occur in M groups. Each oscillator is connected to other oscillators in its group with "attractive" coupling, such that the coupling promotes synchronization within the group.

First-principles model of time-dependent variations in transmission through a fluctuating scattering environment.

Fading is the time-dependent variation in transmitted signal strength through a complex medium due to interference or temporally evolving multipath scattering. In this paper we use random matrix theory (RMT) to establish a first-principles model for fading, including both universal and nonuniversal effects. This model provides a more general understanding of the most common statistical models (Rayleigh fading and Rice fading) and provides a detailed physical basis for their parameters.

Simulation of terahertz generation in corrugated plasma waveguides.

We simulate the response of a corrugated plasma channel to an ultrashort laser pulse in two dimensions with the goal of demonstrating the production of terahertz frequency electromagnetic modes. Corrugated channels support electromagnetic modes that have a Floquet-type dispersion relation and thus consist of a sum of spatial harmonics with subluminal phase velocities. This allows the possibility of phase matching between the ponderomotive potential associated with the laser pulse and the electromagnetic modes of the channel.

Comment on "Long time evolution of phase oscillator systems" [Chaos 19, 023117 (2009)].

In a recent paper by Ott and Antonsen [Chaos 19, 023117 (2009)], it was shown for the case of Lorentzian distributions of oscillator frequencies that the dynamics of a very general class of large systems of coupled phase oscillators time-asymptotes to a particular simplified form given by Ott and Antonsen [Chaos 18, 037113 (2008)]. This comment extends this previous result to a broad class of oscillator distribution functions.

Local synchronization in complex networks of coupled oscillators.

We investigate the effects that network topology, natural frequency distribution, and system size have on the path to global synchronization as the overall coupling strength between oscillators is increased in a Kuramoto network. In particular, we study the scenario recently found by Gómez-Gardeñes et al. [Phys.

The dynamics of network coupled phase oscillators: an ensemble approach.

We consider the dynamics of many phase oscillators that interact through a coupling network. For a given network connectivity we further consider an ensemble of such systems where, for each ensemble member, the set of oscillator natural frequencies is independently and randomly chosen according to a given distribution function. We then seek a statistical description of the dynamics of this ensemble.