The 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.Comment: 4 pages, 1 figure. Published versio

Alternative determinism principle for topological analysis of chaos

The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon which this approach is built, determinism and continuity, apply in any dimension. We propose an alternative framework in which these principles are enforced on triangulated surfaces rather than curves and show that in dimension three our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.Comment: Accepted for publication as Rapid Communication in Physical Review

Dispersion relations for stationary light in one-dimensional atomic ensembles

We investigate the dispersion relations for light coupled to one-dimensional ensembles of atoms with different level schemes. The unifying feature of all the considered setups is that the forward and backward propagating quantum fields are coupled by the applied classical drives such that the group velocity can vanish in an effect known as "stationary light". We derive the dispersion relations for all the considered schemes, highlighting the important differences between them. Furthermore, we show that additional control of stationary light can be obtained by treating atoms as discrete scatterers and placing them at well defined positions. For the latter purpose, a multi-mode transfer matrix theory for light is developed

Excitation of atomic hydrogen to the metasable 2 2S1/2 state by electron impact

Atomic hydrogen excitation to metastable 2 /2/ S sub 1/2 state by electron impac

Polarization of Lyman alpha radiation emitted by H/2S/ atoms in weak electric fields

Polarization prediction in modulated beam of ground state hydrogen atoms crossed by dc electron bea

Rectenna system design

The function of the rectenna in the solar power satellite system is described and the basic design choices based on the desired microwave field concentration and ground clearance requirements are given. One important area of concern, from the EMI point of view, harmonic reradiation and scattering from the rectenna is also designed. An optimization of a rectenna system design to minimize costs was performed. The rectenna cost breakdown for a 56 w installation is given as an example

Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness

Spinning black hole pairs exhibit a range of complicated dynamical behaviors. An interest in eccentric and zoom-whirl orbits has ironically inspired the focus of this paper: the constant radius orbits. When black hole spins are misaligned, the constant radius orbits are not circles but rather lie on the surface of a sphere and have acquired the name "spherical orbits". The spherical orbits are significant as they energetically frame the distribution of all orbits. In addition, each unstable spherical orbit is asymptotically approached by an orbit that whirls an infinite number of times, known as a homoclinic orbit. A homoclinic trajectory is an infinite whirl limit of the zoom-whirl spectrum and has a further significance as the separatrix between inspiral and plunge for eccentric orbits. We work in the context of two spinning black holes of comparable mass as described in the 3PN Hamiltonian with spin-orbit coupling included. As such, the results could provide a testing ground of the accuracy of the PN expansion. Further, the spherical orbits could provide useful initial data for numerical relativity. Finally, we comment that the spinning black hole pairs should give way to chaos around the homoclinic orbit when spin-spin coupling is incorporated.Comment: 16 pages, several figure

Universality Class of the Reversible-Irreversible Transition in Sheared Suspensions

Collections of non-Brownian particles suspended in a viscous fluid and subjected to oscillatory shear at very low Reynolds number have recently been shown to exhibit a remarkable dynamical phase transition separating reversible from irreversible behaviour as the strain amplitude or volume fraction are increased. We present a simple model for this phenomenon, based on which we argue that this transition lies in the universality class of the conserved DP models or, equivalently, the Manna model. This leads to predictions for the scaling behaviour of a large number of experimental observables. Non-Brownian suspensions under oscillatory shear may thus constitute the first experimental realization of an inactive-active phase transition which is not in the universality class of conventional directed percolation.Comment: 4 pages, 2 figures, final versio

Quantifying Spatiotemporal Chaos in Rayleigh-B\'enard Convection

Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-B\'enard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov exponents and the leading order Lyapunov vector with system parameters to quantify states of high-dimensional chaos in fluid convection. We explore the relationship between the time dynamics of the spectrum of Lyapunov exponents and the pattern dynamics. For chaotic dynamics we find that all of the Lyapunov exponents are positively correlated with the leading order Lyapunov exponent and we quantify the details of their response to the dynamics of defects. The leading order Lyapunov vector is used to identify topological features of the fluid patterns that contribute significantly to the chaotic dynamics. Our results show a transition from boundary dominated dynamics to bulk dominated dynamics as the system size is increased. The spectrum of Lyapunov exponents is used to compute the variation of the fractal dimension with system parameters to quantify how the underlying high-dimensional strange attractor accommodates a range of different chaotic dynamics

Multifractal clustering of passive tracers on a surface flow

We study the anomalous scaling of the mass density measure of Lagrangian tracers in a compressible flow realized on the free surface on top of a three dimensional flow. The full two dimensional probability distribution of local stretching rates is measured. The intermittency exponents which quantify the fluctuations of the mass measure of tracers at small scales are calculated from the large deviation form of stretching rate fluctuations. The results indicate the existence of a critical exponent $n_c \simeq 0.86$ above which exponents saturate, in agreement with what has been predicted by an analytically solvable model. Direct evaluation of the multi-fractal dimensions by reconstructing the coarse-grained particle density supports the results for low order moments.Comment: 7 pages, 4 figures, submitted to EP