Mean field theory of assortative networks of phase oscillators

Employing the Kuramoto model as an illustrative example, we show how the use of the mean field approximation can be applied to large networks of phase oscillators with assortativity. We then use the ansatz of Ott and Antonsen [Chaos 19, 037113 (2008)] to reduce the mean field kinetic equations to a system of ordinary differential equations. The resulting formulation is illustrated by application to a network Kuramoto problem with degree assortativity and correlation between the node degrees and the natural oscillation frequencies. Good agreement is found between the solutions of the reduced set of ordinary differential equations obtained from our theory and full simulations of the system. These results highlight the ability of our method to capture all the phase transitions (bifurcations) and system attractors. One interesting result is that degree assortativity can induce transitions from a steady macroscopic state to a temporally oscillating macroscopic state through both (presumed) Hopf and SNIPER (saddle-node, infinite period) bifurcations. Possible use of these techniques to a broad class of phase oscillator network problems is discussed.Comment: 8 pages, 7 figure

Risk aversion, efficient markets and the forward exchange rate

Foreign exchange futures ; Foreign exchange rates ; Interest rates

Spectrum of the Andreev Billiard and Giant Fluctuations of the Ehrenfest Time

The density of states in the semiclassical Andreev billiard is theoretically studied and shown to be determined by the fluctuations of the classical Lyapunov exponent $\lambda$. The rare trajectories with a small value of $\lambda$ give rise to an anomalous increase of the Ehrenfest time $\tau_E\approx |\ln\hbar|/\lambda$ and, consequently, to the appearance of Andreev levels with small excitation energy. The gap in spectrum is obtained and fluctuations of the value of the gap due to different positions of superconducting lead are considered.Comment: 4 pages, 3 figure

2δ2\delta-Kicked Quantum Rotors: Localization and `Critical' Statistics

The quantum dynamics of atoms subjected to pairs of closely-spaced $\delta$-kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the singly-$\delta$-kicked system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase-space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power $L \sim \hbar^{-.75}$ and obtain a regime of near-linear spectral variances which approximate the `critical statistics' relation $\Sigma_2(L) \simeq \chi L \approx {1/2}(1-\nu) L$, where $\nu \approx 0.75$ is related to the fractal classical phase-space structure. The origin of the $\nu \approx 0.75$ exponent is analyzed.Comment: 4 pages, 3 fig

Synchronization in large directed networks of coupled phase oscillators

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 extensions to networks with mixed positive/negative coupling strengths. We compare our theory with numerical simulations and find good agreement

New H_(2)O masers in Seyfert and FIR bright galaxies: III. The southern sample

Context. A relationship between the water maser detection rate and far infrared (FIR) flux densities was established as a result of two 22 GHz maser surveys in a complete sample of galaxies (Dec > −30°) with flux densities of >50 Jy and >30 Jy. Aims. We attempted to discover new maser sources and investigate the galaxies hosting the maser spots by extending previous surveys to southern galaxies with particular emphasis on the study of their nuclear regions. Methods. A sample of 12 galaxies with Dec 50 Jy was observed with the 70-m telescope of the Canberra deep space communication complex (CDSCC) at Tidbinbilla (Australia) in a search for water maser emission. The average 3σ noise level of the survey was 15 mJy for a 0.42 km s^(−1) channel, corresponding to a detection threshold of ∼0.1 L_☉ for the isotropic maser luminosity at a distance of 25 Mpc. Results. Two new detections are reported: a kilomaser with an isotropic luminosity L_(H_(2)O) ~ 5 L_☉ in NGC 3620 and a maser with about twice this luminosity in the merger system NGC 3256. The detections have been followed-up by continuum and spectral line interferometric observations with the Australia Telescope Compact Array (ATCA). In NGC 3256, a fraction (about a third) of the maser emission originates in two hot spots associated with star formation activity, which are offset from the galactic nuclei of the system. The remaining emission may originate in weaker centres of maser activity distributed over the central 50". For NGC 3620, the water maser is coincident with the nuclear region of the galaxy. Our continuum observations indicate that the nature of the nuclear emission is probably linked to particularly intense star formation. Including the historical detection in NGC 4945, the water maser detection rate in the southern sample is 15% (3/20), consistent with the northern sample. The high rate of maser detections in the complete all-sky FIR sample (23%, 15/65) confirms the existence of a link between overall FIR flux density and maser phenomena. A relation between H_(2)O and OH masers in the FIR sample is also discussed

Statistically Locked-in Transport Through Periodic Potential Landscapes

Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a Devil's staircase hierarchy of commensurate trajectories depending on the orientation of the driving force. Recent experiments on colloidal spheres flowing through arrays of optical traps do indeed reveal such a hierarchy,but not with the predicted structure. The microscopic trajectories, moreover,appear to be random, with commensurability emerging only in a statistical sense. We introduce an idealized model for periodically modulated transport in the presence of randomness that captures both the structure and statistics of such statistically locked-in states.Comment: REVTeX with EPS figures, 4 pages, 4 figure

Microelectromagnets for Trapping and Manipulating Ultracold Atomic Quantum Gases

We describe the production and characterization of microelectromagnets made for trapping and manipulating atomic ensembles. The devices consist of 7 fabricated parallel copper conductors 3 micrometer thick, 25mm long, with widths ranging from 3 to 30 micrometer, and are produced by electroplating a sapphire substrate. Maximum current densities in the wires up to 6.5 * 10^6 A / cm^2 are achieved in continuous mode operation. The device operates successfully at a base pressure of 10^-11 mbar. The microstructures permit the realization of a variety of magnetic field configurations, and hence provide enormous flexibility for controlling the motion and the shape of Bose-Einstein condensates.Comment: 4 pages, 3 figure