Synchronization in disordered Josephson junction arrays: Small-world connections and the Kuramoto model

We study synchronization in disordered arrays of Josephson junctions. In the first half of the paper, we consider the relation between the coupled resistively- and capacitively shunted junction (RCSJ) equations for such arrays and effective phase models of the Winfree type. We describe a multiple-time scale analysis of the RCSJ equations for a ladder array of junctions \textit{with non-negligible capacitance} in which we arrive at a second order phase model that captures well the synchronization physics of the RCSJ equations for that geometry. In the second half of the paper, motivated by recent work on small world networks, we study the effect on synchronization of random, long-range connections between pairs of junctions. We consider the effects of such shortcuts on ladder arrays, finding that the shortcuts make it easier for the array of junctions in the nonzero voltage state to synchronize. In 2D arrays we find that the additional shortcut junctions are only marginally effective at inducing synchronization of the active junctions. The differences in the effects of shortcut junctions in 1D and 2D can be partly understood in terms of an effective phase model.Comment: 31 pages, 21 figure

Nanomechanical-resonator-induced synchronization in Josephson junction arrays

We show that a serial array of N nonuniform, underdamped Josephson junctions coupled piezoelectrically to a nanoelectromechanical (NEM) oscillator results in phase locking of the junctions. Our approach is based on a semiclassical solution to a set of coupled differential equations that were generated by the Heisenberg operator equations, which in turn are based on a model Hamiltonian that includes the following effects: the charging and Josephson energies of the junctions, dissipation in the junctions, the effect of a dc bias current, an undamped simple harmonic oscillator (representing the NEM), and an interaction energy (due to the piezoelectric effect) between the NEM and the junctions. Phase locking of the junctions is signaled by a step in the current-voltage (I-V) curve. We find the phase-locked states are (neutrally) stable at the bottom and top of the step but not for bias currents in the middle of the step. Using harmonic balance, we are able to calculate an analytical expression for the location of the resonance step, v_step, in the I-V curve. Because of the multistability of the underdamped junctions, it is possible, with a judicious choice of initial conditions and bias current, to set a desired number N_a≤N of junctions on the resonance step, with N−N_a junctions in the zero-voltage state. We are also able to show that, when Na junctions are in the phase-locked configuration, the time-averaged energy of the NEM oscillator scales like N_a^2

Instabilities in Josephson Ladders with Current Induced Magnetic Fields

We report on a theoretical analysis, consisting of both numerical and analytic work, of the stability of synchronization of a ladder array of Josephson junctions under the influence of current induced magnetic fields. Surprisingly, we find that as the ratio of the mutual to self inductance of the cells of the array is increased a region of unstable behavior occurs followed by reentrant stable synchronization. Analytic work tells us that in order to understand fully the cause of the observed instabilities the behavior of the vertical junctions, sometimes ignored in analytic analyses of ladder arrays, must be taken into account.Comment: RevTeX, 4 pages, 3 figure

Detection and Estimation Theory

Contains research objectives, summary of research and reports on one research project.Joint Services Electronics Programs (U. S. Army, U.S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E

Detection and Estimation Theory

Contains research objectives and summary of research.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DAAB07-71-C-030

Detection and Estimation Theory

Contains research objectives and reports on two research projects.Joint Services Electronics Programs (U. S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 36-039-AMC-03200(E

Food Habits of Sympatric Pitvipers from the West Gulf Coastal Plain, USA

Widespread species that occupy multiple communities exhibit geographic variation in their natural history due to the ecological context of the local community. An animal’s food habitats are a central component to understanding its natural history and ecological role within its community—information that is critical to understanding resource needs of a species, mechanisms of species coexistence, and energy flow in food webs (Litvaitis 2000; Schalk et al. 2014). This information is also crucial for predicting the response of populations to changes in resource availability and, if necessary, inform mitigation strategies (Holycross and Mackessy 2002

Detection and Estimation Theory

Contains research objectives, summary of research and reports on one research project.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DAAB07-71-C-0300National Science Foundation (Grant GX-36331

Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous time limit and state-variable approach to phase-locked loop design

We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [Tsang, Shapiro, and Lloyd, Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to estimation, we design homodyne phase-locked loops that can measure the temporal phase with quantum-limited accuracy. We show that post-processing can further improve the estimation performance, if delay is allowed in the estimation. We also investigate the fundamental uncertainties in the simultaneous estimation of harmonic-oscillator position and momentum via continuous optical phase measurements from the classical estimation theory perspective. In the case of delayed estimation, we find that the inferred uncertainty product can drop below that allowed by the Heisenberg uncertainty relation. Although this result seems counter-intuitive, we argue that it does not violate any basic principle of quantum mechanics.Comment: 11 pages, 6 figures, v2: accepted by PR