Showing papers by "Mauricio Barahona published in 1998"
Patent•
13 May 1998TL;DR: In this paper, a nonlinear characteristic of an autonomous (i.e., non-driven and time-invariant) dynamical system and whether it is chaotic are discussed.
Abstract: Methods and apparatus are provided for detecting the presence of a nonlinear characteristic of an autonomous (i.e., non-driven and time-invariant), dynamical system and for determining whether such nonlinear dynamical system is chaotic. First, a system is determined to be either nonlinear or linear. If the system is determined to be nonlinear, then noise of increasing intensity is incrementally added to a data set representing the analyzed system until the resulting test signal appears to be linear. If the noise limit of the resulting test signal is significantly greater than zero, then the system is determined to be chaotic and the amount of noise added to the data set provides an indication of the relative strength of the chaos. Alternatively, if the noise limit of the resulting test signal is approximately zero, then the system is determined to be nonlinear with periodic or quasi-periodic limit cycles. An optional power spectrum test is described with which it can be confirmed that the system is nonlinear with periodic or quasi-periodic limit cycles.
44 citations
TL;DR: In this article, the dynamics of one-dimensional arrays of Josephson junctions connected in parallel by superconducting wires are studied. But the model is more complicated than that of the purely 1D sine-Gordon system.
14 citations
TL;DR: In this paper, the authors present analytical and numerical studies of pinned superconducting states of open-ended Josephson ladder arrays, neglecting inductances but taking edge effects into account.
Abstract: We present analytical and numerical studies of pinned superconducting states of open-ended Josephson ladder arrays, neglecting inductances but taking edge effects into account. Treating the edge effects perturbatively, we find analytical approximations for three of these superconducting states{emdash}the no-vortex, fully frustrated, and single-vortex states{emdash}as functions of the dc bias current I and the frustration f. Bifurcation theory is used to derive formulas for the depinning currents and critical frustrations at which the superconducting states disappear or lose dynamical stability as I and f are varied. These results are combined to yield a zero-temperature stability diagram of the system with respect to I and f. To highlight the effects of the edges, we compare this dynamical stability diagram to the thermodynamic phase diagram for the infinite system where edges have been neglected. We briefly indicate how to extend our methods to include self-inductances. {copyright} {ital 1998} {ital The American Physical Society}
8 citations
TL;DR: In this article, the row-switched RS states in underdamped two-dimensional Josephson arrays were studied, driven by a uniform dc current under external magnetic field but neglecting self-fields, and the governing equations were cast into a compact differential algebraic system which describes the dynamics of an assembly of Josephson oscillators coupled through the mesh current.
Abstract: When magnetic flux moves across layered or granular superconductor structures, the passage of vortices can take place along channels which develop finite voltage, while the rest of the material remains in the zerovoltage state. We study analytically an example of such mixed dynamics: the row-switched ~RS! states in underdamped two-dimensional Josephson arrays, driven by a uniform dc current under external magnetic field but neglecting self-fields. The governing equations are cast into a compact differential-algebraic system which describes the dynamics of an assembly of Josephson oscillators coupled through the mesh current. We carry out a formal perturbation expansion, and obtain the dc and ac spatial distributions of the junction phases and induced circulating currents. We also estimate the interval of the driving current in which a given RS state is stable. All these analytical predictions compare well with our numerics. We then combine these results to deduce the parameter region ~in the damping coefficient vs magnetic-field plane ! where RS states cannot exist.
8 citations
TL;DR: In this article, the authors derived a stability criterion for superconducting pinned states in two-dimensional arrays of Josephson junctions, and proved that a pinned state is linearly stable if and only if its corresponding stiffness matrix is positive definite.
Abstract: Using the lumped circuit equations, we derive a stability criterion for superconducting pinned states in two-dimensional arrays of Josephson junctions. The analysis neglects quantum, thermal, and inductive effects, but allows disordered junctions, arbitrary network connectivity, and arbitrary spatial patterns of applied magnetic flux and dc current injection. We prove that a pinned state is linearly stable if and only if its corresponding stiffness matrix is positive definite. This algebraic condition can be used to predict the critical current and frustration at which depinning occurs.
3 citations