Noise-induced intermittency in a superconducting microwave resonator

Bachar, Gal; Segev, Eran; Shtempluck, Oleg; Shaw, Steven W.; Buks, Eyal

doi:10.1209/0295-5075/89/17003

Cited by 16 publications

(30 citation statements)

References 31 publications

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“…4, we revisit this and discuss the model's practical significance. We find three discontinuity-induced bifurcations that occur in sequence, from the creation of a periodic orbit of saddle-type (one positive and one negative eigenvalue), to 1 Department of Engineering Mathematics, University of Bristol, Bristol BS8 1TR, United Kingdom. its subsequent role in the catastrophic sliding bifurcation that destroys a self-sustaining thermal oscillation. The sequence of bifurcations is confirmed numerically in the limit of fast heat transfer ǫ → 0, where the system becomes piecewise-linear.…”

Section: Introductionmentioning

confidence: 99%

“…[3,5]. In this paper we study the piecewise smooth model of a superconducting resonator, derived in [1,11,12,13] to explain the appearance of novel self-sustaining oscillations, to show how an attractor is created, and the oscillations destroyed, via a sequence of discontinuity-induced bifurcations whose theory that are novel from both theoretical and experimental perspectives.…”

Section: Introductionmentioning

confidence: 99%

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Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator

Jeffrey

2012

Physica D: Nonlinear Phenomena

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Jeffrey, M. R. (2012). Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator. University of Bristol -Explore Bristol Research General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator Mike R. Jeffrey 1 AbstractThe nonsmooth dynamical model of a superconducting resonator is discussed, based on previous experimental and analytical studies. The device is a superconducting sensor whose key elements are a sensor probe attached to a conducting ring, around which flows an electric current. The ring is interrupted by a microbridge of superconducting material, whose temperature can be altered to sensitively control the device's conductivity. In certain conditions, novel self-sustaining power oscillations are observed, and can suddenly disappear. It was previously shown that this disappearance can be described by a periodic attractor undergoing a catastrophic sliding bifurcation. Here we reveal the sequence of bifurcations that leads up to this event, beginning with the change in stability of a fixed point that creates an attractor, and the birth of a saddle-type periodic orbit by means of a Hopf-like discontinuity-induced bifurcation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator

Jeffrey

2012

Physica D: Nonlinear Phenomena

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“…Based on the qualitative form of (40) we approximate Lε(v) in (38) as Lε(v) = Λε(v) for the sake of the friction model in (5).…”

Section: Closing Remarks and Friction-inspired Modelsmentioning

confidence: 99%

“…[35,39,46,48]), and this is typical of interactions not only in mechanics, but in other physical, chemical and biological systems (e.g. [5,30,28,15,19]). One approach is to take both features to their extreme limit by collapsing Engineering Mathematics, University of Bristol, UK, email: mike.jeffrey@bristol.ac.uk certain of the nonlinearities and faster timescales into a sharp event: a discontinuity.…”

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confidence: 99%

On the mathematical basis of solid friction

Jeffrey

2015

Nonlinear Dyn

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Noname manuscript No.(will be inserted by the editor)The mathematical description of friction between solid bodies Mike R. Jeffrey May 8, 2014 Abstract A piecewise-smooth ordinary differential equation model of a dry-friction oscillator is studied, as a paradigm for the role of nonlinear and hysteretic terms in discontinuities of dynamical systems. The friction discontinuity is a switch in direction of the contact force in the transition between left and rightward slipping motion. Nonlinear terms introduce dynamics that is novel in the context of piecewise-smooth dynamical systems theory (in particular they are outside the standard Filippov convention), but are shown to account naturally for static friction, and moreover provide a simple route to including hysteresis. The nonlinear terms are understood in terms of dummy dynamics at the discontinuity, given a formal derivation here. The result is a three-parameter model built on the minimal mathematical features necessary to account for the key characteristics of dry friction. The effect of compliance can be distinguished from the contact model, and numerical simulations reveal that all behaviours persist under smoothing and under small random perturbations, but nonlinear effects can be made to disappear abruptly amid sufficient noise.

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“…Introduction. Piecewise-smooth dynamical systems continue to find increasing application in modelling stick-slip and impact in rigid body mechanics, switching in electrical control circuits and robotics, temperature dynamics in the phase transitions of superconductors, as well as numerous other biophysical, ecological and industrial problems; see for example [1,2,4,7,11,14,15]. Any of these contain examples of piecewise-smooth systems of the general class discussed here, namely three dimensional flows whose time derivative is discontinuous across a hypersurface or switching manifold, while the flow itself is continuous.…”

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confidence: 99%

Structural Stability of the Two-Fold Singularity

Fernández-García¹,

Garcia²,

Tost³

et al. 2012

SIAM J. Appl. Dyn. Syst.

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Abstract. At a two-fold singularity, the velocity vector of a flow switches discontinuously across a codimension one switching manifold, between two directions that both lie tangent to the manifold. Particularly intricate dynamics arises when the local flow curves towards the switching manifold from both sides, a case referred to as the Teixeira singularity. The flow locally performs two different actions: it winds around the singularity by crossing repeatedly through, and passes through the singularity by sliding along, the switching manifold. The case when the number of rotations around the singularity is infinite has been analysed in detail. Here we study the case when the flow makes a finite -but previously unknown -number of rotations around the singularity between incidents of sliding. We show that the solution is remarkably simple: the maximum and minimum number of rotations made anywhere in the flow differs only by one, and increases incrementally with a single parameter: the angular jump in the flow direction across the switching manifold, at the singularity.

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Noise-induced intermittency in a superconducting microwave resonator

Cited by 16 publications

References 31 publications

Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator

Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator

On the mathematical basis of solid friction

Structural Stability of the Two-Fold Singularity

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