The sympathy of two pendulum clocks: beyond Huygens’ observations

Ramirez, J. Peña; Olvera, Luis Alberto; Nijmeijer, Henk; Álvarez, Joaquín

doi:10.1038/srep23580

Cited by 84 publications

(70 citation statements)

References 37 publications

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“…38 Key properties, such as the frequency of synchronous dynamics, emerge from the coupled system and can be different to those of the individual elements: Huygens' clocks on the shelf can become slow. 39 Further work that explores a wider range of plasma conditions is needed to determine over what range of ELM frequencies synchronization can occur. In particular, during intervals of synchronous dynamics, the phase relationship found in the control system field coils should hold even if the ELM frequency is drifting.…”

Section: Discussionmentioning

confidence: 99%

Control system-plasma synchronization and naturally occurring edge localized modes in a tokamak

et al. 2018

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Edge Localised Modes (ELMs) naturally occur in tokamak plasmas in high confinement mode. We find in ASDEX Upgrade that the plasma can transition into a state in which the control system field coil currents, required to continually stabilize the plasma, continually oscillate with the plasma edge position and total MHD energy. These synchronous oscillations are one-to-one correlated with the occurrence of natural ELMs; the ELMs all occur when the control system coil current is around a specific phase. This suggests a phase synchronous state in which nonlinear feedback between plasma and control system is intrinsic to natural ELMing, and in which the occurrence time of a natural ELM is conditional on the phase of the control system field coil current.

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Section: Discussionmentioning

confidence: 99%

Control system-plasma synchronization and naturally occurring edge localized modes in a tokamak

et al. 2018

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“…Synchronisation is a fascinating and multi-disciplinary topic in modern science, focussed on understanding how a collection of individual bodies adjust their natural rhythms and phases through their interactions with each other and the environment [1][2][3][4][5]. In a striking display of cooperative behaviour, this adjustment can lead to a variety of phenomena such as the 'winking' of fireflies, the behavioural synchrony of groups of strangers or the coupling of a pair of pendulums through a mutual support [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Quantum synchronisation enabled by dynamical symmetries and dissipation

et al. 2020

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In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry-an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit longlived signatures of both phase and frequency-locking.

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“…First described by Huygens, in the classical case of periodic self‐sustained oscillators , interactions or coupling between the individual systems can lead to synchronized behaviors depending on the coupling strength . More specifically, weak coupling results in frequency pulling of one oscillator toward the other but with incomplete synchronization particularly with larger phase shifts and frequency mismatch.…”

Section: Introductionmentioning

confidence: 99%

Capacitive coupling synchronizes autonomous microfluidic oscillators

2018

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Even identically designed autonomous microfluidic oscillators have device-to-device oscillation variability that arises due to inconsistencies in fabrication, materials, and operation conditions. This work demonstrates, experimentally and theoretically, that with appropriate capacitive coupling these microfluidic oscillators can be synchronized. The size and characteristics of the capacitive coupling needed and the range of input flow rate differences that can be synchronized are also characterized. In addition to device-to-device variability, there is also within-device oscillation noise that arises. An additional advantage of coupling multiple fluidic oscillators together is that the oscillation noise decreases. The ability to synchronize multiple autonomous oscillators is also a first step towards enhancing their usefulness as tools for biochemical research applications where multiplicate experiments with identical temporal-stimulation conditions are required.

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The sympathy of two pendulum clocks: beyond Huygens’ observations

Cited by 84 publications

References 37 publications

Control system-plasma synchronization and naturally occurring edge localized modes in a tokamak

Control system-plasma synchronization and naturally occurring edge localized modes in a tokamak

Quantum synchronisation enabled by dynamical symmetries and dissipation

Capacitive coupling synchronizes autonomous microfluidic oscillators

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