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Building better oscillators using nonlinear dynamics and pattern formation

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Abstract

Frequency and time references play an essential role in modern technology and in living systems. The precision of self-sustained oscillations is limited by the effects of noise, which becomes evermore important as the sizes of the devices become smaller. In this paper, we review our recent theoretical results on using nonlinear dynamics and pattern formation to reduce the effects of noise and improve the frequency precision of oscillators, with particular reference to ongoing experiments on oscillators based on nanomechanical resonators. We discuss using resonator nonlinearity, novel oscillator architectures and the synchronization of arrays of oscillators, to improve the frequency precision.

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Acknowledgements

This work would not have been possible without the close collaboration with the Caltech nanomechanical experimental group and the authors acknowledge in particular the important contributions of Michael Roukes, Rassul Karabalin, Matt Matheny and Guillermo Villanueva. Ron Lifshitz, Jeff Moehlis and Kurt Wiesenfeld also contributed to the theoretical ideas. The material is based upon work supported by the National Science Foundation under Grant No. DMR-1003337 and DARPA through the DEFYS programme. JMAA was supported by the Master and Fellows of Corpus Christi College and the California Institute of Technology.

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Authors and Affiliations

  1. Department of Physics, California Institute of Technology, Pasadena, California, 91125, USA

    M C CROSS & EYAL KENIG

  2. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK

    JOHN-MARK A ALLEN

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  1. M C CROSS
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  2. EYAL KENIG
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  3. JOHN-MARK A ALLEN
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Correspondence to M C CROSS.

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CROSS, M.C., KENIG, E. & ALLEN, JM.A. Building better oscillators using nonlinear dynamics and pattern formation. Pramana - J Phys 84, 455–471 (2015). https://doi.org/10.1007/s12043-014-0924-1

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