Logic operations demonstrated with localized vibrations in a micromechanical cantilever array

Masayuki Sato; Naoki Fujita; A. J. Sievers

doi:10.3934/dcdss.2011.4.1287

Article Contents

2011, Volume 4, Issue 5: 1287-1298. Doi: 10.3934/dcdss.2011.4.1287

This issue Previous Article Persistent mobile lattice excitations in a crystalline insulator Next Article Exact solutions for periodic and solitary matter waves in nonlinear lattices

Logic operations demonstrated with localized vibrations in a micromechanical cantilever array

1.
Graduate School of Natural Science and Technology, Kanazawa University, Ishikawa 920-1192
2.
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853-2501

Received: August 31, 2009

Revised: October 31, 2009

Published: September 2011

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Abstract

A method is presented for realizing logic operations in a micro-mechanical cantilever array based on the timed application of a lattice disturbance to control the properties of intrinsic localized modes (ILMs). The application of a specific inhomogeneous field destroys a driver-locked ILM, while the same operation can create an ILM if initially no-ILM exists. Logic states "1" and "0" correspond to "present" or "absent" ILM.

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Mathematics Subject Classification: Primary: 70K40, 70Q05; Secondary: 70K75.

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References

[1]	Q. Chen, L. Huang, Y.-C. Lai and D. Dietz, Dynamical mechanism of intrinsic localized modes in micromechanical oscillator arrays, Chaos, 19 (2009), 013127.doi: 10.1063/1.3078706.
[2]	M. R. M. Crespo da Silva and C. C. Glynn, Nonlinear flexural-flexural-torsional dynamics of inextensional beams II. Forced motions, J. Struct. Mech., 6 (1978), 449.doi: 10.1080/03601217808907349.
[3]	A. J. Dick, A. J. Balachandran and C. D. Mote, Intrinsic localized modes in microresonator arrays and their relationship to nonlinear vibration modes, Nonlin. Dyn., 54 (2008), 13-29.doi: 10.1007/s11071-007-9288-0.
[4]	J. Fajans and L. Friedland, Autoresonant (nonstationary) excitation of pendulums, plutinos, plasmas and other nonlinear oscillators, Am. J. Phys., 69 (2001), 1096-1102.doi: 10.1119/1.1389278.
[5]	S. L. Hurst, "The Logical Processing of Digital Signals," Chap. 1, Crane, Russak & Company, Inc., New York, 1978.
[6]	E. Kenig, R. Lifshitz and M. C. Cross, Pattern selection in parametrically driven arrays of nonlinear resonators, Phys. Rev. E, 79 (2009), 026203.doi: 10.1103/PhysRevE.79.026203.
[7]	E. Kenig, B. A. Malomed, M. C. Cross and R. Lifshitz, Intrinsic localized modes in parametrically-driven arrays of nonlinear resonators, arXiv:0904.1355v1, (2009).
[8]	P. Maniadis and S. Flach, Mechanism of discrete breather excitation in driven micro-mechanical cantilever array, Euro Phys. Lett., 74 (2006), 452-458.doi: 10.1209/epl/i2005-10550-y.
[9]	A. H. Nayfeh and D. T. Mook, "Nonlinear Oscillations," Chap. 4, John Wiley & Sons, New York, 1979.
[10]	T. Rössler and J. B. Page, Intrinsic localized modes in driven anharmonic lattices with realistic potentials, Physics Letters A, 204 (1995), 418.doi: 10.1016/0375-9601(95)00519-9.
[11]	M. Sato, B. E. Hubbard, A. J. Sievers, B. Ilic, D. A. Czaplewski and H. G. Craighead, Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array, Phys. Rev. Lett., 90 (2003), 044102.doi: 10.1103/PhysRevLett.90.044102.
[12]	M. Sato, B. E. Hubbard, L. Q. English, A. J. Sievers, B. Ilic, D. A. Czaplewski and H. G. Craighead, Study of intrinsic localized vibrational modes in micromechanical oscillator arrays, Chaos, 13 (2003), 702.doi: 10.1063/1.1540771.
[13]	M. Sato, B. E. Hubbard, A. J. Sievers, B. Ilic and H. G. Craighead, Optical manipulation of intrinsic localized vibrational energy in cantilever arrays, Europhys. Lett., 66 (2004), 318-323.doi: 10.1209/epl/i2003-10224-x.
[14]	M. Sato, B. E. Hubbard and A. J. Sievers, Nonlinear energy localization and its manipulation in micromechanical oscillator arrays, Rev. Mod. Phys., 78 (2006), 137-157.doi: 10.1103/RevModPhys.78.137.
[15]	M. Sato, S. Yasui, M. Kimura, T. Hikihara and A. J. Sievers, Management of localized energy in discrete nonlinear transmission lines, Euro Phys. Lett., 80 (2007), 3002.doi: 10.1209/0295-5075/80/30002.
[16]	M. Sato and A. J. Sievers, Visualizing intrinsic localized modes with a nonlinear micromechanical array, Low Temperature Physics, 34 (2008), 543-548.doi: 10.1063/1.2957286.
[17]	M. Sato, B. E. Hubbard and A. J. Sievers, to be published.
[18]	M. Spletzer, A. Raman, H. Sumali and J. P. Sullivan, Highly sensitive mass detection and identification using vibration localization in coupled microcantilever arrays, Appl. Phys. Lett., 92 (2008), 114102.doi: 10.1063/1.2899634.
[19]	J. Wiersig, S. Flach and K.-H. Ahn, Discrete breathers in ac-driven nanoelectromechanical shuttle arrays, Appl. Phys. Lett., 93 (2008), 222110.doi: 10.1063/1.3043434.