American Institute of Mathematical Sciences

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October  2011, 4(5): 1287-1298. doi: 10.3934/dcdss.2011.4.1287

Logic operations demonstrated with localized vibrations in a micromechanical cantilever array

Masayuki Sato 1, , Naoki Fujita 1, and  A. J. Sievers 2,

1. 

Graduate School of Natural Science and Technology, Kanazawa University, Ishikawa 920-1192, Japan, Japan
2. 

Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853-2501, United States

Received  September 2009 Revised  November 2009 Published  December 2010

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.
Keywords: cantilever array., discrete breathers, Intrinsic localized mode.
Mathematics Subject Classification: Primary: 70K40, 70Q05; Secondary: 70K7.
Citation: Masayuki Sato, Naoki Fujita, A. J. Sievers. Logic operations demonstrated with localized vibrations in a micromechanical cantilever array. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1287-1298. doi: 10.3934/dcdss.2011.4.1287
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.

show all references

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.

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