American Institute of Mathematical Sciences

Advanced
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 & 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).  doi: 10.1063/1.3078706.  Google Scholar

[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).  doi: 10.1080/03601217808907349.  Google Scholar

[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.  doi: 10.1007/s11071-007-9288-0.  Google Scholar

[4]

J. Fajans and L. Friedland, Autoresonant (nonstationary) excitation of pendulums, plutinos, plasmas and other nonlinear oscillators,, Am. J. Phys., 69 (2001), 1096.  doi: 10.1119/1.1389278.  Google Scholar

[5]

S. L. Hurst, "The Logical Processing of Digital Signals,", Chap. 1, (1978).   Google Scholar

[6]

E. Kenig, R. Lifshitz and M. C. Cross, Pattern selection in parametrically driven arrays of nonlinear resonators,, Phys. Rev. E, 79 (2009).  doi: 10.1103/PhysRevE.79.026203.  Google Scholar

[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).   Google Scholar

[8]

P. Maniadis and S. Flach, Mechanism of discrete breather excitation in driven micro-mechanical cantilever array,, Euro Phys. Lett., 74 (2006), 452.  doi: 10.1209/epl/i2005-10550-y.  Google Scholar

[9]

A. H. Nayfeh and D. T. Mook, "Nonlinear Oscillations,", Chap. 4, (1979).   Google Scholar

[10]

T. Rössler and J. B. Page, Intrinsic localized modes in driven anharmonic lattices with realistic potentials,, Physics Letters A, 204 (1995).  doi: 10.1016/0375-9601(95)00519-9.  Google Scholar

[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).  doi: 10.1103/PhysRevLett.90.044102.  Google Scholar

[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).  doi: 10.1063/1.1540771.  Google Scholar

[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.  doi: 10.1209/epl/i2003-10224-x.  Google Scholar

[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.  doi: 10.1103/RevModPhys.78.137.  Google Scholar

[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).  doi: 10.1209/0295-5075/80/30002.  Google Scholar

[16]

M. Sato and A. J. Sievers, Visualizing intrinsic localized modes with a nonlinear micromechanical array,, Low Temperature Physics, 34 (2008), 543.  doi: 10.1063/1.2957286.  Google Scholar

[17]

M. Sato, B. E. Hubbard and A. J. Sievers,  , to be published., ().   Google Scholar

[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).  doi: 10.1063/1.2899634.  Google Scholar

[19]

J. Wiersig, S. Flach and K.-H. Ahn, Discrete breathers in ac-driven nanoelectromechanical shuttle arrays,, Appl. Phys. Lett., 93 (2008).  doi: 10.1063/1.3043434.  Google Scholar

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).  doi: 10.1063/1.3078706.  Google Scholar

[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).  doi: 10.1080/03601217808907349.  Google Scholar

[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.  doi: 10.1007/s11071-007-9288-0.  Google Scholar

[4]

J. Fajans and L. Friedland, Autoresonant (nonstationary) excitation of pendulums, plutinos, plasmas and other nonlinear oscillators,, Am. J. Phys., 69 (2001), 1096.  doi: 10.1119/1.1389278.  Google Scholar

[5]

S. L. Hurst, "The Logical Processing of Digital Signals,", Chap. 1, (1978).   Google Scholar

[6]

E. Kenig, R. Lifshitz and M. C. Cross, Pattern selection in parametrically driven arrays of nonlinear resonators,, Phys. Rev. E, 79 (2009).  doi: 10.1103/PhysRevE.79.026203.  Google Scholar

[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).   Google Scholar

[8]

P. Maniadis and S. Flach, Mechanism of discrete breather excitation in driven micro-mechanical cantilever array,, Euro Phys. Lett., 74 (2006), 452.  doi: 10.1209/epl/i2005-10550-y.  Google Scholar

[9]

A. H. Nayfeh and D. T. Mook, "Nonlinear Oscillations,", Chap. 4, (1979).   Google Scholar

[10]

T. Rössler and J. B. Page, Intrinsic localized modes in driven anharmonic lattices with realistic potentials,, Physics Letters A, 204 (1995).  doi: 10.1016/0375-9601(95)00519-9.  Google Scholar

[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).  doi: 10.1103/PhysRevLett.90.044102.  Google Scholar

[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).  doi: 10.1063/1.1540771.  Google Scholar

[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.  doi: 10.1209/epl/i2003-10224-x.  Google Scholar

[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.  doi: 10.1103/RevModPhys.78.137.  Google Scholar

[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).  doi: 10.1209/0295-5075/80/30002.  Google Scholar

[16]

M. Sato and A. J. Sievers, Visualizing intrinsic localized modes with a nonlinear micromechanical array,, Low Temperature Physics, 34 (2008), 543.  doi: 10.1063/1.2957286.  Google Scholar

[17]

M. Sato, B. E. Hubbard and A. J. Sievers,  , to be published., ().   Google Scholar

[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).  doi: 10.1063/1.2899634.  Google Scholar

[19]

J. Wiersig, S. Flach and K.-H. Ahn, Discrete breathers in ac-driven nanoelectromechanical shuttle arrays,, Appl. Phys. Lett., 93 (2008).  doi: 10.1063/1.3043434.  Google Scholar

[1]

Xinpeng Wang, Bingo Wing-Kuen Ling, Wei-Chao Kuang, Zhijing Yang. Orthogonal intrinsic mode functions via optimization approach. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-16. doi: 10.3934/jimo.2019098
[2]

Michael Kastner, Jacques-Alexandre Sepulchre. Effective Hamiltonian for traveling discrete breathers in the FPU chain. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 719-734. doi: 10.3934/dcdsb.2005.5.719
[3]

Panayotis Panayotaros. Continuation and bifurcations of breathers in a finite discrete NLS equation. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1227-1245. doi: 10.3934/dcdss.2011.4.1227
[4]

Jesús Cuevas, Bernardo Sánchez-Rey, J. C. Eilbeck, Francis Michael Russell. Interaction of moving discrete breathers with interstitial defects. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1057-1067. doi: 10.3934/dcdss.2011.4.1057
[5]

Jean-Pierre Eckmann, C. Eugene Wayne. Breathers as metastable states for the discrete NLS equation. Discrete & Continuous Dynamical Systems - A, 2018, 38 (12) : 6091-6103. doi: 10.3934/dcds.2018136
[6]

S. Aubry, G. Kopidakis, V. Kadelburg. Variational proof for hard Discrete breathers in some classes of Hamiltonian dynamical systems. Discrete & Continuous Dynamical Systems - B, 2001, 1 (3) : 271-298. doi: 10.3934/dcdsb.2001.1.271
[7]

Vassilis Rothos. Subharmonic bifurcations of localized solutions of a discrete NLS equation. Conference Publications, 2005, 2005 (Special) : 756-767. doi: 10.3934/proc.2005.2005.756
[8]

Panayotis Panayotaros, Felipe Rivero. Multistability and localized attractors in a dissipative discrete NLS equation. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1137-1154. doi: 10.3934/dcdsb.2014.19.1137
[9]

Tetsu Mizumachi, Dmitry Pelinovsky. On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems - S, 2012, 5 (5) : 971-987. doi: 10.3934/dcdss.2012.5.971
[10]

Yoshikazu Katayama, Colin E. Sutherland and Masamichi Takesaki. The intrinsic invariant of an approximately finite dimensional factor and the cocycle conjugacy of discrete amenable group actions. Electronic Research Announcements, 1995, 1: 43-47.

[11]

Qingxu Dou, Jesús Cuevas, J. C. Eilbeck, Francis Michael Russell. Breathers and kinks in a simulated crystal experiment. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1107-1118. doi: 10.3934/dcdss.2011.4.1107
[12]

Philippe G. Ciarlet, Liliana Gratie, Cristinel Mardare. Intrinsic methods in elasticity: a mathematical survey. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 133-164. doi: 10.3934/dcds.2009.23.133
[13]

Xavier Brusset, Per J. Agrell. Intrinsic impediments to category captainship collaboration. Journal of Industrial & Management Optimization, 2017, 13 (1) : 113-133. doi: 10.3934/jimo.2016007
[14]

Leonid Berlyand, Giuseppe Cardone, Yuliya Gorb, Gregory Panasenko. Asymptotic analysis of an array of closely spaced absolutely conductive inclusions. Networks & Heterogeneous Media, 2006, 1 (3) : 353-377. doi: 10.3934/nhm.2006.1.353
[15]

Samuel T. Blake, Andrew Z. Tirkel. A multi-dimensional block-circulant perfect array construction. Advances in Mathematics of Communications, 2017, 11 (2) : 367-371. doi: 10.3934/amc.2017030
[16]

Dario Bambusi, D. Vella. Quasi periodic breathers in Hamiltonian lattices with symmetries. Discrete & Continuous Dynamical Systems - B, 2002, 2 (3) : 389-399. doi: 10.3934/dcdsb.2002.2.389
[17]

Siwei Yu, Jianwei Ma, Stanley Osher. Geometric mode decomposition. Inverse Problems & Imaging, 2018, 12 (4) : 831-852. doi: 10.3934/ipi.2018035
[18]

Nicolas Van Goethem. The Frank tensor as a boundary condition in intrinsic linearized elasticity. Journal of Geometric Mechanics, 2016, 8 (4) : 391-411. doi: 10.3934/jgm.2016013
[19]

Seung-Yeal Ha, Se Eun Noh, Jinyeong Park. Practical synchronization of generalized Kuramoto systems with an intrinsic dynamics. Networks & Heterogeneous Media, 2015, 10 (4) : 787-807. doi: 10.3934/nhm.2015.10.787
[20]

A. Agrachev and A. Marigo. Nonholonomic tangent spaces: intrinsic construction and rigid dimensions. Electronic Research Announcements, 2003, 9: 111-120.

2018 Impact Factor: 0.545

Tools

Metrics

  • PDF downloads (25)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences