Abstract
We investigate a class of nonlinear wave equations subject to periodic forcing and noise, and address the issue of energy optimization. Numerically, we use a pseudo-spectral method to solve the nonlinear stochastic partial differential equation and compute the energy of the system as a function of the driving amplitude in the presence of noise. In the fairly general setting where the system possesses two coexisting states, one with low and another with high energy, noise can induce intermittent switchings between the two states. A striking finding is that, for fixed noise, the system energy can be optimized by the driving in a form of resonance. The phenomenon can be explained by the Langevin dynamics of particle motion in a double-well potential system with symmetry breaking. The finding can have applications to small-size devices such as microelectromechanical resonators and to waves in fluid and plasma.
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References
A. Hamm, T. Tél, R. Graham, Phys. Lett. A 185, 313 (1994)
L. Billings, I.B. Schwartz, J. Math. Bio. 44, 33 (2002)
Y.C. Lai, Z. Liu, L. Billings, I.B. Schwartz, Phys. Rev. E 67, 026210 (2003)
K. Wiesenfeld, F. Moss, Nature 373, 33 (1995)
L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998)
P. Hänggi, Chem. Phys. Chem. 3, 285 (2002)
D. Sigeti, W. Horsthemke, J. Stat. Phys. 54, 1217 (1989)
A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 775 (1997)
Y.C. Lai, Z. Liu, Phys. Rev. Lett. 86, 4737 (2001)
L. Gammaitoni, F. Marchesoni, S. Santucci, Phys. Rev. Lett. 74, 1052 (1995)
S. Barbay, G. Giacomelli, F. Martin, Phys. Rev. E 62, 157 (2000)
S.G. Lee, S. Kim, Phys. Rev. E 72, 061906 (2005)
K. Park, Y.C. Lai, S. Krishnamoorthy, Chaos 17, 043111 (2007)
H.G. Craighead, Science 290, 1532 (2000)
X.M.H. Huang, C.A. Zorman, M. Mehregany, M.L. Roukes, Nature 321, 496 (2003)
S.K. De, N.R. Aluru, Phys. Rev. Lett. 94, 204101 (2005)
S.B. Shim, M. Imboden, P. Mohanty, Science 316, 95 (2007)
A. Hasegawa, K. Mima, Phys. Fluids 21, 87 (1978)
J.D. Meiss, W. Horton, Phys. Fluids 25, 1838 (1982)
K.F. He, A. Salat, Plasma Phys. Controlled Fus. 31, 123 (1989)
C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Dynamics (Springer, Berlin, Germany, 1988)
B. Fornberg, Practical Guide to Pseudospectral Methods (Cambridge University Press, Cambridge, UK, 1998)
S.A. Orszag, Phys. Fluids Supp. II 12, 250 (1969)
P.E. Kloden, E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, Berlin, Germany, 1992)
P.F. Byrd, M.D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists (Springer-Verlag, New York, 1971)
D. Marthaler, D. Armbruster, Y.C. Lai, E.J. Kostelich, Phys. Rev. E 64, 016220 (2001)
K. Park, Y.C. Lai, Europhys. Lett. 70, 432 (2005)
P. Hänggi, P. Talkner, M. Borkovec, Rev. Mod. Phys. 62, 251 (1999)
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Lai, YC., Park, K. & Rajagopalan, L. Stochastic resonance and energy optimization in spatially extended dynamical systems. Eur. Phys. J. B 69, 65–70 (2009). https://doi.org/10.1140/epjb/e2009-00114-7
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DOI: https://doi.org/10.1140/epjb/e2009-00114-7