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Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a coupled map lattice as an example. The optimal arrangement of the control sites is shown to depend on the symmetry properties of the system, while their minimal density depends on the strength of noise in the system.… (More)

- Ron Lifshitz, M. C. Cross
- 2003

The response of a coupled array of nonlinear oscillators to parametric excitation is calculated in the weak nonlinear limit using secular perturbation theory. Exact results for small arrays of oscillators are used to guide the analysis of the numerical integration of the model equations of motion for large arrays. The results provide a qualitative… (More)

The stochastic response of nanoscale oscillators of arbitrary geometry immersed in a viscous fluid is studied. Using the fluctuation-dissipation theorem, it is shown that deterministic calculations of the governing fluid and solid equations can be used in a straightforward manner to directly calculate the stochastic response that would be measured in… (More)

- Yaron Bromberg, M C Cross, Ron Lifshitz
- Physical review. E, Statistical, nonlinear, and…
- 2006

We study the response of a large array of coupled nonlinear oscillators to parametric excitation, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). Using a multiscale analysis, we derive an amplitude equation that captures the slow dynamics of the coupled oscillators just… (More)

- L Guillermo Villanueva, Rassul B Karabalin, Matthew H Matheny, Eyal Kenig, Michael C Cross, Michael L Roukes
- Nano letters
- 2011

We describe and demonstrate a new oscillator topology, the parametric feedback oscillator (PFO). The PFO paradigm is applicable to a wide variety of nanoscale devices and opens the possibility of new classes of oscillators employing innovative frequency-determining elements, such as nanoelectromechanical systems (NEMS), facilitating integration with… (More)

- K-H Chiam, M R Paul, M C Cross, H S Greenside
- Physical review. E, Statistical, nonlinear, and…
- 2003

We describe a numerical procedure to construct a modified velocity field that does not have any mean flow. Using this procedure, we present two results. First, we show that, in the absence of the mean flow, spiral defect chaos collapses to a stationary pattern comprising textures of stripes with angular bends. The quenched patterns are characterized by mean… (More)

- M. C. Cross, Ron Lifshitz
- 2000

The transmission coefficient for vibrational waves crossing an abrupt junction between two thin elastic plates of different widths is calculated. These calculations are relevant to ballistic phonon thermal transport at low temperatures in mesoscopic systems and the Q for vibrations in mesoscopic oscillators. Complete results are derived in a simple scalar… (More)

D. H. Santamore,1,2,3 A. C. Doherty,3,4,5 and M. C. Cross3 1ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 3Department of Physics, California Institute of Technology, Pasadena, California 91125, USA 4Institute for Quantum Information,… (More)

- Zhigang Zheng, Xingang Wang, Michael C Cross
- Physical review. E, Statistical, nonlinear, and…
- 2002

Generalized synchronization in an array of mutually (bidirectionally) coupled nonidentical chaotic oscillators is studied. Coupled Lorenz oscillators and coupled Lorenz-Rossler oscillators are adopted as our working models. With increasing the coupling strengths, the system experiences a cascade of transitions from the partial to the global generalized… (More)

- Nathan Becker, J D Scheel, M C Cross, Guenter Ahlers
- Physical review. E, Statistical, nonlinear, and…
- 2006

Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects the domain-chaos state observed in rotating Rayleigh-Bénard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly stationary… (More)