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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)

- Eyal Kenig, Ron Lifshitz, M C Cross
- Physical review. E, Statistical, nonlinear, and…
- 2009

We study the problem of pattern selection in an array of parametrically driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems, using an amplitude equation recently derived by Bromberg, Cross, and Lifshitz [Phys. Rev. E 73, 016214 (2006)]. We describe the transitions between standing-wave patterns of… (More)

- M C Cross, P C Hohenberg
- Science
- 1994

- 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)

We investigate a scheme that makes a quantum nondemolition (QND) measurement of the excitation level of a mesoscopic mechanical oscillator by utilizing the anharmonic coupling between two beam bending modes. The nonlinear coupling between the two modes shifts the resonant frequency of the readout oscillator in proportion to the excitation level of the… (More)

- In A Recent Letter, Hammar, +6 authors M C Cross
- 2000

son (HBYJ) describe measurement of the interfacial resistance in a ferromagnet/insulator/semiconductor (F/I/S) structure. They argue that hysteretic features observed between temperatures of 75 and 296 K are evidence for spin-dependent transmission through the interface. We believe that their observations can be attributed to other effects. Despite… (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 oscilla-tors. Complete results are calculated in a simple… (More)

- R. Urban, A. Putilin, +4 authors M. L. Roukes
- 2006

Magnetostatic modes of yttrium iron garnet ͑YIG͒ films are investigated by ferromagnetic resonance force microscopy. A thin-film " probe " magnet at the tip of a compliant cantilever introduces a local inhomogeneity in the internal field of the YIG sample. This influences the shape of the sample's magnetostatic modes, thereby measurably perturbing the… (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)