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Intrinsic localized modes in parametrically driven arrays of nonlinear resonators
Eyal Kenig1, Boris A Malomed, M C Cross
1Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
Summary
We explore intrinsic localized modes (ILMs) in nonlinear resonators for MEMS and NEMS applications. Our study reveals ILM creation, stability, bound states, and splitting, confirmed by simulations.
Area of Science:
- Nonlinear dynamics
- Solid-state physics
- Applied physics
Background:
- Intrinsic localized modes (ILMs) are nonlinear waves in discrete systems.
- Parametrically driven nonlinear resonators are relevant for micro- and nanoelectromechanical systems (MEMS/NEMS).
- Understanding ILM behavior is crucial for device applications.
Purpose of the Study:
- To investigate intrinsic localized modes (ILMs) in parametrically driven nonlinear resonator arrays.
- To analyze the creation, stability, and interactions of ILMs.
- To explore potential applications in microelectromechanical and nanoelectromechanical systems (MEMS/NEMS).
Main Methods:
- Derivation of an amplitude equation using the method of multiple scales.
- Analysis of the forced complex Ginzburg-Landau equation, representing nonlinear damping.
- Numerical simulations of the underlying equations of motion.
Main Results:
- ILMs can be created, exhibit stable configurations, and form bound states.
- Under specific conditions, a single ILM can split into two.
- Theoretical predictions are validated through simulations.
Conclusions:
- The study provides a theoretical framework for understanding ILMs in driven nonlinear resonators.
- Findings suggest potential for controlling and utilizing ILMs in MEMS/NEMS devices.
- The results pave the way for experimental verification and further research.
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