Nonlinear Dynamics and Quantum Transport in Small Systems
Abstract
MEMS/NEMS are characterized by their small size, low power consumption, and ultra fast speed. There is a growing interest in the fundamental dynamics of MEMS/NEMS and their potential applications including future military systems. To understand and generate various nonlinear dynamical phenomena including chaos in MEMS/NEMS can thus be of great interest from the standpoint of defense. During the project period, we first focused on understanding the dynamical mechanism of intrinsic localized modes (ILMs) in MEMS oscillator arrays, a phenomenon that had been observed in a number of experiments. We found that spatiotemporal chaos is ubiquitous and it provides a natural platform for actual realization of various ILMs through frequency control. In particular, unstable periodic orbits associated with ILMs are pivotal for chaos to arise and these orbits are key to stabilizing ILMs from spatiotemporal chaos by frequency modulation. We then articulated a global control scheme to induce intrinsic localized modes at an arbitrary site in MEM cantilever arrays. The idea is to locate the particular cantilever beam in the array that one wishes to drive to an oscillating state with significantly higher amplitude than the average, and then apply small adjustments to the electrical signal that drives the whole array system. We developed detailed theoretical and computational analyses to validate the method. The control scheme may be useful in applications where the goal is to defeat certain MEM based electronic devices. Finally, we turned our attention to NEMS and carried out a detailed bifurcation analysis for a common class of electrostatically driven nanowires using a multi-physics model. We found that the nano-scale system can exhibit distinct chaotic states: chaos with symmetry-breaking and extensive chaos possessing the full symmetry of the system. We further explored potential applications of extensive chaos in nanowire systems: ultra-fast random number generators.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 22, 2012
- Accession Number
- ADA565337
Entities
People
- Ying-Cheng Lai
Organizations
- Arizona State University