Nonlinear Dynamics and Quantum Transport in Small Systems

Project: Research project

Project Details


This proposal contains two components in the general area of small-sized systems: nonlinear dynamics in microelectromechanical (MEM) systems and electronic transport in graphene. Small-sized systems such as MEM resonators have become common in many fields of science and engineering. These systems have a relatively simple structure but they show surprisingly rich nonlinear dynamical behaviors such as bistability, chaos, and energy-localized oscillations. The proposed research is motivated by the recognition that small-sized systems will be used increasingly in various devices of DoD interest. A main goal is to understand the nonlinear dynamics of a generic element in many devices: MEM resonantors. Based on the understanding we will investigate strategies to harness or control the dynamics of MEM resonantors to achieve various performances of interest. From the perspective of application, MEM resonators are the key component of actuators embedded in various weapon systems. Assuming that such systems are adversarial, our interest is to devise strategies to defeat them. This leads to the following specific research objectives: (1) inducing chaos in MEM resonantors, (2) dynamics of intrinsic localized modes in micro-oscillator arrays and controlled generation, and (3) disabling MEM resonators by inducing pull-in instability based on nonlinear resonance. Graphene, a novel type of material, has become the subject of intense recent study. The physics of graphene is dominated by a linear relation between the carrier energy and momentum, which is characteristic of relativistic motions. As a result, potential devices made of graphene can possess ultra-fast processing speed that can be orders of magnitude higher than the speed of current semiconductor devices. This would be of significant interest to the DoD. From the standpoint of basic science, graphene provides a testbed for experimenting quantum electrodynamics in solid-state systems. Our proposed research will focus on electronic transport in graphene-based quantum dots, a good understanding of which is essential for development of fundamental devices such as diodes and transistors. We will explore issues such as scarring of classical periodic orbits in quantum-dot systems, conductance fluctuations, and implications to graphene-based device development. While the research is designed to probe the basic physics of graphene, its potential long-term impact can be significant for DoD. 1
Effective start/end date3/1/0911/30/11


  • DOD-USAF-AFRL: Air Force Office of Scientific Research (AFOSR): $588,152.00

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