Synchronization of Nanomechanical Oscillators

该奖项支持一个理论项目，研究不同振荡器集合中的同步现象，特别关注纳米机械振荡器阵列的应用。同步是通过元件之间的相互作用及其非线性行为，形成具有不同固有频率的振荡器相干运动的集体状态。它代表了一个特别有趣和实际重要的集体行为的驱动，非平衡系统。研究的一个重点将是在几十到一百纳米的规模耦合非线性机械设备的大型阵列的同步与定量理解和可控的耦合和非线性。这些纳米机械系统具有独特的特性组合，包括小尺寸，高频率，易于访问和可控的非线性，这使得它们非常适合实现大型耦合振荡器阵列的实验系统，以测试先前存在的理论并引发进一步的扩展。本研究课题是从纳米机械系统的实验实现的前景出发，利用统计力学、动力系统理论、模式形成理论等的思想和方法，对同步进行新的理论研究。第一个是对几个纳米机械振荡器系统的定量分析，这些振荡器可能是实验的第一个目标。这项工作将有助于实验系统的设计，建议实验测量的协议，并将测试的结果，因为他们成为理论模型。第二个推力将是对振荡器大阵列的基本理论的研究，特别是在与纳米机械振荡器大阵列的未来实验工作相关的方向上扩展理解。各种各样的系统将被调查，包括与短范围，幂律长范围，和所有到所有的耦合，使用技术，如真实的空间重整化群方法，膨胀类似于自旋波方法在磁体，和数值模拟。还将研究空间维度的作用、拓扑缺陷的重要性以及噪声驱动波动的影响。拟议的纳米机械振荡器同步研究具有重要的技术应用，将对基础科学的各个领域产生广泛影响，并提供独特的教育机会，特别是用于培训研究生。非技术概述该奖项支持一个理论项目，以研究不同振荡器集合中的同步现象，本研究计画主要研究奈米机械振子阵列的应用，研究具有不同固有频率的振子系统。特别有趣的振荡器是许多微小的振动梁，比人类头发的直径小一万到十万倍，即纳米尺度。 当振荡器达到它们的运动步调一致的状态时，同步发生。这是振荡器或振动梁之间相互作用的结果。同步发生在自然界和人工制造的系统中的许多不同环境中。10到100纳米尺度的耦合机械设备的大阵列位于光刻制造技术的最前沿，提供了一个独特的实验室来测试理论，并具有许多潜在的技术应用，例如精密的时钟和灵敏的探测器，甚至低至单分子水平。不同振荡器的集体行为在基础科学的广泛领域也很重要，包括大脑神经元和心脏肌肉细胞的动力学，以及激光器的相干分组以制造高功率源。从仔细研究纳米机械系统中获得的对同步的一般现象的更深入理解将影响这些和其他研究领域。该奖项提供了独特的教育机会，特别是为培养研究生。它代表了基础研究，并有助于未来器件和纳米器件技术的知识基础。

TECHNICAL SUMMARYThis award supports a theoretical project to study the phenomenon of synchronization in collections of disparate oscillators, with a special focus on the application to arrays of nanomechanical oscillators.Synchronization is the formation of collective states of coherent motion of oscillators with diverse intrinsic frequencies, through the interaction between the elements and their nonlinear behavior. It represents a particularly interesting and practically important collective behavior of a driven, non-equilibrium system. A focus of the research will be the synchronization of large arrays of coupled nonlinear mechanical devices at the scale of tens to a hundred nanometers with quantitatively understood and controllable coupling and nonlinearity. These nanomechanical systems possess a unique combination of properties, including small size, high frequencies, and easily accessible and controllable nonlinearities, which make them extremely well-suited for realizing an experimental system of large coupled oscillator arrays, to test preexisting theory and to provoke further extensions. This project is a renewed theoretical study of synchronization exploiting ideas and methods from statistical mechanics, dynamical systems theory, and pattern formation theory, motivated by the prospect of experimental realization in nanomechanical systems.The project will have two main thrusts. The first is a quantitative analysis of the systems of a few nanomechanical oscillators that will likely be the first target of experiment. This effort will help the design of experimental systems, suggest protocols for experimental measurements, and will test the results as they become available against the theoretical models. The second thrust will be a study of the basic theory of large arrays of oscillators, extending the understanding particularly in directions relevant to future experimental work on large arrays of nanomechanical oscillators. A variety of systems will be investigated, including ones with short range, power-law long range, and all-to-all coupling, using techniques such as real space renormalization group methods, expansions analogous to spin-wave methods in magnets, and numerical simulations. The role of spatial dimension, the importance of topological defects, and effects of noise driven fluctuations, will also be investigated.The proposed study of synchronization in nanomechanical oscillators has important technological applications, will have a broad impact on diverse areas of basic science, and provides unique educational opportunities, particularly for training graduate students.NON-TECHNICAL SUMMARYThis award supports a theoretical project to study the phenomenon of synchronization in collections of disparate oscillators, with a special focus on the application to arrays of nanomechanical oscillators.This research project involves the study of systems of oscillators, each with different intrinsic frequencies. Oscillators of particular interest are many tiny vibrating beams some ten thousand to a hundred thousand times smaller than the diameter of a human hair, the nanometer scale. Synchronization occurs when the oscillators reach a state where their motion is in lock-step. This is a consequence of the interactions among the oscillators or vibrating beams. Synchronization occurs in many different contexts in nature and in artificially fabricated systems. Large arrays of coupled mechanical devices at the scale of ten to a hundred nanometers lie on the forefront of lithographic fabrication technology, provide a unique laboratory to test theory, and have many potential technological applications such as exquisitely precise clocks, and sensitive detectors even down to the single molecule level. The collective behavior of disparate oscillators is also important in wide areas of basic science, including the dynamics of neurons in the brain and muscle cells in the heart, and the coherent grouping of lasers to make high power sources. A deeper understanding of the general phenomenon of synchronization gained from the careful study of nanomechanical systems will impact these and other areas of research. This award provides unique educational opportunities, particularly for training graduate students. It represents fundamental research and contributes to the intellectual foundation of future device and nanoscale device technologies.