Synchronization of Nanomechanical Oscillators

纳米机械振荡器的同步

• 批准号: 1003337
• 负责人: Michael Cross
• 金额: $ 27万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1003337&HistoricalAwards=false
• 关键词: Synchronization; Nanomechanical; Oscillators

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.

技术摘要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。它代表了一个受驱动的非平衡系统的一种特别有趣且具有实际意义的集体行为。研究的重点将是在数十到一百纳米尺度上实现大规模耦合非线性机械装置的同步，并具有定量理解和可控的耦合和非线性。这些纳米力学系统具有独特的性能组合，包括小尺寸、高频以及易于访问和控制的非线性，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，以测试现有的理论并引发进一步的扩展。该项目是对同步开发的新理论研究，利用统计力学、动力系统理论和模式形成理论的思想和方法，其动机是纳米机械系统中实验实现的前景。该项目有两个主要目标。第一个是对一些纳米机械振荡器系统的定量分析，这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，提出实验测量协议，并将根据理论模型测试结果。第二个重点是研究大型振荡器阵列的基本理论，特别是在与未来大型纳米机械振荡器阵列实验工作相关的方向上扩展理解。将使用实空间重正化群方法、类似于磁体中自旋波方法的展开以及数值模拟等技术来研究各种系统，包括短程系统、幂律长程系统和全对全耦合系统。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也将得到研究。所提出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的影响，并提供独特的教育机会，特别是对于培训研究生。非技术摘要该奖项支持一个研究现象的理论项目 不同振荡器集合中的同步，特别关注纳米机械振荡器阵列的应用。该研究项目涉及振荡器系统的研究，每个振荡器具有不同的固有频率。人们特别感兴趣的振荡器是许多微小的振动梁，其直径比人类头发的直径（纳米级）小一万到十万倍。 当振荡器达到其运动同步的状态时，就会发生同步。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。十到一百纳米尺度的大型耦合机械装置阵列位于光刻制造技术的最前沿，为测试理论提供了独特的实验室，并且具有许多潜在的技术应用，例如精确的时钟和甚至单分子水平的灵敏探测器。不同振荡器的集体行为在基础科学的广泛领域也很重要，包括大脑中神经元和心脏中肌肉细胞的动力学，以及用于制造高功率源的激光的连贯分组。通过仔细研究纳米机械系统而获得的对同步一般现象的更深入的理解将影响这些和其他领域的研究。该奖项提供了独特的教育机会，特别是对于培训研究生。它代表了基础研究，并为未来器件和纳米级器件技术的知识基础做出了贡献。