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.

技术摘要奖支持一个理论项目，该项目旨在研究降低振荡器集合中同步的现象，特别关注纳米力学振荡器的阵列的应用。相关是通过与本质上的互动和不合格的行为和他们之间的互动和他们之间的互动和他们之间的互动和他们之间的互动和他们之间的互动和他们的行为相结合的集体状态的形成。它代表了一个特别有趣且实际上重要的集体行为，这是一个驱动的非平衡系统。该研究的重点将是在数十纳米到一百个纳米的大量耦合非线性机械设备的同步，并具有定量理解和可控制的耦合和非线性。这些纳米力学系统具有独特的属性组合，包括小尺寸，高频和易于访问且可控制的非线性，这非常适合实现大型耦合振荡器阵列的实验系统，以测试预先存在的理论并引起进一步的扩展。该项目是一项重新研究的理论研究，该研究是从统计力学，动力学系统理论和模式形成理论中利用思想和方法的同步研究，这是由纳米力学系统实验实现的前景所激发的。该项目将具有两个主要的力量。第一个是对一些纳米力学振荡器的系统进行定量分析，这可能是实验的第一个目标。这项工作将有助于设计实验系统，建议实验测量方案，并将测试结果在与理论模型可用时测试。第二个推力将是对大型振荡器的基本理论的研究，尤其是在与大型纳米力学振荡器有关的未来实验性工作有关的方向上扩展了理解。将研究各种系统，包括使用真实空间重新归一化方法的技术，包括较短的范围，幂律远距离远程和全耦合，类似于磁铁中的自旋波方法的扩展以及数值模拟。空间维度的作用，拓扑缺陷的重要性以及噪声驱动的波动的影响也将得到研究。拟议的纳米力学振荡器中同步研究的研究具有重要的技术应用，将对基础科学的多元化领域产生广泛的影响，并为培训研究生提供了独特的教育机会。在不同的振荡器集合中的同步，特别关注纳米力学振荡器阵列的应用。本研究项目涉及振荡器系统的研究，每个研究都具有不同的固有频率。特别感兴趣的振荡器是许多微小的振动梁，比人头发的直径（纳米尺度）小约100万到十万倍。 当振荡器到达运动处于锁定状态的状态时，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为制造系统中的许多不同情况下。大量的耦合机械设备在十到一百个纳米的规模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，例如精确的精确时钟，甚至敏感的探测器甚至降至单分子水平。在基础科学的广泛领域，包括大脑中神经元和心脏中肌肉细胞的动力学以及激光器的相干分组以使高功率来源成为高功率，这也很重要。对从仔细研究纳米力学系统获得的同步的一般现象的更深入了解将影响这些研究的这些领域和其他研究领域。该奖项提供了独特的教育机会，特别是对于培训研究生而言。它代表了基本研究，并为未来设备和纳米级设备技术的知识基础做出了贡献。