Synchronization of Nanomechanical Oscillators

技术总结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，特别关注在纳米机械振荡器阵列中的应用。同步是通过元素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和重要的集体行为。研究的重点将是在几十到一百纳米尺度上利用定量地理解和控制耦合和非线性的大阵列耦合的非线性机械装置的同步。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。该项目是基于纳米机械系统实验实现的前景，从统计力学、动力系统理论和图案形成理论出发，对同步开发思想和方法进行了新的理论研究。该项目将有两个主要推动力。第一个是对几个纳米机械振荡器系统的定量分析，这些振荡器很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，建议实验测量的方案，并将在结果可用时与理论模型进行测试。第二个推力将是研究大型振荡器阵列的基本理论，特别是在与未来关于大型纳米机械振荡器阵列的实验工作相关的方向上扩展理解。我们将使用实空间重整化群方法、类似于磁体中自旋波方法的展开式和数值模拟等技术来研究各种系统，包括具有短程、幂规律长程和全对全耦合的系统。还将研究空间维度的作用，拓扑缺陷的重要性，以及噪声驱动的波动的影响。拟议的纳米机械振荡器同步研究具有重要的技术应用，将对基础科学的不同领域产生广泛影响，并提供独特的教育机会，特别是对研究生的培训。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，特别是在纳米机械振荡器阵列中的应用。该研究项目涉及对振荡器系统的研究，每个振荡器系统具有不同的固有频率。特别令人感兴趣的振荡器是许多微小的振动梁，大约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处于锁步状态时，同步就发生了。这是振荡器或振动梁相互作用的结果。在自然界和人工制造的系统中，同步发生在许多不同的环境中。在光刻制造技术的前沿，存在着十到一百纳米级的大规模机械耦合器件阵列，为验证理论提供了独特的实验室，并具有许多潜在的技术应用，如精密的时钟，甚至是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，包括大脑神经元和心脏肌肉细胞的动力学，以及为制造高功率源而对激光进行相干分组。通过对纳米机械系统的仔细研究而获得对同步这一普遍现象的更深层次的理解，将对这些和其他研究领域产生影响。该奖项提供了独特的教育机会，特别是在培养研究生方面。它代表了基础研究，并为未来器件和纳米器件技术的智能基础做出了贡献。

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.