Collaborative Research: Exploring Dynamic Complex Behaviors in Many-Degree-of-Freedom, Coupled Micro- and Nano-systems

谐振微和纳米机电系统在从化学传感到信号处理的应用空间中提供了独特的机会，这是由于其相对于更传统的系统的上级灵敏度和选择性度量。不幸的是，尽管经过三十年的研究努力，这些设备仍然受到吞吐量或它们可以感测/处理的信息量的显著限制。一个有吸引力的解决方案，这个约束是设计大阵列的小规模，耦合谐振器，并随后利用固有的复杂的行为，可以出现在这样的系统。然而，该技术解决方案在分析和预测设计方面都存在困难，特别是随着单个谐振器数量的增加。经典的工程方法在应用于多自由度系统时往往会崩溃，特别是在存在噪声和设备间变化的情况下。该项目将提供一个新的框架，用于理解这些谐振微/纳系统所表现出的各种集体和紧急行为，这可能会导致新的功能，激发新传感器的开发，如人工“鼻子”（多分析物化学传感器），过滤器，机械操作信号处理单元以及基于机械操作的人工记忆设备。该项目在一个框架内利用建模，分析和预测设计，该框架将通过微型实验进行验证。此外，该项目将其研究纳入核心本科课程，利用工程应用来激励初学者，以提高工程项目的保留率。为耦合，谐振微/纳米系统创建新的建模，分析和设计框架将使有效的分析策略能够表征大型，耦合的微/纳谐振器阵列（包括数百、数千和数百万个组成谐振器）在存在噪声、参数不确定性和伴随的电子器件的情况下操作。研究小组将通过局部（机械）和全局（电磁）耦合阵列的有针对性的微尺度实验来验证这些分析技术，并确定无意参数变化，噪声和组成元素的随机故障对观察到的动态的影响。该分析将基于多自由度系统的积分微分模型，该模型将允许任意大量的本构谐振器，以及伴随的微扰分析方法，导致耦合的全局动态的预测描述。该奖项还将支持开发新的主题模块，强调基础数学主题与工程分析和设计之间的关系，以及在阿克伦大学核心数学课程中部署这些模块，该课程以提高工程项目中的保留率和入学率为导向。最后，将开发和分发（通过开放访问渠道）与耦合微/纳米谐振器阵列相关的新课程材料和流式视频讲座。 这些材料将探索系统？在实际应用中使用。

Resonant micro- and nano-electromechanical systems provide unique opportunities in application spaces ranging from chemical sensing to signal processing due to their superior sensitivity and selectivity metrics in relation to more conventional systems. Unfortunately, despite three decades of research efforts, these devices still suffer from significant limitations on throughput, or on the amount of information they can sense/process. One attractive solution to this constraint is to design large arrays of small-scale, coupled resonators, and subsequently exploit the inherently complex behavior that can arise within such systems. However, this technical solution presents difficulties in terms of both analysis and predictive design, especially with an increasing number of individual resonators. Classical engineering approaches tend to break down when applied to many-degree-of-freedom systems, particularly in the presence of noise and device-to-device variations. This project will provide a new framework for understanding various collective and emergent behaviors exhibited by these resonant micro/nano systems, which could lead to new functionalities that inspire the development of new sensors, such as artificial "noses" (multi-analyte chemical sensors), filters, mechanically operating signal processing units as well as artificial memory devices based on mechanical operation. The project leverages modeling, analysis, and predictive design within a framework that will be validated through microscale experimentation. In addition, the project will integrate its research into the core undergraduate curriculum, using engineering applications to motivate beginning students, with a goal of increasing retention in engineering programs.The creation of a new modeling, analysis, and design framework for coupled, resonant micro/nanosystems will enable efficient analysis strategies capable of characterizing the linear and nonlinear dynamics of large, coupled micro/nanoresonator arrays (comprising of hundreds, thousands, and millions of constituent resonators) operating in the presence of noise, parametric uncertainty, and accompanying electronics. The research team will validate these analytical techniques through targeted microscale experimentation with locally- (mechanically) and globally- (electromagnetically) coupled arrays and determine the influence of unintentional parameter variations, noise, and the random failure of constituent elements on observed dynamics. The analysis will be based on integro-differential models for the many-degree-of-freedom systems that will allow for arbitrarily large numbers of constitutive resonators, together with accompanying perturbative analysis methods, leading to a predictive description of the coupled, global dynamics. The award will also support the development of new topical modules emphasizing the relationship between foundational mathematical topics and engineering analysis and design, as well as the deployment of these within the core mathematics curriculum at The University of Akron, which is guided by the desire to enhance retention and matriculation rates within engineering programs. Finally, new course materials and streaming video lectures associated with coupled micro/nanoresonator arrays will be developed and distributed (via open access channels). These materials will explore the systems? use in practical application.