Collaborative Research: The Nonlinear Stochastic Dynamics of Micro and Nanomechanical Systems

技术继续在纳米尺度上取得巨大进步，产生了前所未有的能力。目前，热波动还没有驱动纳米系统脱离其线性体系，在那里它们的动力学是很好的理解。然而，随着下一代技术的发展，机械系统变得越来越小，它们的性能受到组成设备和周围介质的分子的随机热运动的限制，因为热波动已经足够将机械系统驱动到非线性状态。发展对纳米机械系统在这种非线性状态下波动的理解是这项工作的重点。三维纳米打印技术将用于制造结构，以研究仅受温度驱动时的非线性行为。利用系统中存在的波动和耗散之间的基本关系，可以从理论上理解非线性行为。这些发现将为实现下一代纳米技术提供必要的见解，预计其性能将远远超过当前的技术水平。纳米尺度系统的随机动力学是许多重要现象的核心。目前，人们对机械系统保持在线性状态下的随机动力学有了很好的理解。然而，在理解纳米机械系统的非线性波动方面仍然存在许多重要的挑战。为了建立这种理解，最先进的纳米制造和测量方法，加上分析和数值方法的发展来描述和预测这些动力学，将被利用。直接激光写入系统将用于制造结构，当仅由温度驱动时，它们将表现出高度非线性随机动力学。用外差干涉仪测量软聚合物材料结构的非线性随机动力学将进行实验研究。对系统动力学的物理理解将利用强大的涨落耗散定理建立起来。动力学将被扰动地探测，并将使用因式分解方法来创建一种确定性方法来描述强非线性系统的动力学。在理解单模态振动的非线性波动之后，将研究复杂结构的不同模态振动之间的耦合。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Technology continues to make great strides at the nanoscale, resulting in unprecedented capabilities. Currently, thermal fluctuations have not driven nano systems outside their linear regime where their dynamics are well understood. However, as mechanical systems are made smaller for next-generation technologies, their performance is becoming limited by the random thermal movements of the molecules that make up the device and surrounding medium as the thermal fluctuations are becoming sufficient to drive the mechanical system into a nonlinear regime. Developing an understanding of the fluctuations of nano mechanical systems in this nonlinear regime is the focus of this work. Three-dimensional nanoprinting will be employed to create structures designed to study nonlinear behavior when driven by the temperature alone. A theoretical understanding of the nonlinear behavior will be created by utilizing the fundamental relationship between the fluctuations and the dissipation present in the system. The findings will provide the insights necessary to realize the next generation of nanotechnology where performance is anticipated to be well beyond the current state-of-the art.The stochastic dynamics of nanoscale systems are at the heart of many important phenomena. Currently, there is a good understanding of stochastic dynamics when a mechanical system remains in the linear regime. However, many important challenges remain in understanding nonlinear fluctuations of nanomechanical systems. In order to build this understanding, state-of-the-art nanofabrication and measurement approaches, coupled with the development of analytical and numerical methods to describe and predict these dynamics, will be utilized. A direct laser write system will be used to fabricate structures tailored to exhibit highly nonlinear stochastic dynamics when driven by temperature alone. The nonlinear stochastic dynamics of structures constructed from soft polymeric materials will be experimentally studied using measurements from a heterodyne interferometer. A physical understanding of the system dynamics will be built using the powerful fluctuation-dissipation theorem. The dynamics will be probed perturbatively and a factorization approach will be used to create a deterministic approach to describe the dynamics of strongly nonlinear systems. After developing an understanding of the nonlinear fluctuations of a single mode of oscillation, the coupling between the different modes of oscillation of a complex structure will be investigated.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.