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

技术继续在纳米尺度上取得长足进步，从而产生了前所未有的能力。 目前，热波动还没有驱动纳米系统的线性制度之外，他们的动态是很好地理解。 然而，随着下一代技术的机械系统变得更小，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，因为热波动变得足以将机械系统驱动到非线性状态。 发展的非线性政权的纳米力学系统的波动的理解是这项工作的重点。 三维纳米打印将用于创建设计用于研究仅由温度驱动时的非线性行为的结构。 通过利用系统中存在的波动和耗散之间的基本关系，将建立对非线性行为的理论理解。 我们的研究结果将提供必要的见解，以实现下一代的纳米技术的性能预计将远远超出目前的最先进的。纳米级系统的随机动力学是许多重要现象的核心。 目前，有一个很好的理解随机动力学时，机械系统保持在线性政权。 然而，在理解纳米力学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，将利用最先进的纳米制造和测量方法，再加上分析和数值方法的发展来描述和预测这些动态。 直接激光写入系统将被用来制造结构定制，表现出高度非线性随机动力学时，由温度单独驱动。 利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特性。 系统动力学的物理理解将建立使用强大的波动耗散定理。 动力学将探讨微扰和因式分解的方法将被用来创建一个确定性的方法来描述强非线性系统的动态。 在对单一振动模式的非线性波动有了了解之后，将对复杂结构的不同振动模式之间的耦合进行研究。该奖项反映了NSF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. Our 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.