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

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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.