The goals of the proposed project are to develop a fundamental understanding of the interplay of noise and nonlinearity in micro- and nano-scale electromechanical system (M/NEMS) resonators, and to exploit this knowledge for the development of novel applications in the areas of sensing and signal processing. The fundamental work will be geared towards the generation of predictive analytical and computational tools that can be employed in device development, and these results will be used to design M/NEMS devices with unprecedented selectivity and sensitivity. The methods to be employed include those from the fields of nonlinear dynamical systems, the theory of fluctuations, and experimental methods for M/NEMS. Fluctuations in M/NEMS arise from thermal and/or quantum noise, or can be intentionally injected from external sources. Even small noise can induce large changes in nonlinear system response, resulting in high sensitivity to external signals or environmental conditions. By careful tuning of the system parameters and inputs (periodic and/or noise), and with an understanding of how parameter changes affect switching, one can attain dramatic, predictable, and measurable changes in the system response. For sensor applications these changes are tied to environmental sources, while for signal processing the changes are linked to the modulation of an external signal. This proposal develops systematic methods for predicting these quantities for nonlinear M/NEMS resonators, based on the theory of noise-activated switching. The results from the analysis will guide the experimental efforts, which will implement the proposed techniques in novel schemes for mass and magnetic field detection, and for amplification of targeted signal quantities.
The broader impacts of the proposed research include the cross-disciplinary collaboration and training of students between physics and engineering, and the integration of existing computational, analytical, and experimental techniques to develop new concepts and approaches for sensing and signal processing. The fundamental aspects of the work also have potential applicability in other fields in which there is inherent interplay between nonlinearity and fluctuations, such as epidemiology and other areas of quantitative biology. In addition, the PIs will actively participate in outreach programs to high school students, including the High School Engineering Institute at Michigan State University and the Student Science Training Program at the University of Florida. The general topics of micro-and nano-technology, and the applications developed in the proposed work, will be used to help promote science and engineering to high school students in these programs.
Very small scale devices, with dimensions on the order of micrometers, offer unique features for a wide range of technologies. One of the fundamental challenges for these systems is that, due to their size, small fluctuations, modeled by noise, can have a dramatic effect on their dynamic response. The goal of this collaborative research project was to develop a fundamental understanding of the role of noise on the dynamic behavior of micro-electro-mechanical systems, and to exploit this knowledge for the development of novel sensing schemes. The research achieved theoretical advances with practical consequences, as verified by results from our experimental collaborators at the Hong Kong University of Science and Technology. The grant supported two graduate students, leading to successful completion of a PhD degree and an MS degree. These students were given broad multidisciplinary training in mechanical and electrical engineering and physics, as required to make advances in this leading-edge technology. The results of the research have allowed us to study different types of noise that play an important role in the devices of interest. We have considered the noise that arises in mass sensors from molecules attaching and detaching to a microbeam, as well as from diffusion of molecules along the microbeam, and how this noise affects the frequency response of the devices. This theory has been used by experimentalists to explain the effect of the "mysterious" friction in short-range atomic force microscopy. We have also found a complete solution of the problem of the shape of the probability distribution and the rate of switching between coexisting stable states induced by shot noise, including the scaling behavior of the switching rate; these results have been confirmed by detailed experiments done by our experimental collaborators. We have predicted that, unexpectedly, if the noise comes from dynamical coupling to its source, it can lead to the onset of bistability in the vibrating system. We have found that the noise can actually help determine system parameters and we proposed a way to exploit this mechanism; the method relies on swiftly driving the system past an instability point at which one of its stable states disappears. We have also started to research of large rare fluctuations in a broad class of systems of current interest that display time-delayed friction forces. The broader impacts of the project included the following activities: support for two undergraduate students who contributed to the research, international collaboration with leading experimentalists, student training and advances in research that cut across traditional disciplines, and participation of the PI in outreach programs. Specifically, the PI was the lead organizer and lecturer for the mechanical engineering components of the High School Engineering Institute and Spartan Engineering for Teens outreach programs. These week-long summer programs are geared towards talented middle and high school students, 25% of whom are from groups currently underrepresented in engineering. They are geared to inspiring young people to consider technical careers by describing the important role engineers play in society.
