Non-Technical Abstract: Fluctuations play a crucial role in many physical and biological phenomena at the micro- and nanoscale. A system can be induced to switch out of a metastable state when fluctuations are sufficiently large. Even though such transitions may occur infrequently, they largely determine the behavior of systems with multiple stable states. The goal of this Faculty Early Career Award at the University of Florida is to study fluctuation-induced switching in a mechanical device with features as small as a millionth of a meter. When this device is periodically driven, it oscillates with one of two distinct amplitudes. In the presence of fluctuations, the oscillation amplitude switches between the two stable values. The research will focus on revealing generic fluctuation phenomena that occur not only in our micro-scale mechanical system but also in other nonequilibrium systems. Such studies will answer open questions and enhance the understanding of fluctuations in systems that are far from equilibrium. Even though the proposed research is of fundamental nature, the findings could open possibilities for new detection schemes and signal-processing applications using micro-scale mechanical devices. In terms of outreach, the program will provide summer research experiences for high school students. Furthermore, demonstration materials will be developed for the students to bring back to their schools to further enhance the educational impact. Micromechanical devices will also be used to enhance teaching in an introductory mechanics course.
The goal of this Faculty Early Career Award at the University of Florida is to study activated switching between coexisting stable states in systems far from thermal equilibrium. Experimental studies will be carried out using an underdamped nonlinear micromechanical torsional oscillator. Under a sufficiently strong periodic driving field, the oscillator possesses two stable dynamical states with different oscillation amplitudes within a certain range of driving frequencies. The research will focus on revealing the scaling behaviors of the activation barrier with varying system parameters and generic features of fluctuations in the parameter range where stationary populations of the stable states are close to each other. Such studies will allow verification of the existing predictions, answer open questions on fluctuations in nonequilibrium systems and stimulate new theoretical research. Even though the proposed research is of fundamental nature, the findings could open possibilities for novel sensing schemes and signal-processing applications using micromechanical devices. In terms of outreach, the program will provide summer research experiences for high school students. Furthermore, demonstration materials will be developed for the students to bring back to their schools to further enhance the educational impact. Micromechanical devices will also be used to enhance teaching in an introductory mechanics course.
Fluctuation induced switching between coexisting states underlies many phenomena in science and technology, from transitions in biomolecules to device failures. Switching is random by nature: they occur at random time intervals and follow different paths in each switching event. In this research program, we demonstrated that, nevertheless, the switching paths form narrow tubes in the space of dynamical variables. We fabricated a micromechanical torsional oscillator and drive it into parametric resonance so that there are two stable oscillating states. Noise is injected to induce switching. The measured switching path distribution in phase space is demonstrated to peak around the most probable switching path. The results suggest a way of effective and selective control of switching rates. We also explored fluctuation-induced transitions at driving frequencies where two or three stable states coexist. Near bifurcation points where the number of stable states change, the activation barriers are found have a power law dependence on frequency that is consistent with the notion that the scaling is system-independent. The intellectual merit of the research is determined by the fundamental character of the problem of fluctuations in systems far from thermal equilibrium, coupled with its relevance to important areas of materials research. The research has revealed generic features in a broad class of phenomena related to switching between coexisting stable states, and discovered new phenomena which have no analog in equilibrium systems. The broader impact of the research is determined by its immediate relevance to a large number of applications. The project is relevant to the growing body of studies of nonequilibrium micro- and nanosystems, where activated escape plays a crucial role. These include systems that display hysteresis, such as Josephson junctions, nanomechanical oscillators, nanomagnets, and semiconductor lasers. The graduated students supported under this award have completed their PhD studies. They are both well-equipped to contribute to the development of science and technology of this nation. One of them is now working in a national lab and the other is an employee of a technology company. The graduate student and the PI jointly supervised the summer research of a high school student during summer 2007 under the Student Science Training Program. Under this program, the high school student undertook a 7-week research project in the PI's lab. The main purpose of this program is to stimulate the scientific interests of students and encourage them to consider science and engineering as a potential career choice. To enhance the educational impact, the PI and graduate student also worked with the participating student to construct a demonstration based on a micromechanical torsional mirror that was brought back to his school after the program. The demo was constructed using simple components including a laser pointer and a toggle switch around a micromechanical device. While the participating student gained invaluable research experience, we aim to extend the impact to other students and stimulate their curiosity after the participating student returned to his high school. Furthermore, the PI and graduate students supported by this award also served as a judge for the high school science fair of the local county.
