****NON-TECHNICAL ABSTRACT**** Chaos and solitons are two important branches of nonlinear science that have attracted interest over a wide range of disciplines, including mathematics, physics, biology, and engineering. Chaos is the idea that outcomes are highly sensitive to initial conditions: a butterfly flaps its wings in New York and there is a storm in Tokyo. Solitons are localized waves like tsunamis, and frequently occur in weakly nonlinear systems. Usually one believes that chaos and solitons are opposed to each other ? a soliton can be strongly perturbed and yet persists, for example, making it difficult to stop, say, a tsunami. This project will seek connections between chaos and solitons. Specifically, the project will take advantage of spin waves (a travelling disturbance in the magnetic order) in magnetic film systems to explore these connections. On the applied side, the project will develop a new secure communication scheme that exploits the solitons in feedback rings. This is a joint program between one experimental group and one theoretical group in two universities. Through the training of students in both experimental and theoretical nonlinear dynamical methods, the project will help young scientists cross the divide between ?theory land? and physical reality, leading to both better experiments and better theories. The education portion also includes the incorporation of nonlinear dynamics and chaos into undergraduate and graduate curricula and reaching out to students in disadvantaged high schools in Colorado.
This project will take advantage of spin waves in magnetic film systems to explore a possible crossover between solitons and chaos. The project will explore ?chaotic carrier solitons? ? solitons with chaotic carrier waves. A magneto-dynamic probe will be used to study the evolution of a pulse of chaotic spin waves and the formation of an envelope soliton from such a pulse. The project will also explore ?chaotic solitons? ? solitons that have coherent carrier waves but exhibit chaotic behaviors in time. The work will include the study of chaotic soliton excitation through modulational instability and chaotic solitons in magnetic film feedback rings. On the applied side, the project will develop a new secure communication scheme that exploits the soliton-associated Fermi-Pasta-Ulam recurrence in feedback rings. For all the projects, theoretical modeling will inspire, support, and interpret experimental work. The education portion focuses on the incorporation of nonlinear dynamics and chaos into undergraduate and graduate curricula both through core courses and through the design of new electives, as well as training of undergraduate and graduate researchers and reaching out to students in disadvantaged high schools.
The main outcomes or findings of the NSF project No. 0906489 include the following: (1) the first experimental and numerical observation of chaotic solitons - solitons that circulate in an active feedback ring but have their amplitudes vary with time in a chaotic manner; (2) the first experimental and numerical observation of the formation of bright envelope solitons from waves with a repulsive nonlinearity; (3) the experimental demonstration of easy tuning of the properties of chaotic spin waves, such as the correlation dimension and the autocorrelation function; (4) the experimental demonstration of tunable microwave chaotic oscillators that make use of nonlinear spin waves in magnetic thin film-based active feedback rings; (5) the experimental demonstration of a new microwave pulse compression technique that utilizes nonlinear spin waves in magnetic thin film strips; (6) the first experimental observation of chaotic excitations in nanoscale spin torque oscillators; and (7) the numerical demonstration of complex solitary wave dynamics, pattern formation, and chaos in nonlinear systems that are governed by the gain-loss nonlinear Schrödinger equation. The projects have supported in part 4 graduate students and 6 undergraduate students, as well as research experiences for 3 international visiting professors and 4 high school students. Students from the experimental group learned numerical simulation and chaos characterization techniques and carried out simulations on solitons and the characterization of experimentally measured chaotic signals. Students from the theory group learned spin-wave measurement techniques and participated in nonlinear spin-wave experiments. The work supported either fully or partially by this project has led to over 35 publications.
