Nonlinear Dynamics
Meurice, Polyzou, Skiff
Nonlinear dynamics is the study of systems that are described
by nonlinear equations of motion. Chaos is a topic of
particular interest. This topic is important in almost every
branch of science and engineering. Our faculty study chaos two
ways: as a phenomenon of classical mechanics, and as quantum
chaos, which is the study of the interface between the quantum
and classical descriptions for classically chaotic systems.
The department offers a second semester of classical mechanics
devoted to nonlinear dynamics.
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Our inter-disciplinary research in nonlinear dynamics allows
students to choose an experimental or theoretical project.
Students can choose a theoretical project and apply the methods
of chaos to field theory or to the many body problem.
Additionally, students may choose an experimental project,
studying the observable effects of chaos in plasmas, where the
exchange of energy amongst waves and particles is chaotic. Our
previous work on chaos has been published in leading journals
such as Physical Review Letters and reported as
invited talks at major conferences. One of our previous PhD
students received a major national prize for a thesis on
nonlinear dynamics.
- Topics related to lattice field theory or renormalization group; chaos in classical lattice field theory
- Applications of the KAM theorem: action-angle variables, small denominators, resonance in systems of coupled oscillators, construction of scaling variables
- Employment of former students: postdocs at major universities in the US and Ireland; senior research scientist in driving simulation project; software engineer in industry; college instructor
- Students are involved weekly in two seminars
- Students travel to summer schools and conferences
Wayne Polyzou, Theoretical nonlinear dynamics
- Primary research area is nuclear and particle theory
- Quantum chaos, constrained Hamiltonian systems, scaling phenomena, wavelets
Frederick Skiff, Experiments and simulations of chaos
- Primary research area is experimental plasma physics; many of these problems involve nonlinear dynamics
- Analysis of time series and the analysis of chaotic signals; experiments and simulations of interacting sound and radio frequency waves; spatio-temporal chaos
- Experimental facilities include: 3-meter linear magnetized-plasma device for waves and spectroscopy, single-frequency scanning lasers for high-resolution laser spectroscopy
- Students also interact with group members, and they participate in the plasma seminar and interact with other theoretical and experimental faculty
- Students develop skills including designing and building apparatus, electronics, computation