Physics 250 - 001
Computational Dynamics of Complex Systems:
Phase Transitions
Winter Quarter, 2009
John Rundle
Professor of Physics and Geology
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Physics 250 - 001 Computational Dynamics of Complex Systems: Phase Transitions
Winter Quarter, 2009
John Rundle Professor of Physics and Geology
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BACKGROUND The effects of
nonlinearity and complexity represent the most critical constraint on
systems throughout all areas of science and engineering, including neural
networks, earthquakes, driven foams, magnetic de-pinning transitions in
superconductors, and in engineered systems, which include the power grid,
the World Wide Web, transportation systems, control systems, and human
systems. The purpose of this course is to develop the knowledge and tools
to understand the dynamics of these systems, and how system states and
transitions can be described in terms of general (and possibly universal)
organizing principles. COURSE CONTENT Complex nonlinear systems typically undergo phase transitions, in which fluctuations become important in the dynamics of the system leading to a dramatic changes in the properties, parameters and dynamics of the system. Such phase transitions, which can be of either first or second order, have been studied in many other contexts, especially in liquid-gas-solid thermal systems, and in magnetic systems. This course is targeted towards students who are interested in exploring phase transitions, nucleation, and critical phenomena in complex systems. We will discuss scaling and show how scaling exponents can be calculated. We will place these ideas into a physical context and discuss the tools, both computational and theoretical, that have been developed to understand complexity. We will discuss the emergent space-time patterns that are associated with the dynamics, and learn how to characterize these patterns and use the results for applications.
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