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Applied Mathematics & Statistics, and Scientific Computation

PHYS 615: Nonlinear Dynamics of Extended Systems (Fall 2010)

2:00-3:15, Tuesday/Thursday

Instructor: Michelle Girvan
Email: girvan@umd.edu
Phone: 301-405-1610

This is a topics course in complex extended systems aimed at level of first year graduate students. Broadly speaking, a complex system is a set of interacting elements that are nonlinearly coupled to give rise to emergent behavior. Complex systems arise in various physical, biological, technological and social contexts. Hence, the study of complex systems is inherently interdisciplinary. This course primarily focuses on how a physics perspective coupled with a computational approach can lend insights into complex systems.

The course has no explicit prerequisites. A strong undergraduate math background that includes differential equations, linear algebra, and basic probability and statistics is assumed. A knowledge of statistical physics at the undergraduate level is also valuable, but the course is designed to be accessible to graduate students from non-physics disciplines. Some experience with computer programming is necessary.

Primarily, the course will be taught from a series of seminal research papers. The course will include four problem sets and a final project in the form of a formal research proposal. Students will identify a line of original research in the area of complex systems and write a report which includes: motivation of the problem, relevant background, an outline for the proposed work, and some preliminary investigations.

Topics include:
  • Cellular automata and agent based modeling: How complexity can arise from simple nonlinear interaction rules
  • Econophysics and social physics: The application of statistical physics beyond natural systems
  • On overview of power law distributions in natural systems: From earthquakes to avalanches
  • Self-organized criticality and highly-optimized tolerance: two theories to explain the ubiquity of power law distributions in natural systems
  • Simulated annealing: Using physics to inspire computation
  • Complex Networks: How the pattern of connectivity between interacting elements can have a big effect on system dynamics
  • Computational Mechanics: Using computational methods to detect and quantify structure in natural processes