
PHYS 615: Nonlinear Dynamics of Extended Systems (Fall 2010)
2:003:15, Tuesday/Thursday
Instructor: Michelle Girvan
Email: girvan@umd.edu
Phone: 3014051610
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 nonphysics 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
 Selforganized criticality and highlyoptimized 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



