Physics 250 - 001
The Tipping Point:
Nucleation and Growth in Complex Systems with Numerical Applications
Winter Quarter, 2010
John Rundle
Professor of Physics and Geology
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Physics 250 - 001
The Tipping Point: Nucleation and Growth in Complex Systems with Numerical Applications
Winter Quarter, 2010
John Rundle Professor of Physics and Geology
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BACKGROUND and COURSE CONTENT Complex systems
are observed to undergo sudden changes in behavior when the system "tips"
from one dominant dynamical pattern to another. The transition in system
dynamics is associated with the nucleation and growth of fluctuations,
together with a threshold in the state space of the system. The threshold
can be characterized as a "tipping point". Tipping points, or first-order
transitions, can be associated with stock market crashes, earthquakes,
hurricanes, and epidemics. In this course we will examine the dynamics of
nucleation and growth in complex systems. We will develop the tools to
understand the effects of tipping points, and how these lead to the
appearance of fractals and scaling phenomena. We will examine the role of
fluctuations, and how these lead to selection of new dynamical states, and
we will illuminate the role of the "spinodal" the classical limit of
stability of the system. Students in this course will study the dynamics
of a variety of complex systems that demonstrate tipping points through
the development and use of analytical and numerical methods.
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