The following MIT course announcement may be of interest to the
Physics of Computation community:
Simple Models of Complex Physical Systems
12.517 G(2) 3-0-9
Spring, 1998
Instructor: Prof. Daniel Rothman, dan@segovia.mit.edu, Rm 54-626, 253-7861
TA: Peter Dodds, dodds@segovia.mit.edu, Rm 54-627, 253-7278
Many systems, both physical and otherwise, follow simple dynamics at a
small scale while exhibiting complex behavior at a large scale. This
course introduces several modern theoretical approaches to the study of
such problems.
The first half of the course introduces discrete (cellular automata) models
of fluids and shows how hydrodynamic equations may be derived for these
models. Students will also learn how these models can exhibit phase
transitions, form fluid interfaces, and describe multiphase flow.
The second half of the course will cover two other topics: percolation
and surface growth. Percolation is used to introduce concepts such as
scaling, fractals, and renormalization. The section on surfaces will
illustrate how these concepts apply in a setting far from equilibrium, in
addition to introducing some stochastic differential equations.
Applications to problems in earth science are discussed in each topic.
The first meeting is Tuesday 3 February at 10:30 am in Room 54-317.
Unless interested students have schedule conflicts
(please contact the instructor by email if you cannot attend this meeting)
the class will meet thereafter on Tuesdays and Thursdays
from 10:30--12:00 in the same place. Advanced undergraduates are welcome.
Tentative Syllabus
I. Cellular automata models of hydrodynamics (~13 lectures)
Text: D. H. Rothman and S. Zaleski, Lattice-gas cellular automata:
simple models of complex hydrodynamics, Cambridge University Press, 1997.
o Two routes to hydrodynamics: continuum mechanics vs cellular automata
o Inviscid lattice-gas hydrodynamics
o Viscosity
o Lattice-Boltzmann method
o Miscible fluids
o Immiscible lattice gases
o Liquid-gas models
o Interfaces, phase separation, and multiphase flow
II. Percolation theory (~6 lectures)
Text: D. Stauffer and A. Aharony, Introduction to percolation theory,
2nd ed., Taylor and Francis, 1991.
o Critical behavior, scaling, and fractals
o Finite-size scaling
o Real-space renormalization
o Applications to flow through porous media
III. Dynamical models of surface growth (~7 lectures)
Text: A. L. Barabasi and H. E. Stanley, Fractal concepts in surface
growth, Cambridge University Press, 1995.
o Self-affine surfaces
o Discrete and continuum models
o Dynamical scaling
o Analysis of linear and nonlinear stochastic equations
o Applications to geomorphology