PHYSICS 251 -- CHAOS, COMPLEXITY, AND COMPUTERS (updated 1997-98)
(crosslisted with Math 292 and ComSci 279)
- Prerequisite
- One year of calculus and two quarters of physics at any
level. Computer experience not necessary, but helpful.
- Purpose of Course
- To teach how chaotic behavior arises in the behavior of simple systems.
We shall choose examples from classical mechanics, hydrodynamics,
population biology, all intended to illustrate how deterministic systems can
have apparently random behavior.
- To be an introduction to the use of computers in the physical sciences.
Specifically, we aim to teach the student how to use graphic methods and
small computers to get solutions to small scientific problems.
- Programming Language
- Java
- Level
- Java Now! by Jamsa
Exploring Java by Niemeyer and Peck
- Syllabus
- Laboratory 1: Getting Started
- Computation: Basics of Macintosh, CodeWarrior, and Java
Physics: Understanding geometry of ballistic particle motion in enclosed
spaces
- Laboratory 2: From Maps to Chaos
- Computation: Using Java arrays and classes; writing Java methods;
graphics
Physics: Dynamical systems; the logistic map
- Laboratory 3: Fixed Points, Cycles, and Chaos
- Computation: Understanding and constructing Java objects; Newton-
Raphson method
Physics: Stability of orbits
- Laboratory 4: Newton's Laws: Sums, Integrals, and Orbits
- Computation: Inheritance in Java; Runge-Kutta methods for solving
differential equations
Physics: Newton's laws
- Laboratory 5: Displaying Solutions to Differential Equations
- Computation: Animation techniques; double-buffering and threading
Physics: Evolution of regions in phase space
- Laboratory 6: Higher-Dimensional Dynamical Systems
- Hamiltonian
systems; the standard map; classification of orbits of two-dimensional
systems; Lyapunov exponents
- Laboratory 7: Fractals I
- Computation: Recursion
Physics: Definition of fractals; relevance to dynamical systems
- Laboratory 8: Fractals II
- Universality of period-doubling bifurcation sequence of one-dimensional
maps; fractals elsewhere in nature
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