Lectures: Difference between revisions
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*[[Media:vibrations_glasses.pdf|PDF]] | *[[Media:vibrations_glasses.pdf|PDF]] | ||
===Vibrational normal modes=== | ===Vibrational normal modes in disordered one-dimensional systems=== | ||
* P. B. Allen and J. Kelner, ''Evolution of a vibrational wave packet on a disordered chain'', Am. J. Phys. '''66''', 497 (1998). [http://math.mit.edu/~kelner/Publications/Docs/KAAJP.pdf [PDF]] | * P. B. Allen and J. Kelner, ''Evolution of a vibrational wave packet on a disordered chain'', Am. J. Phys. '''66''', 497 (1998). [http://math.mit.edu/~kelner/Publications/Docs/KAAJP.pdf [PDF]] | ||
Revision as of 22:37, 15 March 2012
Lecture 1: Computation as a tool for discovery in physics
Lecture 2: Numerical methods for ordinary differential equations
- Example for stiff behavior of ODE: stiff.m (flame propagation).
- Chapter 7 in C. Moler, Numerical Computing with Matlab (SIAM, Philadelphia, 2004).
- Chapter 16 in W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery: Numerical Recipes: The Art of Scientific Computing (CUP, Cambridge, 2007).
Lecture 3: Introduction to deterministic chaos
- T. Tél and M. Gruiz, Chaotic Dynamics (CUP, Cambridge, 2006).
Lecture 4: Vibrational normal modes: From glasses to Fermi-Pasta-Ulam problem
Vibrational normal modes in disordered one-dimensional systems
- P. B. Allen and J. Kelner, Evolution of a vibrational wave packet on a disordered chain, Am. J. Phys. 66, 497 (1998). [PDF]
- J. Fabian, Decay of localized vibrational states in glasses: A one-dimensional example, Phys. Rev. B 55, R3328 (1997). [PDF]
50th Anniversary of the Fermi-Pasta-Ulam Problem
- Focus issue of "Chaos": THE "FERMI-PASTA-ULAM" PROBLEM-THE FIRST 50 YEARS.
- S. Flach, M. V. Ivanchenko, O. I. Kanakov, and K. G. Mishagin, Periodic orbits, localization in normal mode space, and the Fermi-Pasta-Ulam problem, Am. J. Phys. 76, 453 (2008). [PDF].
- Fermi-Pasta-Ulam nonlinear lattice oscillations, T. Dauxois and S. Ruffo (2008), Scholarpedia, 3(8):5538.
