Lectures: Difference between revisions
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== Lecture 1: Computation as a tool for discovery in physics == | == Lecture 1: Computation as a tool for discovery in physics == | ||
*[[Media:computational_tools.pdf|PDF]] | *[[Media:computational_tools.pdf|PDF]] | ||
*[http://www-e.uni-magdeburg.de/mertens/publications/cise.pdf Computational complexity for physicists] | |||
*[[Real numbers and numerical precision]] | *[[Real numbers and numerical precision]] | ||
== Lecture 2: Numerical methods for ordinary differential equations == | == Lecture 2: Numerical methods for ordinary differential equations == | ||
*PDF | *[[Media:numerical_ODE.pdf|PDF]] | ||
*C. Moler, [http://www.mathworks.com/moler/chapters.html Numerical Computing with Matlab] (SIAM, Philadelphia, 2004). | *Example for stiff behavior of ODE: [[Media:stiff.m|stiff.m]] (flame propagation). | ||
*W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery: [http://www.nr.com/ Numerical Recipes: The Art of Scientific Computing] (CUP, Cambridge, 2007). | *[http://www.mathworks.com/moler/odes.pdf Chapter 7] in C. Moler, [http://www.mathworks.com/moler/chapters.html Numerical Computing with Matlab] (SIAM, Philadelphia, 2004). | ||
*[http://www.nrbook.com/a/bookfpdf.php Chapter 16] in W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery: [http://www.nr.com/ Numerical Recipes: The Art of Scientific Computing] (CUP, Cambridge, 2007). | |||
== Lecture 3: Introduction to deterministic chaos == | == Lecture 3: Introduction to deterministic chaos == | ||
*PDF | *[[Media:deterministic_chaos.pdf|PDF]] | ||
*D. Gonze, [http://homepages.ulb.ac.be/~dgonze/TEACHING/autocorrel.pdf Autocorrelation function]. | |||
*T. Tél and M. Gruiz, [http://chaoticdynamics.net/ Chaotic Dynamics] (CUP, Cambridge, 2006). | *T. Tél and M. Gruiz, [http://chaoticdynamics.net/ Chaotic Dynamics] (CUP, Cambridge, 2006). | ||
== Lecture 4: Vibrational | == Lecture 4: Vibrational normal modes: From glasses to Fermi-Pasta-Ulam problem == | ||
*PDF | *[[Media:vibrations_glasses.pdf|PDF]] | ||
===Vibrational | ===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]] | ||
* J. Fabian, ''Decay of localized vibrational states in glasses: A one-dimensional example'', Phys. Rev. B '''55''', R3328 (1997). [http://link.aps.org/doi/10.1103/PhysRevB.55.R3328 PDF] | * J. Fabian, ''Decay of localized vibrational states in glasses: A one-dimensional example'', Phys. Rev. B '''55''', R3328 (1997). [http://link.aps.org/doi/10.1103/PhysRevB.55.R3328 [PDF]] | ||
===50th Anniversary of the Fermi-Pasta-Ulam Problem=== | ===50th Anniversary of the Fermi-Pasta-Ulam Problem=== | ||
* | *Focus issue of "Chaos": [http://chaos.aip.org/resource/1/chaoeh/v15/i1?§ion=focus-issue-the-fermi-pasta-ulam-problem-the-first-50-years&page=1 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). [http://dx.doi.org/10.1119/1.2820396 [PDF]]. | |||
*[http://www.scholarpedia.org/article/Fermi-Pasta-Ulam_nonlinear_lattice_oscillations Fermi-Pasta-Ulam nonlinear lattice oscillations], T. Dauxois and S. Ruffo (2008), Scholarpedia, 3(8):5538. | |||
*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). [http://dx.doi.org/10.1119/1.2820396 PDF]. | |||
*Fermi-Pasta-Ulam nonlinear lattice oscillations, T. Dauxois and S. Ruffo (2008), Scholarpedia, 3(8):5538. | |||
== Lecture | == Lecture 5: Monte Carlo Simulations in Statistical Physics == | ||
*PDF | *[[Media:monte_carlo_statphys.pdf|PDF]] | ||
== Lecture | == Lecture 6: Numerical algorithms for time-dependent Schrödinger equation == | ||
* PDF | *[[Media:quantum_numerics.pdf|PDF]] | ||
== Lecture | == Lecture 7: Interdisciplinary Topics in Complex Systems == | ||
*PDF | *[[Media:complexity.pdf|PDF]] | ||
Latest revision as of 22:23, 22 April 2014
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
- D. Gonze, Autocorrelation function.
- 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.
