METHODS OF COMPUTATIONAL PHYSICS (Spring 2009)
Course Number: Phys 516
Class Number: 50614R
Instructor:
Aiichiro Nakano;
office: VHE 610; phone: (213) 821-2657; email: anakano@usc.edu
Lecture: 10:00-10:50 M W F, GFS 216
Office Hour: 15:00-16:50 F
Prerequisites: Basic knowledge of calculus and undergraduate physics;
familiarity with a programming language such as C or Fortran.
Textbooks:
T. Pang,
"An Introduction to Computational Physics, 2nd Ed." (Cambridge Univ. Press, 2006)
--sample C, Fortran 77, and Fortran 90 programs available on line.
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling,
"Numerical Recipes, 3rd Ed." (Cambridge Univ. Press, 2007)--available online
(C,
Fortran 77, and
Fortran 90)
Course Description
Students will learn basic elements of computational methods and acquire hands-on
experience in their practical use in the context of computer simulations to solve
physics problems.
Molecular dynamics simulation of the oxidation of an aluminum nanoparticle.
Syllabus
- Monte Carlo (MC) simulation of spins--Ising model
- Numerical vs. MC integration: Simpson's rule, Gaussian quadrature
(orthogonal functions--recursive function evaluation, generating function)
- Probability: Importance sampling, Markov chain, Metropolis algorithm
- Random number generation (RNG)
- Statistics: Variance, standard deviation, standard deviation of the MC mean
- Cluster analysis: Graphs, search, stack
- MC simulation of stock price--geometric Brownian motion
- Random walk: Einstein's law, central-limit theorem
- Random variable: Black-Scholes analysis
- Coordinate transformation: Jacobian, Box-Muller algorithm for RNG of normal distribution
- Interpolation: Least square fit of data
- Molecular dynamics (MD) simulation of particles--Newton's second law of motion
- Numerical differentiation
- Ordinary differential equation (ODE): Symplectic integrators
- Minimization of functions: Conjugate gradient method
- Hybrid MD/MC simulation
- Quantum dynamics simulation of an electron--time-dependent Schrodinger equation
- Partial differential equation (PDE)
- Fourier analysis: Spectral analysis, fast Fourier transform (FFT)
- Electronic structures of molecules--quantum mechanical eigenvalue problem
- Linear algebra: Matrix, orthogonal transformation, rank, singular value decomposition
- Matrix eigensystems: Housholder transformation, QL decomposition
- Root finding: Newton-Raphson method
Announcements
- 1/26/09 (M): Discussion session for HW 1 from 5:00pm in VHE 610.
- 2/11/09 (W): Discussion session for HW 2 from 5:00pm in VHE 610.
- 2/20/09 (F): Discussion session for HW 3 from 3:30pm in VHE 610.
- 2/27/09 (F): Discussion session for HW 4 from 11:00am in VHE 610.
- 3/13/09 (F): Discussion session for HW 5 from 3:30pm in VHE 610.
- 3/30/09 (M): Discussion session for HW 6 from 3:30pm in VHE 610.
- 4/08/09 (W): Attend a lecture by Prof. Nathan Lewis
of Caltech: "Sun-light driven hydrogen formation
by membrane-supported photoelectrochemical water splitting".
- 4/10/09 (F): Discussion session for HW 7 from 3:30pm in VHE 610.
- 4/22/09 (W): Discussion session for HW 8 from 3:30pm in VHE 610.
- 4/24/09 (F): Please pick up the lecture notes on kinetic Monte Carlo at VHE 610
if you have not got them yet.
- 5/01/09 (F): If you use PowerPoint for your final presentation,
please email me the electronic file in advance.
Lecture Notes and References
Reading List and Links
- Monte Carlo simulations:
U. Wolff, Phys. Rev. Lett. 62, 361 (1989);
D. Kandel, et al., Phys. Rev. Lett. 60, 1591 (1988);
B. A. Berg & T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992);
F. Wang & D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001);
B. Mehlig, et al., Phys. Rev. B 45, 679 (1992)
- Molecular dynamics integrator:
M. Tuckerman, B. J. Berne, & G. J. Martyna, J. Chem. Phys. 97, 1990 (1992)
- Higher-order symplectic integrators:
H. Yoshida, Phys. Lett. A 150, 262 (1990)
-
Backward error analysis for numerical integrators:
S. Reich, SIAM J. Numer. Anal. 36, 1549 (1999)
- Transferable tight-binding models for silicon:
I. Kwon, et al., Phys. Rev. B, 49, 7242 (1994)
- Tight-binding parameters
at the Naval Research Laboratory
- Density-matrix algorithms for quantum
renormalization groups:
S. R. White, Phys. Rev. B, 48, 10345 (1993)
-
An introduction to Monte Carlo simulations of surface reactions:
A. P. J. Jansen, arXiv:cond-mat/0303028
-
Theoretical foundations of dynamical Monte Carlo simulations:
K. A. Fichthorn and W. H. Weinberg, J. Chem Phys. 95, 1090 (1991)
- Molecular kinetics simulation:
A. Nakano, Comput. Phys. Commun. 176, 292 (2007);
ibid. 178, 280 (2008)
- Multiscale Simulation Methods in Molecular Sciences:
J. Grotendorst, N. Attig, S. Bluegel, and D. Marx
(John von Neumann Institute for Computing, Juelich, Germany, 2009)
Assignments
- 1: Monte Carlo basics (due Wednesday, Jan. 28)
- 2: Monte Carlo simulation of spins (due Friday, Feb. 13)
- 3: Molecular dynamics simulation (due Monday, Feb. 23)
- 4: Quantum dynamics basics (due Monday, Mar. 2)
- 5: Quantum dynamics programming--spectral method (due Friday, Mar. 13)
- 6: Stochastic simulation of stock price (due Wednesday, Apr. 1)
- 7: Tight binding model of electronic structures (due Monday, Apr. 13)
- 8: Quantum Monte Carlo simulation (due Friday, Apr. 24)
- Final project (due Wednesday, May 13);
a brief presentation on your project is required on Friday, May 1.
Source Codes
- Monte Carlo basics: hit.c, mean.c, gauleg-driver.c, gauleg.c
- Molecular dynamics basics: md.c, md.h, md.in
- Quantum dynamics basics: qd.c, qd.h, qd.in, qd1.c, qd1.h, qd1.in, four1.c
- Stochastic simulation: diffuse.c
- Tight binding model of electronic structures: tb_util.c, eigen.c, singular.c, svdcmp.c