COURSE TIME:
TuTh 10:30 am -12:00 pm, Roessler 158.
INSTRUCTOR: Richard Scalettar, scalettar@physics.ucdavis.edu
OFFICE: Physics-Geology 409.
OFFICE HOURS: Mo. 2:00-4:00; or by appointment.
REQUIRED TEXT: None
USEFUL BOOKS:
`Numerical Methods for Physics', A. Garcia
'Computational Physics', Rubin H. Landau and Manuel J. Paez
GENERAL DESCRIPTION:
This course will describe the use of computational methods to solve physics problems which cannot be treated by conventional analytic approaches. To develop confidence in our programs, we will show how these numerical techniques can reproduce analytic methods (when those methods can be applied). We will therefore spend some considerable time reviewing and developing `standard' mathematical methods.
DETAILED DESCRIPTION/SYLLABUS:
[0] Molecular Dynamics (Kepler Problem, Kirkwood gaps)[1] Diffusion Equation (heat flow in inhomogeneous rod)
[2] Random Walks (Random number generators, diffusion limited aggregation)
[3] Laplace Equation (electrostatic potential, fields)
[4] Matrices (eigensystems, normal modes, localization)
[5] Schroedinger equation (shooting method, Lenard-Jones potential)
[6] Monte Carlo Methods (Ising model)
ASSIGNMENT ONE
Molecular Dynamics: Kepler Problem
ASSIGNMENT TWO
Partial Differential Equations: Diffusion
ASSIGNMENT THREE
Random Numbers and Random Walks; Partial Differential Equations: Electrostatic Potential
ASSIGNMENT FOUR
Matrix Inversion and Diagonalization: Localized Phonons
ASSIGNMENT FIVE
Heisenberg Model by Exact Diagonalization; Time Independent Schroedinger Equation
ASSIGNMENT SIX
Monte Carlo for a Single Variable
ASSIGNMENT SEVEN
Field Theory; Ising Model
Numerical Recipes Home Page
IMPORTANT NOTE:
PROGRAMS BELOW WHICH USE NUMERICAL RECIPES ROUTINES ARE TO BE USED ONLY FOR THE HOMEWORK PROBLEMS ASSIGNED IN CLASS! FOR OTHER USES YOU SHOULD PURCHASE A COPY OF THE NUMERICAL RECIPES BOOK.
FILE FOR INVERTER IN FORTRAN:
invert2.f
FILE FOR DIAGONALIZER IN FORTRAN:
diag2.f
FILES FOR DIAGONALIZER IN C:
Notes on compilation and use
jacobi.c
nrutil.c
nrutil.h
jacobi_test.c
input.txt
FILE FOR INVERTER IN C:
invert2.c
FILES FOR RANDOM NUMBER GENERATOR IN FORTRAN:
ran2.f
FILES FOR RANDOM NUMBER GENERATOR IN C:
Notes on compilation and use
r1279.c
r1279.h
test.c