Instructor:

Robert D. Young

I. Texts:

H. Gould & J. Tobochnik, Computer Simulation Methods -- Applications to Physical Systems. Part 2, Addison-Wesley, 1988.

D.W. Heermann, Computer Simulation Methods in Theoretical Physics, Springer-Verlag, New York, 1990.

1. Distributed computer systems
1.1 RISC processors and UNIX O/S
1.2 Graphical user interfaces: Macintosh interface and X-windows
1.3 Programming language and graphics tools: FORTRAN, NCAR graphics, KaleidaGraph; etc.
1.4 Networking: Ethernet and token ring networks, TCP/IP and FTP protocols.

2. Stochastic and deterministic methods of simulating physical systems
2.1 Monte Carlo techniques
2.2 Molecular dynamics

3. Numerical integration -- Monte Carlo techniques
3.1 Physics problem--Mass, center-of-mass, and moment of inertia for a 2-D object with non-uniform density
3.2 Mathematical and numerical problem
(i) Comparison of methods for numerical integration of functions of one variable using interpolating polynomials and Monte Carlo techniques
(ii) Numerical integration of functions of two or more variables using Monte Carlo Techniques

4. Approach to equilibrium -- entropy
4.1 Physics problem--Simulation of the relaxation of a multi-particle, two-level system. Calculation of Boltzmann entropy.
4.2 Mathematical and numerical problem
(i) Monte Carlo simulation of two-level transitions; computation of relaxation function.
(ii) Computation of entropy using method of coincidence rate

5. Entropy of a period-doubling system
5.1 Physics problem--Period-doubling dynamics and transition to chaotic motion.
5.2 Mathematical and numerical problem
(i) Calculation of dependence ofattractors on control parameters of nonlinear difference equations; stable attractors; transition to chaotic dynamics and strange attractors.
(ii) Entropy of dynamic systems with strange attractors.

6. Random walks--diffusion
6.1 Physics problem--1-D and 2-D random walks; self- avoiding random walks (SAW); diffusion; 2-D polymer models.
6.2 Mathematical and numerical problem
(i) Monte Carlo simulation of 1-D and 2-D random walks; time dependence of rms displacement.
(ii) Monte Carlo simulation of a SAW

7. Canonical ensemble, Boltzmann Distributions, and the Metropolis method
7.1 Physics problem--Boltzmann distribution of a ideal, classical gas; Equilibration and correlation times of 2-D Ising spin model
7.2 Mathematical and numerical problem--Metropolis algorithm and Monte Carlo simulation.

8. Monte Carlo simulation of a quantum system
8.1 Physics problem--Random walk simulation of time-dependent Schödinger equation; ground state of harmonic and anharmonic quantum oscillator.
8.2 Mathematical and numerical problem
(i)Monte Carlo simulation of quantum walker obeying Schrödinger equation
(ii) Application to ground state energy and wave function of harmonic and anharmonic quantum oscillator

9. Molecular dynamics of many particle systems
9.1 Physics Problem--dynamical behavior of interacting many particle system; energy and temperature of a classical gas interacting via a Lennard-Jones potential
9.2 Mathematical and numerical problem--Velocity form of the Verlet algorithm with periodic boundary conditions