CZ3272 Monte Carlo and Molecular Dynamics (Elective, 3 MC)

Synopsis
Prerequisites: CZ3105 and PC2230 or CM3231(can be co requisite)
Introduction to Markov chain Monte Carlo, Monte Carlo numerical integration, Metropolis algorithm, cluster algorithms, and integrators in molecular dynamics. Topics to be considered include simulation of phase transitions in physical systems, the structure of liquids and solids (from molecular dynamics simulations), and computation of physical quantities (total energy, pressure, equation of state, etc).

Instructor
Dr. Chen Yu Zong
Department of Computational Science
National University of Singapore
Office: Blk S17 Room 07-24
Tel: 6874-6877. Fax: 6774-6756
E-mail: yzchen@cz3.nus.edu.sg
Web: http://www.cz3.nus.edu.sg/~yzchen (Lots of info about biocomputing)

Schedule

• Lectures:
  • S17-07-41. Thur 800-1000
• Labs:
  • Y3 Lab. Fri 900-1000
• Tutorials:
  • S17-07-41. Fri 900-1000
• Grade:
  • Final exam 40%,
  • Mid-term exam 30%,
  • Lab 30%
• Exams:
  • Two mid-terms
  • One final exam

Module Outline

• Introduction
• Section  1: Introduction.
• Review of Numerical Methods
• Section  2: Linear algebra etc.
• Random Numbers
• Section  3: Random numbers and random number generators.
• Percolation Theory and Simulation
• Section  4: Percolation,  methematical models and physical quantities.
• Section  5: Critical behavior and critical exponents.
• Section  6: Exact solution in one dimention.
• Section  7: Computer simulation of site percolation and random resistor network.
• Monte Carlo Simulation
• Section  8: What is Monte Carlo?
• Section  9: Random variables of specified distribution
• Section 10: Monte Carlo evaluaton of finite integrals.
• Section 11: Importance sampling.
• Section 12: Metropolis algorithm and application examples.
• Section 13: Metropolis algorithm application examples.
• Molecular Dynamics
• Section 14: Integration schemes.
• Section 15: Simplectic algorithms and Molecular dynamics of few body problem.
• Section 16: Lennard-Jones fluid.
• Section 17: Lennard-Jones fluid, part II.
• Section 18: Molecular dynamics in canonical and grand canonical ensembles.
• Simulation in Chemistry and Biology
• Section 19: Numerical solutions to rate equations in chemical reaction.
• Section 20: Simulation of protein motions.

Lab Schedule

• Lab 1: Random number generators. Week 4
• Lab 2: Percolation (site percolation, random resistor network). Week 6
• Lab 3: Monte Carlo (site percolation simulation using Ising model). Week 8
• Lab 4: Molecular dynamics (3 body problem). Week 10

Tutorials

• Numerical methods and random numbers. Week 3
• Percolation. Week 5
• Monte Carlo. Week 7
• Molecular dynamics. Week 9

Recommended Text:

• Lecture Notes of Computational Techniques in Theoretical Physics. By Wang JianShen, Chen Kan and Zhang Fei.

The following files are downloable Postscript-version of the text.
 

• Part 1
• Part 2
• Part 3
• Part 4

References:

1. Introduction to Percolation Theory. 2nd Ed., D. Stauffer and A. Aharony,. Taylor & Francis, 1992.
2. Monte Carlo Simulation in Statistical Physics - An Introduction. K. Binder and D. W. Heermann, Springer-Verlag, 1988.
3. Computer Simulation Methods in Theoretical Physics.  2nd Ed., D. W. Heermann, Springer-Verlag, 1990.
4. Parallel Algorithms in Computational Science, D. W. Heermann and A. N. Burkit, Springer-Verlag, 1991.

Computational Physics. Nicholas J. Giordano. Prentice Hall, 1997.

Links to similar courses:

• Computer simulations in the natural sciences course at SDSU in US.
• Computational physics course at Carleton in Canada.
• Computational physics course at Imperial College of Science, Technology and Medicine in UK.
• Simulation and visualization tools in physics course at Cornell in US.