Computational Physics of Complex Systems  (77732)

 Prof. Ofer Biham
 Office: Danciger B, room 210
 Phone: 02-6584363
 Email: biham@phys.huji.ac.il

 Class times:
 Monday     12:00 - 13:45
 Thursday     8:00 -   8:45
 
 Office hours: Monday 14:00-16:00, or any other time by a phone or email appointment.

 Syllabus

Review of phase transitions and critical phenomena,
Ising models, Markov processes.
 
Monte Carlo methods for equilibrium statistical physics:
Metropolis, heat-bath algorithms.
 
Cluster algorithms: Swendsen-Wang, Wolff algorithms.
 
Simulations of statistical physics out of thermal equilibrium:
kinetic Monte Carlo methods and applications to diffusion and
pattern formation problems with conserved order parameter.
 
Rate equation and master equation methods for particle diffusion,
cluster nucleation and chemical reactions. Simulations of stochastic
systems using Langevin and Fokker-Planck equations.

Simulations of thin film growth using kinetic Monte Carlo methods.
Chemical reaction networks on surfaces. The role of fluctuations
in reaction networks on small grains and the master equation.
Growth of rough surfaces, scaling and the Kardar-Parisi-Zhang
equation.

Spin glasses, minimization problems: Simulated annealing and
other techniques.

Simulations of dynamical systems using cellular automata:
applications to traffic flow, sandpiles and granular flow.
 
Random number generators, tests of randomness, generating
desired distributions: Gaussian distribution, power-law
distributions.
 
Fractal growth phenomena, fractal analysis, emergence of
power-law distributions in dynamical models, distribution
of wealth, stock market fluctuations, Levy flights, the Pareto
distribution and the Zipf plot.


 Bibliography
 

•   M.E.J. Newman and G.T. Barkema, Monte Carlo Methods in Statistical Physics

•   H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena

•   J.J. Binney, N.J. Dowrick, A.J. Fisher and M.E.J. Newman, The theory of critical phenomena

•   W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes: the art of scientific computing
  

•   F.S. Acton, Numerical methods that work

•   N. Gershenfeld, The nature of mathematical modeling

•   M. Mezard, G. Parisi and M.A. Virasoro,  Spin Glass theory and beyond
  

  Credit and Grades

  There will be four homework problem sets. The final grade will consist
  of the grade of the final exam (60 percent) and the grades of the
  homework sets (10 percent each).

 Homework 

 Problem set no.   1       
 Problem set no.   2     
 Problem set no.   3      
 Problem set no.   4      
 
 

URL: http://www.phys.huji.ac.il/~biham/CPhome.html