Monte Carlo Simulation

Short description and context

Monte Carlo Simulation

Monte Carlo is one of a very small number of integration algorithms that can be used to calculate integrals over large numbers of variables. This method is used widely in atomistic simulation, where it used to calculate ensemble averages, and also in statistics where it can be used to calculate expectations for particular complex random variables.

Syllabus Aims

  • You should be able to explain what we mean by importance sampling.
  • You should be able to explain and implement the metropolis sampling algorithm.
  • You should be able to explain how ensemble averages can be computed using Monte Carlo simulations.
  • You should be able to explain how problems with ergodicity affect the accuracy of the ensemble averages calculated using Monte Carlo

Written Notes

Description and link

Module

Author

Notes on the theory of Monte Carlo simulation. SOR3012 J. F. McCann

Videos

Description and link

Module

Author

A very brief introduction to the theory of Monte Carlo sampling. AMA4004 G. Tribello
Video explaining how block averages should be calculated from correlated data sets. AMA4004 G. Tribello

Applying your knowledge

Description and link

Module

Author

An exercise that will take you through the process of writing your own Monte Carlo code. AMA4004 G. Tribello
A programming exercise that calls on you to build a Monte Carlo code and to investigate how the properties of the system change with temperature and field strength. AMA4004 G. Tribello

Contact Details

School of Mathematics and Physics,
Queen's University Belfast,
Belfast,
BT7 1NN

Email: g.tribello@qub.ac.uk
Website: mywebsite