- Illinois PHYS 466, Lecture 4: Molecular Dynamics
- Illinois PHYS 466, Lecture 1: Introduction
- Illinois PHYS 466, Lecture 11: Importance Sampling
- Illinois PHYS 466, Lecture 3: Basics of Statistical Mechanics
- Illinois PHYS 466, Lecture 19: The Ising Model
- Illinois PHYS 466, Lecture 5: Interatomic Potentials
- Illinois PHYS 466, Lecture 17: Simulation of Polymers
- Illinois PHYS 466, Lecture 16: Free Energies from Simulations
- Illinois PHYS 466, Lecture 8: Temperature and Pressure Controls
Fundamentals of Monte Carlo
What is Monte Carlo?
- Named at Los Alamos in 1940’s after the casino.
- Any method which uses (pseudo)random numbers> as an essential part of the algorithm.
- A method for doing highly dimensional integrals by sampling the integrand.
- Often a Markov chain, called Metropolis MC.
Stochastic - not deterministic!
- Simple example: Buffon’s needle - Monte Carlo determination of π
- MC is advantageous for high dimensional integrals -the best general method
- Improved Numerical Integration
- Other reasons to do Monte Carlo
- Probability Distributions
- Mappings of random variables
- What is Mapping Doing?
- Interpreting the Mapping
- Example: Drawing from Normal Gaussian
- Reminder: Gauss’ Central Limit Theorem
- Cumulants: κn Mean = κ1 Variance= κ2 Skewness = κ3 Kurtosis= κ4
- Approach to normality
- Conditions on Central Limit Theorem
- 2d histogram of occurrences of means
Researchers should cite this work as follows:
David M. Ceperley; Omar N Sobh (2009), "Illinois PHYS 466, Lecture 10: Sampling," https://nanohub.org/resources/6507.