Monte Carlo Methods in Statistical Mechanics . Aziz Abdellahi CEDER group. Materials Basics Lecture : 08/18/2011. What is Monte Carlo ?. Monte Carlo is an administrative area of the principality of Monaco. Famous for its casinos ! .
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Materials Basics Lecture : 08/18/2011
Finding the value of π (“shooting darts”)The simplest Monte Carlo method
Monte Carlo method that will be discussed in this talk
Example of results obtained from MC : LixFePO4 (Li-ion battery cathode)
Results obtained in the Ceder group (using Monte Carlo)
Finding a numerical approximation to the partition function
Importance sampling : Sample states according to their actual probabilityMonte Carlo or “Importance Sampling”
Monte Carlo : Methodology actual probabilityMonte Carlo or “Importance Sampling”
Building the chain : The Metropolis Algorithm actual probabilityMetropolis Algorithm
Why does the Metropolis algorithm work ? actual probabilityMetropolis algorithm (3)
It can be shown that all selection criteria that respect the condition of detailed balance produce correct sampling :
Monte Carlo in Statistical Mechanics actual probabilityConclusion
Other Monte Carlo methods in engineering