Course: Advanced sampling techniques

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Simulation of Biomolecules – p. 2 Monte Carlo: History • A Monte Carlo (MC) method is a technique that involves using random numbers and probability to solve problems. • Enrico Fermi in the 1930s and Stanislaw Ulam in 1946 first had the idea. • Ulam later contacted John von Neumann at the Los Alamos Scientific Laboratory who at that time was investigating radiation shielding and the distance that neutrons would likely travel through various materials. • Ulam and von Neumann suggested to solve this problem by modeling the experiment on a computer using chance. • Being secret, their work required a code name. Von Neumann chose the name "Monte Carlo" in reference to games of chance, a popular attraction in Monte Carlo, Monaco. • Random <strong>sampling</strong> dates back to the 18th and 19th centuries where needle throwing experiments were used to calculate geometric probabilties (George Louis Leclerc, a.k.a. Comte de Buffon, 1777).
Simulation of Biomolecules – p. 3 Monte Carlo: The Idea • Laplace, in the early 1800s generalized Buffon’s needle throwing experiments and recognized it as a method for calculating π: • The left figure is simply a unit circle circumscribed by a square. It is easier to examine just one quadrant of the circle, as in the right figure. • If you are a very poor dart player, it is easy to imagine throwing darts randomly at the right figure. It should be apparent that #darts hitting shaded area #darts hitting inside square = area of shaded area area of square i.e.
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Course: Advanced sampling techniques

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