lec30_11272006 - 10.34, Numerical Methods Applied to...

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10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #30: Modeling intrinsically Stochastic processes. Multiscale Modeling. ∫∫ ∫∫ ∫∫ ∫∫ ∫∫ ∫∫ = = q d q w q w q p q d q w q d q w q f I N N N ) ( ) ( ) ( ) ( ) ( ) ( " " " ∫∫ ∫∫ = q d q p q f I N ) ( ) ( " () I N q f N i i N = = 1 lim where N is the number of sample points and q i is drawn from the partition function p(q ). Will have statistical sampling error N f f I MC 2 2 δ where () N q f f N i i = = 1 2 2 | f | ~ p t best weigh f f- f ~ rapidly very converge not does 1 small = > < = ∫∫ ∫∫ q pd p f I N dI N " Suppose one samples 10 6 points. To obtain an additional significant figure requires 10 8 points, so it is difficult to acquire another significant figure. Often, only w(q ) is known, not p(q ) Metropolis Method {q , …, q N } randomly choose dq if w(q N + δ q ) w(q N ) w(q N
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 10.302 taught by Professor Clarkcolton during the Fall '04 term at MIT.

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lec30_11272006 - 10.34, Numerical Methods Applied to...

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