lec32_12012006 - 10.34, Numerical Methods Applied to...

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Unformatted text preview: 10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #32: Kinetic Monte Carlo and Turbulence Modeling. Thermal Relaxation p i (E,t) C+D A B Figure 1. Energy diagram. Branching Fraction : + = = + = d t p d t p t p P T t D C i B i A D C B ) , ( ) , ( )) , ( , , ; ( One approach: ... ) ( = i p dt d {track entire distribution} Second approach: Kinetic Monte Carlo (Gillespie) {track individual molecule} initial conditions: i = A; , t t t rand t t Z E k E k new coll disc isom = = + + = ) ln( ) ( ) ( 1 Pick rand2: if rand2 < k isom (E) i new = B E new = E e l s e i f r a n d 2 < ( k isom (E)+k disc (E)) i new = C+D else i new = i old r a n d o m E E new E + E Dilute in A so we can assume A does not interact with other molecules Cite as: William Green, Jr., course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. Problem Set 11 w a t e r organic r vitE vitC vitE vitC Figure 2.Figure 2....
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lec32_12012006 - 10.34, Numerical Methods Applied to...

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