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Eden modelsimple model for tumor growth or epidemic spreadEach site that is a neighbour of an occupied sitehas an equal probability of being filled.Make a list of neighbour sites (red).Pick one at random. Add it to cluster (green).Neighbours of this site then become red….There can be more than one growth site in acolumn. Can get overhangs.c47Eden cluster = 1/3ξ = 1/248
Ballistic depositionParticles fall vertically from above andstick when they touch a particle below or aneighbour on one side.Pick a column i. Let particle fall till ittouches a neighbour. Possible growth sitesare indicated in red. Only one possible siteper column.c = 1/3ξ = 1/249KPZ equation:Growth equationsEdwards Wilkinson equation: hxt( , )tS.F. Edwards and D.R. Wilkinson (1982) = 1/4 and ξ = 1/2h( x, t)hxt( , ) h h 2( x, t)t2M. Kardar, G. Parisi and Y.-C. Zhang (1986) = 1/3 and ξ = 1/2noise50
Page 1 and 2: Monte Carlo MethodsNicholas Constan
Page 3 and 4: Calculation of π1x 2 + y 2 = 1 124
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