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Shape of dropL = 257, V = 6613, g = 0.001after 51057 MC updatesaveraged over 20 samples.Contact angle θ is functionof temperature and vanisheswhen approaching T c .θ39Solid on solid model (SOS)adatoms andsurface growthinterface without islands and without overhangsHN E h hi, j:nnij40
Irreversible growth• T. Vicsek, „Fractal Growth Phenomena“(World Scientific, Singapore, 1989• A.-L. Barabasi and H.E. Stanley, „FractalConcepts in Surface Growth“ (CambridgeUniv. Press, 1995)• H.J. Herrmann, „Geometric ClusterGrowth Models and Kinetic Gelation“,Phys. Rep. 136, 153 (1986)41Irreversible growthNo thermal equilibrium• Deposition and aggregation patterns• Fluid instabilities• Electric breakdown• Biological morphogenesis• Fracture and Fragmentation42
Page 1 and 2: Monte Carlo MethodsNicholas Constan
Page 3 and 4: Calculation of π1x 2 + y 2 = 1 124
Page 5 and 6: Error of integrationconventional me
Page 7 and 8: Not smooth integralsg(x)ax ineed mo
Page 9 and 10: M(RT) 2 algorithmN.C. Metropolis, A
Page 11 and 12: Detailed balancedp( X , t)dt pY ( )
Page 13 and 14: The Ising ModelBinary variables:i1,
Page 15 and 16: Binary mixtures(lattice gas)Conside
Page 17 and 18: Ising interface+++ +NH E J ij+i, j
Page 19: Ising interfaceAdd next-nearest nea
Page 23 and 24: Random deposition with surface diff
Page 25 and 26: Ballistic depositionParticles fall
Page 27 and 28: DLA clustersfractaldimensiond f = 1
Page 29 and 30: Dielectric breakdown57Dielectric br
Page 31 and 32: Dielectric breakdown modelη = 0.16
Page 33 and 34: Simulated Annealing (SA)S. Kirckpat
Page 35 and 36: Slow coolingT 0T 1T 20Different coo
Page 37 and 38: Solving equationsFinding the soluti
Page 39 and 40: Bisection methodTake two starting v
Page 41 and 42: N-dimensionalequationsBex a N-dimen
Page 43 and 44: N-dimensionalsecant methodIf the de
Page 45 and 46: Euler methodStart with y 0 and iter
Page 47 and 48: The order of a methodIf the error a
Page 49 and 50: Fourth order Runge - Kuttak1tf( y ,
Page 51 and 52: Example RK4Butcher array:its stage
Page 53 and 54: Example q = p = 2y ny t ( 1 )
Page 55 and 56: Adaptive time-stepΔtδ expectedDef
Page 57 and 58: Richardson extrapolationCalculate f
Page 59 and 60: 3th order predictor- correctoruse e
Page 61 and 62: Comparison of methodsΔtfor fixed n

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