FindMinimum and Module

*To*: mathgroup at smc.vnet.net*Subject*: [mg113120] FindMinimum and Module*From*: Versiane UFOP <versiane.ufop at gmail.com>*Date*: Wed, 13 Oct 2010 23:26:43 -0400 (EDT)

Dear Mathematica users I would like to request any help with the code below, which I have been struggling in the last couple of weeks. I am trying to use FindMinimum to find the best k value that fits experimental data (extração) using the code enclosed in a Module structure. This is a heterogeneous kinetics problem where the Shrinking Core Model is modified to incorporate particle size distribution and k is a rate constant. As many of you always express here FindRoot does not produce the expected outcome and give the standard message ""The function value...is not a real number at {k} = {0.03`}". I would very much appreciate any help. The code is: mean := 100; std := 10; a = 5.032; b = 2.974; dmax = 190; u = 1; extração = {{0, 0.}, {10, 0.068973}, {20, 0.105011}, {30, 0.127376}, {40, 0.152779}, {50, 0.177607}, {60, 0.186656}, {80, 0.224261}, {100, 0.25433}, {120, 0.275795}} f[D_] := (1/(b^a*Gamma[a]))*D^(a - 1)*Exp[-D/b] t := Table[extração[[i, 1]], {i, Length[extração]}] model = ConstantArray[0, {Length[extração]}] conversion[(k_)?NumericQ] := Module[{dmin, rn, n, d, y, w, unconvt}, For[j = 1, j <= Length[t], j++, dmin = (k*t[[j]])^0.5; rn = (dmax - dmin)/(2*u) + 1; n = Round[rn]; d = Table[dmin + (2*i - 1)*u, {i, n}]; w = Table[y /. FindRoot[1 - 3*(1 - y)^(2/3) + 2*(1 - y) == (k/d[[i]]^2)*t[[j]], {y, 0.3}], {i, n}]; unconvt = 1 - Sum[(1 - w[k][[i]])*N[Integrate[f[D], {D, d[[i]] - u, d[[i]] + u}]], {i, 1, n}]; model[[j]] = unconvt; ]; model1 = {t, model}; x = Transpose[model1]; ] fit[(k_)?NumericQ] := Sum[(conversion[k][extração[[i, 1]]] - extração[[i, 2]])^2, {i, 1, Length[extração]}]; FindMinimum[{fit[k], k > 0}, {k, 0.03}] -- Prof. Versiane Albis Leão Bio&Hidrometallurgy Laboratories Department of Metallurgical and Materials Engeng. Universidade Federal de Ouro Preto, Brazil.