1 | #pragma rtGlobals=1 // Use modern global access method. |
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2 | #pragma IgorVersion=6.1 |
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3 | |
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4 | //////////////////////////////////////////////// |
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5 | // GaussUtils.proc and PlotUtils.proc MUST be included for the smearing calculation to compile. |
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6 | // Adopting these into the experiment will insure that they are always present. |
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7 | //////////////////////////////////////////////// |
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8 | // |
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9 | // This function calculates the total coherent scattered intensity from stacked discs (tactoids) with a core/layer |
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10 | // structure. Assuming the next neighbor distance (d-spacing) in a stack of parallel discs obeys a Gaussian |
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11 | // distribution, a strcture factor S(q) proposed by Kratky and Porod in 1949 is used in this function. |
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12 | // |
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13 | // 04 JUL 01 DLH |
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14 | // |
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15 | // SRK - 2007 |
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16 | // this model needs 76 Gauss points for a proper smearing calculation |
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17 | // since there can be sharp interference fringes that develop from the stacking |
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18 | //////////////////////////////////////////////// |
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19 | |
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20 | Proc PlotStackedDiscs(num,qmin,qmax) |
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21 | Variable num=500,qmin=0.001,qmax=1.0 |
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22 | Prompt num "Enter number of data points for model: " |
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23 | Prompt qmin "Enter minimum q-value (A^-1) for model: " |
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24 | Prompt qmax "Enter maximum q-value (A^-1) for model: " |
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25 | |
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26 | make/o/D/n=(num) xwave_scyl,ywave_scyl |
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27 | xwave_scyl = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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28 | make/o/D coef_scyl = {0.01,3000.,10.,15.,4.0e-6,-4.0e-7,5.0e-6,1,0,1.0e-3} |
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29 | make/o/t parameters_scyl = {"scale","Disc Radius (A)","Core Thickness (A)","Layer Thickness (A)","Core SLD (A^-2)","Layer SLD (A^-2)","Solvent SLD(A^-2)","# of Stacking","GSD of d-Spacing","incoh. bkg (cm^-1)"} |
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30 | Edit parameters_scyl,coef_scyl |
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31 | |
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32 | Variable/G root:g_scyl |
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33 | g_scyl := StackedDiscs(coef_scyl,ywave_scyl,xwave_scyl) |
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34 | // ywave_scyl := StackedDiscs(coef_scyl,xwave_scyl) |
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35 | Display ywave_scyl vs xwave_scyl |
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36 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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37 | Label bottom "q (A\\S-1\\M)" |
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38 | Label left "Intensity (cm\\S-1\\M)" |
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39 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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40 | |
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41 | AddModelToStrings("StackedDiscs","coef_scyl","parameters_scyl","scyl") |
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42 | End |
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43 | /////////////////////////////////////////////////////////// |
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44 | |
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45 | /////////////////////////////////////////////////////////// |
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46 | // - sets up a dependency to a wrapper, not the actual SmearedModelFunction |
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47 | Proc PlotSmearedStackedDiscs(str) |
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48 | String str |
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49 | Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4) |
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50 | |
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51 | // if any of the resolution waves are missing => abort |
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52 | if(ResolutionWavesMissingDF(str)) //updated to NOT use global strings (in GaussUtils) |
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53 | Abort |
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54 | endif |
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55 | |
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56 | SetDataFolder $("root:"+str) |
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57 | |
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58 | // Setup parameter table for model function |
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59 | make/o/D smear_coef_scyl = {0.01,3000.,10.,15.,4.0e-6,-4.0e-7,5.0e-6,1,0,1.0e-3} |
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60 | make/o/t smear_parameters_scyl = {"scale","Disc Radius (A)","Core Thickness (A)","Layer Thickness (A)","Core SLD (A^-2)","Layer SLD (A^-2)","Solvent SLD (A^-2)","# of Stacking","GSD of d-Spacing","incoh. bkg (cm^-1)"} |
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61 | Edit smear_parameters_scyl,smear_coef_scyl |
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62 | |
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63 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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64 | // make extra copy of experimental q-values for easy plotting |
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65 | Duplicate/O $(str+"_q") smeared_scyl,smeared_qvals |
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66 | SetScale d,0,0,"1/cm",smeared_scyl |
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67 | |
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68 | Variable/G gs_scyl=0 |
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69 | gs_scyl := fSmearedStackedDiscs(smear_coef_scyl,smeared_scyl,smeared_qvals) //this wrapper fills the STRUCT |
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70 | |
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71 | Display smeared_scyl vs smeared_qvals |
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72 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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73 | Label bottom "q (A\\S-1\\M)" |
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74 | Label left "Intensity (cm\\S-1\\M)" |
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75 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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76 | |
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77 | SetDataFolder root: |
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78 | AddModelToStrings("SmearedStackedDiscs","smear_coef_scyl","smear_parameters_scyl","scyl") |
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79 | End |
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80 | |
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81 | /////////////////////////////////////////////////////////////// |
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82 | |
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83 | //AAO version |
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84 | Function StackedDiscs(cw,yw,xw) : FitFunc |
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85 | Wave cw,yw,xw |
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86 | |
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87 | #if exists("StackedDiscsX") |
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88 | yw = StackedDiscsX(cw,xw) |
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89 | #else |
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90 | yw = fStackedDiscs(cw,xw) |
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91 | #endif |
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92 | return(0) |
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93 | End |
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94 | /////////////////////////////////////////////////////////////// |
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95 | // unsmeared model calculation |
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96 | /////////////////////////// |
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97 | Function fStackedDiscs(w,x) : FitFunc |
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98 | Wave w |
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99 | Variable x |
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100 | |
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101 | //The input variables are (and output) |
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102 | //[0] Scale |
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103 | //[1] Disc Radius (A) |
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104 | //[2] Disc Core Thickness (A) |
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105 | //[3] Disc Layer Thickness (A) |
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106 | //[4] Core SLD (A^-2) |
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107 | //[5] Layer SLD (A^-2) |
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108 | //[6] Solvent SLD (A^-2) |
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109 | //[7] Number of Discs Stacked |
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110 | //[8] Gaussian Standrad Deviation of d-Spacing |
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111 | //[9] background (cm^-1) |
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112 | |
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113 | Variable scale,length,bkg,rcore,thick,rhoc,rhol,rhosolv,N,gsd |
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114 | scale = w[0] |
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115 | rcore = w[1] |
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116 | length = w[2] |
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117 | thick = w[3] |
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118 | rhoc = w[4] |
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119 | rhol = w[5] |
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120 | rhosolv = w[6] |
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121 | N = w[7] |
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122 | gsd = w[8] |
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123 | bkg = w[9] |
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124 | // |
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125 | // the OUTPUT form factor is <f^2>/Vcyl [cm-1] |
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126 | // |
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127 | |
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128 | // local variables |
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129 | Variable nord,ii,va,vb,contr,vcyl,nden,summ,yyy,zi,qq,halfheight,kk,sqq,dexpt,d |
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130 | Variable answer |
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131 | |
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132 | d=2*thick+length |
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133 | |
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134 | String weightStr,zStr |
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135 | |
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136 | weightStr = "gauss76wt" |
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137 | zStr = "gauss76z" |
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138 | |
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139 | |
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140 | // if wt,z waves don't exist, create them |
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141 | // 20 Gauss points is not enough for cylinder calculation |
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142 | |
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143 | if (WaveExists($weightStr) == 0) // wave reference is not valid, |
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144 | Make/D/N=76 $weightStr,$zStr |
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145 | Wave w76 = $weightStr |
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146 | Wave z76 = $zStr // wave references to pass |
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147 | Make76GaussPoints(w76,z76) |
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148 | // printf "w[0],z[0] = %g %g\r", w76[0],z76[0] |
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149 | else |
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150 | if(exists(weightStr) > 1) |
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151 | Abort "wave name is already in use" // execute if condition is false |
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152 | endif |
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153 | Wave w76 = $weightStr |
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154 | Wave z76 = $zStr // Not sure why this has to be "declared" twice |
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155 | // printf "w[0],z[0] = %g %g\r", w76[0],z76[0] |
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156 | endif |
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157 | |
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158 | |
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159 | // set up the integration |
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160 | // end points and weights |
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161 | nord = 76 |
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162 | va = 0 |
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163 | vb = Pi/2 |
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164 | halfheight = length/2.0 |
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165 | |
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166 | // evaluate at Gauss points |
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167 | // remember to index from 0,size-1 |
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168 | |
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169 | qq = x //current x point is the q-value for evaluation |
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170 | summ = 0.0 // initialize integral |
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171 | ii=0 |
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172 | do |
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173 | // Using 76 Gauss points |
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174 | zi = ( z76[ii]*(vb-va) + vb + va )/2.0 |
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175 | yyy = w76[ii] * Stackdisc_kern(qq, rcore, rhoc,rhol,rhosolv, halfheight,thick,zi,gsd,d,N) |
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176 | summ += yyy |
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177 | |
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178 | ii+=1 |
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179 | while (ii<nord) // end of loop over quadrature points |
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180 | // |
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181 | // calculate value of integral to return |
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182 | |
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183 | answer = (vb-va)/2.0*summ |
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184 | |
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185 | // contrast is now explicitly included in the core-shell calculation |
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186 | |
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187 | //Normalize by total disc volume |
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188 | //NOTE that for this (Fournet) definition of the integral, one must MULTIPLY by Vcyl |
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189 | //Calculate TOTAL volume |
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190 | // length is the total core thickness |
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191 | |
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192 | vcyl=Pi*rcore*rcore*(2*thick+length)*N |
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193 | answer /= vcyl |
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194 | |
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195 | //Convert to [cm-1] |
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196 | answer *= 1.0e8 |
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197 | |
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198 | //Scale |
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199 | answer *= scale |
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200 | |
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201 | // add in the background |
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202 | answer += bkg |
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203 | |
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204 | Return (answer) |
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205 | |
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206 | End //End of function StackDiscs() |
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207 | |
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208 | /////////////////////////////////////////////////////////////// |
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209 | |
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210 | // F(qq, rcore, rhoc,rhosolv, length, zi) |
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211 | // |
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212 | Function Stackdisc_kern(qq, rcore, rhoc,rhol,rhosolv, length,thick,dum,gsd,d,N) |
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213 | Variable qq, rcore, rhoc,rhol,rhosolv, length,thick,dum,gsd,d,N |
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214 | |
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215 | // qq is the q-value for the calculation (1/A) |
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216 | // rcore is the core radius of the cylinder (A) |
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217 | // rho(n) are the respective SLD's |
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218 | // length is the *Half* CORE-LENGTH of the cylinder = L (A) |
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219 | // dum is the dummy variable for the integration (x in Feigin's notation) |
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220 | |
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221 | //Local variables |
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222 | Variable totald,dr1,dr2,besarg1,besarg2,area,sinarg1,sinarg2,t1,t2,retval,kk,sqq,dexpt |
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223 | |
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224 | dr1 = rhoc-rhosolv |
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225 | dr2 = rhol-rhosolv |
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226 | area = Pi*rcore*rcore |
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227 | totald=2*(thick+length) |
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228 | |
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229 | besarg1 = qq*rcore*sin(dum) |
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230 | besarg2 = qq*rcore*sin(dum) |
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231 | |
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232 | sinarg1 = qq*length*cos(dum) |
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233 | sinarg2 = qq*(length+thick)*cos(dum) |
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234 | |
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235 | t1 = 2*area*(2*length)*dr1*(sin(sinarg1)/sinarg1)*(bessJ(1,besarg1)/besarg1) |
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236 | t2 = 2*area*dr2*(totald*sin(sinarg2)/sinarg2-2*length*sin(sinarg1)/sinarg1)*(bessJ(1,besarg2)/besarg2) |
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237 | |
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238 | retval =((t1+t2)^2)*sin(dum) |
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239 | |
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240 | // loop for the structure facture S(q) |
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241 | |
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242 | kk=1 |
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243 | sqq=0.0 |
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244 | do |
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245 | dexpt=qq*cos(dum)*qq*cos(dum)*d*d*gsd*gsd*kk/2.0 |
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246 | sqq=sqq+(N-kk)*cos(qq*cos(dum)*d*kk)*exp(-1.*dexpt) |
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247 | |
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248 | kk+=1 |
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249 | while (kk<N) |
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250 | |
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251 | // end of loop for S(q) |
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252 | |
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253 | sqq=1.0+2.0*sqq/N |
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254 | |
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255 | retval *= sqq |
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256 | |
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257 | return retval |
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258 | |
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259 | End //Function Stackdisc() |
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260 | |
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261 | /////////////////////////////////////////////////////////////// |
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262 | |
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263 | // this model needs 76 Gauss points for a proper smearing calculation |
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264 | // since there can be sharp interference fringes that develop from the stacking |
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265 | Function SmearedStackedDiscs(s) :FitFunc |
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266 | Struct ResSmearAAOStruct &s |
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267 | |
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268 | ////the name of your unsmeared model is the first argument |
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269 | Smear_Model_76(StackedDiscs,s.coefW,s.xW,s.yW,s.resW) |
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270 | |
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271 | return(0) |
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272 | End |
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273 | |
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274 | |
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275 | //wrapper to calculate the smeared model as an AAO-Struct |
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276 | // fills the struct and calls the ususal function with the STRUCT parameter |
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277 | // |
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278 | // used only for the dependency, not for fitting |
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279 | // |
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280 | Function fSmearedStackedDiscs(coefW,yW,xW) |
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281 | Wave coefW,yW,xW |
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282 | |
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283 | String str = getWavesDataFolder(yW,0) |
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284 | String DF="root:"+str+":" |
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285 | |
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286 | WAVE resW = $(DF+str+"_res") |
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287 | |
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288 | STRUCT ResSmearAAOStruct fs |
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289 | WAVE fs.coefW = coefW |
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290 | WAVE fs.yW = yW |
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291 | WAVE fs.xW = xW |
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292 | WAVE fs.resW = resW |
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293 | |
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294 | Variable err |
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295 | err = SmearedStackedDiscs(fs) |
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296 | |
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297 | return (0) |
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298 | End |
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