1 | #pragma rtGlobals=1 // Use modern global access method. |
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2 | #pragma IgorVersion = 6.0 |
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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 is for the form factor of a polydisperse spherical particle, with a core-shell structure |
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10 | // the polydispersity of the overall (core+shell) radius is described by a Schulz distribution |
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11 | // the ratio R(core)/ R (total) is constant |
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12 | // |
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13 | // 06 NOV 98 SRK |
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14 | //////////////////////////////////////////////// |
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15 | |
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16 | Proc PlotPolyCoreShellRatio(num,qmin,qmax) |
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17 | Variable num=128,qmin=0.001,qmax=0.7 |
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18 | Prompt num "Enter number of data points for model: " |
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19 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
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20 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
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21 | |
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22 | Make/O/D/n=(num) xwave_pcr,ywave_pcr |
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23 | xwave_pcr = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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24 | Make/O/D coef_pcr = {1.,60,10,.2,1e-6,2e-6,3e-6,0.001} |
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25 | Make/O/t parameters_pcr = {"scale","avg core rad (A)","avg shell thickness (A)","overall polydisp (0,1)",,"SLD core (A-2)","SLD shell (A-2)","SLD solvent (A-2)","bkg (cm-1)"} |
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26 | Edit parameters_pcr,coef_pcr |
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27 | Variable/G root:g_pcr |
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28 | g_pcr := PolyCoreShellRatio(coef_pcr,ywave_pcr,xwave_pcr) |
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29 | // ywave_pcr := PolyCoreShellRatio(coef_pcr,xwave_pcr) |
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30 | Display ywave_pcr vs xwave_pcr |
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31 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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32 | Label bottom "q (\\S-1\\M)" |
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33 | Label left "Intensity (cm\\S-1\\M)" |
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34 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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35 | |
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36 | AddModelToStrings("PolyCoreShellRatio","coef_pcr","pcr") |
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37 | End |
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38 | |
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39 | /////////////////////////////////////////////////////////// |
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40 | // - sets up a dependency to a wrapper, not the actual SmearedModelFunction |
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41 | Proc PlotSmearedPolyCoreShellRatio(str) |
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42 | String str |
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43 | Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4) |
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44 | |
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45 | // if any of the resolution waves are missing => abort |
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46 | if(ResolutionWavesMissingDF(str)) //updated to NOT use global strings (in GaussUtils) |
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47 | Abort |
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48 | endif |
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49 | |
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50 | SetDataFolder $("root:"+str) |
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51 | |
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52 | // Setup parameter table for model function |
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53 | Make/O/D smear_coef_pcr = {1.,60,10,.2,1e-6,2e-6,3e-6,0.001} |
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54 | make/o/t smear_parameters_pcr = {"scale","avg core rad (A)","avg shell thickness (A)","overall polydisp (0,1)",,"SLD core (A-2)","SLD shell (A-2)","SLD solvent (A-2)","bkg (cm-1)"} |
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55 | Edit smear_parameters_pcr,smear_coef_pcr |
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56 | |
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57 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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58 | // make extra copy of experimental q-values for easy plotting |
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59 | Duplicate/O $(str+"_q") smeared_pcr,smeared_qvals //**** mod |
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60 | SetScale d,0,0,"1/cm",smeared_pcr //**** mod |
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61 | |
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62 | Variable/G gs_pcr=0 |
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63 | gs_pcr := fSmearedPolyCoreShellRatio(smear_coef_pcr,smeared_pcr,smeared_qvals) //this wrapper fills the STRUCT |
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64 | |
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65 | Display smeared_pcr vs smeared_qvals |
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66 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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67 | Label bottom "q (\\S-1\\M)" |
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68 | Label left "Intensity (cm\\S-1\\M)" |
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69 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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70 | |
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71 | SetDataFolder root: |
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72 | AddModelToStrings("SmearedPolyCoreShellRatio","smear_coef_pcr","pcr") |
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73 | End |
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74 | |
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75 | |
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76 | //AAO version |
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77 | Function PolyCoreShellRatio(cw,yw,xw) : FitFunc |
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78 | Wave cw,yw,xw |
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79 | |
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80 | #if exists("PolyCoreShellRatioX") |
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81 | yw = PolyCoreShellRatioX(cw,xw) |
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82 | #else |
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83 | yw = fPolyCoreShellRatio(cw,xw) |
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84 | #endif |
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85 | return(0) |
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86 | End |
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87 | |
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88 | /////////////////////////////////////////////////////////////// |
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89 | // unsmeared model calculation |
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90 | /////////////////////////// |
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91 | //C CALC'S THE FORM FACTOR FOR A MONOMODAL |
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92 | //c POPULATION OF POLYDISPERSE SHERES WITH A |
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93 | //c CORE AND SHELL TYPE SLD DISTRIBUTION. IT |
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94 | //c ASSUMES THAT THE CORE RADIUS IS A CONSTANT |
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95 | //c FRACTION (P) OF THE SHELL RADIUS. |
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96 | //c |
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97 | //c |
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98 | //c REF.: "DETERMINATION OF THE STRUCTURE AND DYNAMICS OF |
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99 | //c MICELLAR SOLUTIONS BY NEUTRON SMALL-ANGLE SCATTERING" |
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100 | //c BY J.B.HAYTER IN PHYSICS OF AMPHIPHILES--MICELLES, |
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101 | //c VESICLES, AND MICROEMULSIONS ED BY DEGIORGIO,V; CORTI,M, |
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102 | //c PP59-93,1983. |
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103 | //c |
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104 | //c EQNS: 32-37 |
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105 | //c |
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106 | Function fPolyCoreShellRatio(w,x) : FitFunc |
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107 | Wave w;Variable x |
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108 | |
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109 | //assign nice names to the input wave |
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110 | //w[0] = scale |
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111 | //w[1] = core radius [] |
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112 | //w[2] = shell thickness [] |
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113 | //w[3] = polydispersity index (0<p<1) |
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114 | //w[4] = SLD core [^-2] |
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115 | //w[5] = SLD shell [^-2] |
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116 | //w[6] = SLD solvent [^-2] |
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117 | //w[7] = bkg [cm-1] |
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118 | Variable scale,corrad,thick,shlrad,pp,drho1,drho2,sig,zz,bkg |
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119 | Variable sld1,sld2,sld3,zp1,zp2,zp3,vpoly |
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120 | |
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121 | scale = w[0] |
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122 | corrad = w[1] |
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123 | thick = w[2] |
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124 | sig = w[3] |
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125 | sld1 = w[4] |
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126 | sld2 = w[5] |
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127 | sld3 = w[6] |
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128 | bkg = w[7] |
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129 | |
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130 | //calculations on input parameters |
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131 | shlrad = corrad + thick |
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132 | zz = (1/sig)^2-1 |
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133 | drho1 = sld1-sld2 //core-shell |
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134 | drho2 = sld2-sld3 //shell-solvent |
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135 | zp1 = zz + 1. |
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136 | zp2 = zz + 2. |
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137 | zp3 = zz + 3. |
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138 | vpoly = 4*Pi/3*zp3*zp2/zp1/zp1*(corrad+thick)^3 |
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139 | |
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140 | //local variables |
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141 | Variable pi43,c1,c2,form,volume,arg1,arg2 |
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142 | |
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143 | PI43=4.0/3.0*PI |
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144 | Pp=CORRAD/SHLRAD |
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145 | VOLUME=PI43*SHLRAD*SHLRAD*SHLRAD |
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146 | C1=DRHO1*VOLUME |
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147 | C2=DRHO2*VOLUME |
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148 | |
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149 | // the beta factor is not calculated |
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150 | // the calculated form factor <f^2> has units [length^2] |
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151 | // and must be multiplied by number density [l^-3] and the correct unit |
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152 | // conversion to get to absolute scale |
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153 | |
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154 | // DO 10 I=1,NPTSM |
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155 | // F=P*P*P*C1*FNT1(QVALSM(I)*P*SHLRAD,Z) |
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156 | // 2 +C2*FNT1(QVALSM(I)*SHLRAD,Z) |
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157 | // FAVE2=F*F |
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158 | |
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159 | arg1 = x*shlrad*pp |
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160 | arg2 = x*shlrad |
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161 | |
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162 | FORM=(Pp^6.0)*C1*C1*FNT2(arg1,Zz) |
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163 | form += C2*C2*FNT2(arg2,Zz) |
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164 | form += 2.0*C1*C2*FNT3(arg2,Pp,Zz) |
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165 | |
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166 | //convert the result to [cm^-1] |
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167 | |
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168 | //scale the result |
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169 | // - divide by the polydisperse volume, mult by 10^8 |
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170 | form /= vpoly |
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171 | form *= 1.0e8 |
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172 | form *= scale |
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173 | |
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174 | //add in the background |
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175 | form += bkg |
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176 | |
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177 | RETURN (form) |
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178 | END |
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179 | ////////////////////////////////////// |
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180 | //cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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181 | //c |
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182 | //c FUNCTION FNT1(Y,Z) |
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183 | //c |
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184 | Function FNT1(Yy,Zz) |
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185 | Variable yy,zz |
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186 | |
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187 | //local variables |
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188 | Variable z1,z2,uu,vv,ww,term1,term2,fnt1 |
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189 | |
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190 | Z1=Zz+1.0 |
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191 | Z2=Zz+2.0 |
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192 | Uu=Yy/Z1 |
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193 | Vv=ATAN(Uu) |
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194 | Ww=ATAN(2.0*Uu) |
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195 | TERM1=SIN(Z1*Vv)/((1.0+Uu*Uu)^(Z1/2.0)) |
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196 | TERM2=Yy*COS(Z2*Vv)/((1.0+Uu*Uu)^(Z2/2.0)) |
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197 | FNT1=3.0/Yy/Yy/Yy*(TERM1-TERM2) |
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198 | |
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199 | RETURN (fnt1) |
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200 | END |
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201 | |
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202 | //cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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203 | //c |
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204 | //c FUNCTION FNT2(Y,Z) |
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205 | //c |
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206 | FUNCTION FNT2(Yy,Zz) |
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207 | Variable yy,zz |
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208 | |
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209 | //local variables |
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210 | Variable z1,z2,z3,uu,ww,term1,term2,term3,fnt2 |
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211 | |
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212 | Z1=Zz+1.0 |
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213 | Z2=Zz+2.0 |
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214 | Z3=Zz+3.0 |
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215 | Uu=Yy/Z1 |
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216 | Ww=ATAN(2.0*Uu) |
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217 | TERM1=COS(Z1*Ww)/((1.0+4.0*Uu*Uu)^(Z1/2.0)) |
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218 | TERM2=2.0*Yy*SIN(Z2*Ww)/((1.0+4.0*Uu*Uu)^(Z2/2.0)) |
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219 | TERM3=1.0+COS(Z3*Ww)/((1.0+4.0*Uu*Uu)^(Z3/2.0)) |
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220 | FNT2=(4.50/Z1/Yy^6.0)*(Z1*(1.0-TERM1-TERM2)+Yy*Yy*Z2*TERM3) |
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221 | |
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222 | RETURN (fnt2) |
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223 | END |
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224 | |
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225 | //cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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226 | //c |
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227 | //c FUNCTION FNT3(Y,P,Z) |
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228 | //c |
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229 | FUNCTION FNT3(Yy,Pp,Zz) |
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230 | Variable yy,pp,zz |
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231 | |
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232 | //local variables |
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233 | Variable z1,z2,z3,yp,yn,up,un,vp,vn,term1,term2,term3,term4,term5,term6,fnt3 |
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234 | |
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235 | Z1=Zz+1 |
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236 | Z2=Zz+2 |
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237 | Z3=Zz+3 |
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238 | YP=(1.0+Pp)*Yy |
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239 | YN=(1.0-Pp)*Yy |
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240 | UP=YP/Z1 |
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241 | UN=YN/Z1 |
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242 | VP=ATAN(UP) |
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243 | VN=ATAN(UN) |
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244 | TERM1=COS(Z1*VN)/((1.0+UN*UN)^(Z1/2.0)) |
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245 | TERM2=COS(Z1*VP)/((1.0+UP*UP)^(Z1/2.0)) |
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246 | TERM3=COS(Z3*VN)/((1.0+UN*UN)^(Z3/2.0)) |
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247 | TERM4=COS(Z3*VP)/((1.0+UP*UP)^(Z3/2.0)) |
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248 | TERM5=YN*SIN(Z2*VN)/((1.0+UN*UN)^(Z2/2.0)) |
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249 | TERM6=YP*SIN(Z2*VP)/((1.0+UP*UP)^(Z2/2.0)) |
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250 | FNT3=(4.5/Z1/Yy^6.0) |
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251 | fnt3 *=(Z1*(TERM1-TERM2)+Yy*Yy*Pp*Z2*(TERM3+TERM4)+Z1*(TERM5-TERM6)) |
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252 | |
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253 | RETURN (fnt3) |
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254 | END |
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255 | ///////////////////////////////// |
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256 | |
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257 | // this is all there is to the smeared calculation! |
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258 | Function SmearedPolyCoreShellRatio(s) :FitFunc |
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259 | Struct ResSmearAAOStruct &s |
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260 | |
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261 | ////the name of your unsmeared model is the first argument |
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262 | Smear_Model_20(PolyCoreShellRatio,s.coefW,s.xW,s.yW,s.resW) |
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263 | |
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264 | return(0) |
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265 | End |
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266 | |
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267 | //wrapper to calculate the smeared model as an AAO-Struct |
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268 | // fills the struct and calls the ususal function with the STRUCT parameter |
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269 | // |
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270 | // used only for the dependency, not for fitting |
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271 | // |
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272 | Function fSmearedPolyCoreShellRatio(coefW,yW,xW) |
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273 | Wave coefW,yW,xW |
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274 | |
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275 | String str = getWavesDataFolder(yW,0) |
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276 | String DF="root:"+str+":" |
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277 | |
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278 | WAVE resW = $(DF+str+"_res") |
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279 | |
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280 | STRUCT ResSmearAAOStruct fs |
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281 | WAVE fs.coefW = coefW |
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282 | WAVE fs.yW = yW |
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283 | WAVE fs.xW = xW |
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284 | WAVE fs.resW = resW |
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285 | |
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286 | Variable err |
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287 | err = SmearedPolyCoreShellRatio(fs) |
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288 | |
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289 | return (0) |
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290 | End |
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