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32 | <body> |
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33 | <div class="header"><h1 class="heading"><a href="../index.html"> |
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34 | <span>Home</span></a></h1> |
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35 | <h2 class="heading"><span>2.1.3.5. Lamellarpc</span></h2> |
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36 | </div> |
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37 | <div class="topnav"> |
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38 | |
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39 | <p> |
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40 | «  <a href="lamellarFFHG.html">2.1.3.4. Lamellar ffhg</a> |
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41 |   ::   |
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42 | <a class="uplink" href="../index.html">Contents</a> |
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43 |   ::   |
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44 | <a href="../ref/models/shape-paracrystal.html">2.1.4. Paracrystal Functions</a>  Â» |
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45 | </p> |
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46 | |
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47 | </div> |
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48 | <div class="content"> |
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49 | |
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50 | |
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51 | <div class="section" id="lamellarpc"> |
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52 | <span id="id1"></span><h1>2.1.3.5. Lamellarpc<a class="headerlink" href="#lamellarpc" title="Permalink to this headline">¶</a></h1> |
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53 | <p>Random lamellar sheet with paracrystal structure factor</p> |
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54 | <table border="1" class="docutils"> |
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55 | <colgroup> |
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56 | <col width="22%" /> |
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57 | <col width="45%" /> |
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58 | <col width="16%" /> |
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59 | <col width="18%" /> |
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60 | </colgroup> |
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61 | <thead valign="bottom"> |
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62 | <tr class="row-odd"><th class="head">Parameter</th> |
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63 | <th class="head">Description</th> |
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64 | <th class="head">Units</th> |
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65 | <th class="head">Default value</th> |
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66 | </tr> |
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67 | </thead> |
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68 | <tbody valign="top"> |
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69 | <tr class="row-even"><td>scale</td> |
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70 | <td>Source intensity</td> |
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71 | <td>None</td> |
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72 | <td>1</td> |
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73 | </tr> |
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74 | <tr class="row-odd"><td>background</td> |
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75 | <td>Source background</td> |
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76 | <td>cm<sup>-1</sup></td> |
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77 | <td>0</td> |
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78 | </tr> |
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79 | <tr class="row-even"><td>thickness</td> |
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80 | <td>sheet thickness</td> |
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81 | <td>â«</td> |
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82 | <td>33</td> |
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83 | </tr> |
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84 | <tr class="row-odd"><td>Nlayers</td> |
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85 | <td>Number of layers</td> |
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86 | <td>None</td> |
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87 | <td>20</td> |
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88 | </tr> |
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89 | <tr class="row-even"><td>spacing</td> |
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90 | <td>d-spacing of paracrystal stack</td> |
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91 | <td>â«</td> |
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92 | <td>250</td> |
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93 | </tr> |
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94 | <tr class="row-odd"><td>spacing_polydisp</td> |
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95 | <td>d-spacing of paracrystal stack</td> |
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96 | <td>â«</td> |
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97 | <td>0</td> |
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98 | </tr> |
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99 | <tr class="row-even"><td>sld</td> |
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100 | <td>layer scattering length density</td> |
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101 | <td>10<sup>-6</sup>â«<sup>-2</sup></td> |
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102 | <td>1</td> |
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103 | </tr> |
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104 | <tr class="row-odd"><td>solvent_sld</td> |
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105 | <td>Solvent scattering length density</td> |
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106 | <td>10<sup>-6</sup>â«<sup>-2</sup></td> |
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107 | <td>6.34</td> |
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108 | </tr> |
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109 | </tbody> |
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110 | </table> |
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111 | <p>The returned value is scaled to units of cm<sup>-1</sup>.</p> |
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112 | <p>This model calculates the scattering from a stack of repeating lamellar |
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113 | structures. The stacks of lamellae (infinite in lateral dimension) are |
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114 | treated as a paracrystal to account for the repeating spacing. The repeat |
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115 | distance is further characterized by a Gaussian polydispersity. <strong>This model |
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116 | can be used for large multilamellar vesicles.</strong></p> |
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117 | <p><em>2.1.33.1. Definition</em></p> |
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118 | <p>The scattering intensity <em>I(q)</em> is calculated as</p> |
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119 | <img alt="model/img/image145.jpg" src="model/img/image145.jpg" /> |
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120 | <p>The form factor of the bilayer is approximated as the cross section of an |
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121 | infinite, planar bilayer of thickness <em>t</em></p> |
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122 | <img alt="model/img/image146.jpg" src="model/img/image146.jpg" /> |
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123 | <p>Here, the scale factor is used instead of the mass per area of the |
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124 | bilayer (<em>G</em>). The scale factor is the volume fraction of the material in |
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125 | the bilayer, <em>not</em> the total excluded volume of the paracrystal. |
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126 | <em>Z</em><sub>N</sub><em>(q)</em> describes the interference effects for aggregates |
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127 | consisting of more than one bilayer. The equations used are (3-5) |
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128 | from the Bergstrom reference below.</p> |
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129 | <p>Non-integer numbers of stacks are calculated as a linear combination of |
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130 | the lower and higher values</p> |
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131 | <img alt="model/img/image147.jpg" src="model/img/image147.jpg" /> |
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132 | <p>The 2D scattering intensity is the same as 1D, regardless of the orientation |
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133 | of the <em>q</em> vector which is defined as</p> |
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134 | <div class="math"> |
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135 | \[Q = \sqrt{Q_x^2 + Q_y^2}\]</div> |
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136 | <p>The parameters of the model are <em>Nlayers</em> = no. of layers, and |
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137 | <em>pd_spacing</em> = polydispersity of spacing.</p> |
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138 | <table border="1" class="docutils"> |
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139 | <colgroup> |
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140 | <col width="40%" /> |
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141 | <col width="23%" /> |
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142 | <col width="37%" /> |
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143 | </colgroup> |
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144 | <thead valign="bottom"> |
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145 | <tr class="row-odd"><th class="head">Parameter name</th> |
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146 | <th class="head">Units</th> |
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147 | <th class="head">Default value</th> |
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148 | </tr> |
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149 | </thead> |
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150 | <tbody valign="top"> |
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151 | <tr class="row-even"><td>background</td> |
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152 | <td>cm<sup>-1</sup></td> |
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153 | <td>0</td> |
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154 | </tr> |
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155 | <tr class="row-odd"><td>scale</td> |
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156 | <td>None</td> |
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157 | <td>1</td> |
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158 | </tr> |
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159 | <tr class="row-even"><td>Nlayers</td> |
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160 | <td>None</td> |
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161 | <td>20</td> |
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162 | </tr> |
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163 | <tr class="row-odd"><td>pd_spacing</td> |
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164 | <td>None</td> |
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165 | <td>0.2</td> |
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166 | </tr> |
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167 | <tr class="row-even"><td>sld_layer</td> |
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168 | <td>â«<sup>-2</sup></td> |
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169 | <td>1e-6</td> |
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170 | </tr> |
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171 | <tr class="row-odd"><td>sld_solvent</td> |
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172 | <td>â«<sup>-2</sup></td> |
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173 | <td>6.34e-6</td> |
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174 | </tr> |
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175 | <tr class="row-even"><td>spacing</td> |
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176 | <td>â«</td> |
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177 | <td>250</td> |
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178 | </tr> |
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179 | <tr class="row-odd"><td>thickness</td> |
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180 | <td>â«</td> |
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181 | <td>33</td> |
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182 | </tr> |
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183 | </tbody> |
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184 | </table> |
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185 | <img alt="model/img/image148.jpg" src="model/img/image148.jpg" /> |
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186 | <p><em>Figure. 1D plot using the default values above (w/20000 data point).</em></p> |
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187 | <p>Our model uses the form factor calculations implemented in a C library |
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188 | provided by the NIST Center for Neutron Research (Kline, 2006).</p> |
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189 | <p>REFERENCE</p> |
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190 | <p>M Bergstrom, J S Pedersen, P Schurtenberger, S U Egelhaaf, |
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191 | <em>J. Phys. Chem. B</em>, 103 (1999) 9888-9897</p> |
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192 | </div> |
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193 | |
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194 | |
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195 | </div> |
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196 | <div class="bottomnav"> |
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197 | |
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198 | <p> |
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199 | «  <a href="lamellarFFHG.html">2.1.3.4. Lamellar ffhg</a> |
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200 |   ::   |
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201 | <a class="uplink" href="../index.html">Contents</a> |
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202 |   ::   |
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203 | <a href="../ref/models/shape-paracrystal.html">2.1.4. Paracrystal Functions</a>  Â» |
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204 | </p> |
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205 | |
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