1 | r""" |
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2 | Definition |
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3 | ---------- |
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4 | |
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5 | This model is a trivial extension of the CoreShell function to a larger number |
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6 | of shells. The scattering length density profile for the default sld values |
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7 | (w/ 4 shells). |
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8 | |
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9 | .. figure:: img/core_multi_shell_sld_default_profile.jpg |
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10 | |
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11 | SLD profile of the core_multi_shell object from the center of sphere out |
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12 | for the default SLDs.* |
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13 | |
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14 | The 2D scattering intensity is the same as *P(q)* above, regardless of the |
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15 | orientation of the *q* vector which is defined as |
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16 | |
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17 | .. math:: |
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18 | |
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19 | q = \sqrt{q_x^2 + q_y^2} |
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20 | |
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21 | .. note:: **Be careful!** The SLDs and scale can be highly correlated. Hold as |
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22 | many of these parameters fixed as possible. |
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23 | |
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24 | .. note:: The outer most radius (= *radius* + *thickness*) is used as the |
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25 | effective radius for *S(Q)* when *P(Q)* \* *S(Q)* is applied. |
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26 | |
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27 | For information about polarised and magnetic scattering, see |
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28 | the :doc:`magnetic help <../sasgui/perspectives/fitting/mag_help>` documentation. |
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29 | |
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30 | Our model uses the form factor calculations implemented in a c-library provided |
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31 | by the NIST Center for Neutron Research (Kline, 2006). |
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32 | |
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33 | References |
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34 | ---------- |
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35 | See the :ref:`core_shell_sphere <core_shell_sphere>` model documentation. |
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36 | |
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37 | L A Feigin and D I Svergun, |
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38 | *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, |
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39 | Plenum Press, New York, 1987. |
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40 | |
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41 | **Author:** NIST IGOR/DANSE **on:** pre 2010 |
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42 | |
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43 | **Last Modified by:** in progress **on:** March 20, 2016 |
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44 | |
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45 | **Last Reviewed by:** in progress **on:** March 20, 2016 |
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46 | """ |
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47 | |
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48 | |
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49 | |
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50 | from __future__ import division |
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51 | |
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52 | import numpy as np |
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53 | from numpy import inf, nan |
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54 | from math import fabs, exp, expm1 |
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55 | |
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56 | name = "core_multi_shell" |
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57 | title = "This model provides the scattering from a spherical core with 1 to 4 \ |
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58 | concentric shell structures. The SLDs of the core and each shell are \ |
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59 | individually specified." |
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60 | |
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61 | description = """\ |
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62 | Form factor for a core muti-shell (up to 4) sphere normalized by the volume. |
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63 | Each shell can have a unique thickness and sld. |
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64 | |
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65 | background:background, |
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66 | rad_core0: radius of sphere(core) |
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67 | thick_shell#:the thickness of the shell# |
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68 | sld_core0: the SLD of the sphere |
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69 | sld_solv: the SLD of the solvent |
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70 | sld_shell: the SLD of the shell# |
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71 | A_shell#: the coefficient in the exponential function |
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72 | |
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73 | |
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74 | scale: 1.0 if data is on absolute scale |
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75 | volfraction: volume fraction of spheres |
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76 | radius: the radius of the core |
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77 | sld: the SLD of the core |
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78 | thick_shelli: the thickness of the i'th shell from the core |
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79 | sld_shelli: the SLD of the i'th shell from the core |
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80 | sld_solvent: the SLD of the solvent |
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81 | background: incoherent background |
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82 | |
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83 | """ |
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84 | |
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85 | category = "shape:sphere" |
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86 | |
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87 | |
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88 | # ["name", "units", default, [lower, upper], "type","description"], |
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89 | parameters = [["volfraction", "", 0.05, [0,1],"", |
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90 | "volume fraction of spheres"], |
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91 | ["sld_core", "1e-6/Ang^2", 1.0, [-inf, inf], "", |
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92 | "Core scattering length density"], |
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93 | ["radius", "Ang", 200., [0, inf], "volume", |
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94 | "Radius of the core"], |
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95 | ["sld_solvent", "1e-6/Ang^2", 6.4, [-inf, inf], "", |
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96 | "Solvent scattering length density"], |
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97 | ["n", "", 1, [0, 10], "volume", |
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98 | "number of shells"], |
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99 | ["sld[n]", "1e-6/Ang^2", 1.7, [-inf, inf], "", |
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100 | "scattering length density of shell k"], |
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101 | ["thickness[n]", "Ang", 40., [0, inf], "volume", |
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102 | "Thickness of shell k"], |
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103 | ] |
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104 | |
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105 | #source = ["lib/sph_j1c.c", "onion.c"] |
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106 | |
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107 | def Iq(q, *args, **kw): |
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108 | return q |
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109 | |
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110 | def Iqxy(qx, *args, **kw): |
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111 | return qx |
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112 | |
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113 | |
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114 | def profile(volfraction, sld_core, radius, sld_solvent, n, sld, thickness): |
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115 | """ |
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116 | SLD profile |
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117 | |
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118 | :return: (r, beta) where r is a list of radius of the transition points\ |
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119 | and beta is a list of the corresponding SLD values. |
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120 | |
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121 | """ |
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122 | # r = [] |
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123 | # beta = [] |
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124 | # # for core at r=0 |
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125 | # r.append(0) |
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126 | # beta.append(self.params['sld_core0']) |
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127 | # # for core at r=rad_core |
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128 | # r.append(self.params['rad_core0']) |
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129 | # beta.append(self.params['sld_core0']) |
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130 | # |
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131 | # # for shells |
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132 | # for n in range(1, self.n_shells+1): |
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133 | # # Left side of each shells |
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134 | # r0 = r[len(r)-1] |
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135 | # r.append(r0) |
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136 | # exec "beta.append(self.params['sld_shell%s'% str(n)])" |
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137 | # |
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138 | # # Right side of each shells |
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139 | # exec "r0 += self.params['thick_shell%s'% str(n)]" |
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140 | # r.append(r0) |
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141 | # exec "beta.append(self.params['sld_shell%s'% str(n)])" |
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142 | # |
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143 | # # for solvent |
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144 | # r0 = r[len(r)-1] |
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145 | # r.append(r0) |
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146 | # beta.append(self.params['sld_solv']) |
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147 | # r_solv = 5*r0/4 |
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148 | # r.append(r_solv) |
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149 | # beta.append(self.params['sld_solv']) |
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150 | # |
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151 | # return r, beta |
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152 | # above is directly from old code -- below is alotered from Woitek's first |
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153 | # cut an the onion. Seems like we should be consistant? |
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154 | |
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155 | total_radius = 1.25*(sum(thickness[:n]) + radius + 1) |
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156 | |
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157 | r = [] |
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158 | beta = [] |
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159 | |
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160 | # add in the core |
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161 | r.append(0) |
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162 | beta.append(sld) |
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163 | r.append(radius) |
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164 | beta.append(sld) |
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165 | |
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166 | # add in the shells |
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167 | for k in range(n): |
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168 | # Left side of each shells |
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169 | r0 = r[-1] |
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170 | r.append(r0) |
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171 | beta.append(sld[k]) |
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172 | r.append(r0 + thickness[k]) |
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173 | beta.append(sld[k]) |
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174 | # add in the solvent |
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175 | r.append(r[-1]) |
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176 | beta.append(sld_solvent) |
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177 | r.append(total_radius) |
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178 | beta.append(sld_solvent) |
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179 | |
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180 | return np.asarray(r), np.asarray(beta) |
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181 | |
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182 | def ER(radius, n, thickness): |
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183 | n = n[0] # n cannot be polydisperse |
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184 | return np.sum(thickness[:n], axis=0) + radius |
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185 | |
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186 | def VR(radius, n, thick_shell): |
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187 | return 1.0, 1.0 |
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188 | |
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189 | demo = dict(volfraction = 1.0, |
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190 | sld = 6.4, |
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191 | radius = 60, |
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192 | sld_solvent = 6.4, |
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193 | n = 1, |
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194 | sld_shell = [2.0], |
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195 | thick_shell = [10]) |
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