1 | static double |
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2 | shell_volume(double radius, double thickness) |
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3 | { |
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4 | return M_4PI_3 * (cube(radius+thickness) - cube(radius)); |
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5 | } |
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6 | |
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7 | static double |
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8 | form_volume(double radius, double thickness) |
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9 | { |
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10 | return M_4PI_3 * cube(radius+thickness); |
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11 | } |
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12 | |
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13 | |
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14 | static double |
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15 | radius_effective(int mode, double radius, double thickness) |
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16 | { |
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17 | // case 1: outer radius |
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18 | return radius + thickness; |
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19 | } |
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20 | |
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21 | static void |
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22 | Fq(double q, |
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23 | double *F1, |
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24 | double *F2, |
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25 | double sld, |
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26 | double sld_solvent, |
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27 | double volfraction, |
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28 | double radius, |
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29 | double thickness) |
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30 | |
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31 | /* |
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32 | scattering from a unilamellar vesicle. |
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33 | same functional form as the core-shell sphere, but more intuitive for |
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34 | a vesicle |
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35 | */ |
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36 | |
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37 | { |
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38 | double vol,contrast,f; |
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39 | |
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40 | // core first, then add in shell |
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41 | contrast = sld_solvent-sld; |
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42 | vol = M_4PI_3*cube(radius); |
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43 | f = vol * sas_3j1x_x(q*radius) * contrast; |
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44 | |
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45 | //now the shell. No volume normalization as this is done by the caller |
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46 | contrast = sld-sld_solvent; |
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47 | vol = M_4PI_3*cube(radius+thickness); |
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48 | f += vol * sas_3j1x_x(q*(radius+thickness)) * contrast; |
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49 | |
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50 | //rescale to [cm-1]. |
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51 | // With volume fraction as part of the model in the dilute limit need |
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52 | // to return F2 = Vf <fq^2>. In order for beta approx. to work correctly |
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53 | // need F1^2/F2 equal to <fq>^2 / <fq^2>. By returning F1 = sqrt(Vf) <fq> |
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54 | // and F2 = Vf <fq^2> both conditions are satisfied. |
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55 | // Since Vf is the volume fraction of vesicles of all radii, it is |
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56 | // constant when averaging F1 and F2 over radii and so pops out of the |
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57 | // polydispersity loop, so it is safe to apply it inside the model |
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58 | // (albeit conceptually ugly). |
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59 | *F1 = 1e-2 * sqrt(volfraction) * f; |
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60 | *F2 = 1.0e-4 * volfraction * f * f; |
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61 | } |
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