1 | double form_volume(double radius, double thickness, double length); |
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2 | double Iq(double q, double radius, double thickness, double length, double sld, |
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3 | double solvent_sld); |
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4 | double Iqxy(double qx, double qy, double radius, double thickness, double length, double sld, |
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5 | double solvent_sld, double theta, double phi); |
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6 | |
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7 | //#define INVALID(v) (v.radius_core >= v.radius) |
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8 | |
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9 | // From Igor library |
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10 | static double |
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11 | _hollow_cylinder_scaling(double integrand, double delrho, double volume) |
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12 | { |
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13 | return 1.0e-4 * square(volume * delrho) * integrand; |
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14 | } |
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15 | |
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16 | static double |
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17 | _fq(double qab, double qc, |
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18 | double radius, double thickness, double length) |
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19 | { |
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20 | const double lam1 = sas_2J1x_x((radius+thickness)*qab); |
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21 | const double lam2 = sas_2J1x_x(radius*qab); |
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22 | const double gamma_sq = square(radius/(radius+thickness)); |
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23 | //Note: lim_{thickness -> 0} psi = sas_J0(radius*qab) |
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24 | //Note: lim_{radius -> 0} psi = sas_2J1x_x(thickness*qab) |
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25 | const double psi = (lam1 - gamma_sq*lam2)/(1.0 - gamma_sq); //SRK 10/19/00 |
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26 | const double t2 = sas_sinx_x(0.5*length*qc); |
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27 | return psi*t2; |
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28 | } |
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29 | |
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30 | double |
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31 | form_volume(double radius, double thickness, double length) |
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32 | { |
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33 | double v_shell = M_PI*length*(square(radius+thickness) - radius*radius); |
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34 | return v_shell; |
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35 | } |
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36 | |
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37 | |
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38 | double |
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39 | Iq(double q, double radius, double thickness, double length, |
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40 | double sld, double solvent_sld) |
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41 | { |
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42 | const double lower = 0.0; |
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43 | const double upper = 1.0; //limits of numerical integral |
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44 | |
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45 | double summ = 0.0; //initialize intergral |
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46 | for (int i=0;i<76;i++) { |
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47 | const double cos_theta = 0.5*( Gauss76Z[i] * (upper-lower) + lower + upper ); |
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48 | const double sin_theta = sqrt(1.0 - cos_theta*cos_theta); |
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49 | const double form = _fq(q*sin_theta, q*cos_theta, |
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50 | radius, thickness, length); |
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51 | summ += Gauss76Wt[i] * form * form; |
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52 | } |
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53 | |
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54 | const double Aq = 0.5*summ*(upper-lower); |
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55 | const double volume = form_volume(radius, thickness, length); |
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56 | return _hollow_cylinder_scaling(Aq, solvent_sld - sld, volume); |
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57 | } |
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58 | |
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59 | double |
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60 | Iqxy(double qx, double qy, |
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61 | double radius, double thickness, double length, |
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62 | double sld, double solvent_sld, double theta, double phi) |
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63 | { |
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64 | double q, sin_alpha, cos_alpha; |
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65 | ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); |
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66 | const double qab = q*sin_alpha; |
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67 | const double qc = q*cos_alpha; |
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68 | |
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69 | const double form = _fq(qab, qc, radius, thickness, length); |
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70 | |
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71 | const double vol = form_volume(radius, thickness, length); |
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72 | return _hollow_cylinder_scaling(form*form, solvent_sld-sld, vol); |
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73 | } |
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