Changeset fa8011eb in sasmodels for sasmodels/models/elliptical_cylinder.py
- Timestamp:
- Feb 24, 2016 3:51:27 PM (8 years ago)
- Branches:
- master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
- Children:
- d51ea74
- Parents:
- c8dcbdf
- File:
-
- 1 edited
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sasmodels/models/elliptical_cylinder.py
rb7c2fce rfa8011eb 10 10 to any of the orientation angles, and also for the minor radius and the ratio of the ellipse radii. 11 11 12 .. image:: img/elliptical_cylinder_geometry.gif12 .. figure:: img/elliptical_cylinder_geometry.gif 13 13 14 * Figure.* *a* = *r_minor* and |nu|\ :sub:`n` = $r_ratio$ (i.e., $r_major / r_minor$).14 *a* = *r_minor* and |nu|\ :sub:`n` = $r_ratio$ (i.e., $r_major / r_minor$). 15 15 16 16 The function calculated is 17 17 18 18 .. math:: 19 19 20 I(\mathbf{q})=\frac{1}{V_{cyl}}\int{d\psi}\int{d\phi}\int{p(\theta,\phi,\psi)F^2(\mathbf{q},\alpha,\psi)\sin(\theta)d\theta} 20 21 … … 22 23 23 24 .. math:: 25 24 26 F(\mathbf{q},\alpha,\psi)=2\frac{J_1(a)\sin(b)}{ab} 25 27 \\ … … 40 42 P(q) = scale <F^2> / V 41 43 42 The returned value is scaled to units of |cm^-1|.43 44 44 To provide easy access to the orientation of the elliptical cylinder, we define the axis of the cylinder using two 45 45 angles |theta|, |phi| and |bigpsi|. As for the case of the cylinder, the angles |theta| and |phi| are defined on … … 49 49 All angle parameters are valid and given only for 2D calculation; ie, an oriented system. 50 50 51 .. image:: img/elliptical_cylinder_geometry_2d.jpg51 .. figure:: img/elliptical_cylinder_geometry_2d.jpg 52 52 53 *Figure. Definition of angles for 2D*53 Definition of angles for 2D 54 54 55 .. image:: img/core_shell_bicelle_fig2.jpg55 .. figure:: img/core_shell_bicelle_fig2.jpg 56 56 57 *Figure. Examples of the angles for oriented elliptical cylinders against the detector plane.*57 Examples of the angles for oriented elliptical cylinders against the detector plane. 58 58 59 59 NB: The 2nd virial coefficient of the cylinder is calculated based on the averaged radius (= sqrt(*r_minor*\ :sup:`2` \* *r_ratio*)) … … 61 61 62 62 63 .. image:: img/elliptical_cylinder_comparison_1d.jpg63 .. figure:: img/elliptical_cylinder_comparison_1d.jpg 64 64 65 *Figure. 1D plot using the default values (w/1000 data point).*65 1D plot using the default values (w/1000 data point). 66 66 67 67 Validation … … 73 73 and 76 degrees are taken for the angles of |theta|, |phi|, and |bigpsi| respectively). 74 74 75 .. image:: img/elliptical_cylinder_validation_1d.gif75 .. figure:: img/elliptical_cylinder_validation_1d.gif 76 76 77 *Figure. Comparison between 1D and averaged 2D.*77 Comparison between 1D and averaged 2D. 78 78 79 79 In the 2D average, more binning in the angle |phi| is necessary to get the proper result. The following figure shows 80 80 the results of the averaging by varying the number of angular bins. 81 81 82 .. image:: img/elliptical_cylinder_averaging.gif82 .. figure:: img/elliptical_cylinder_averaging.gif 83 83 84 *Figure. The intensities averaged from 2D over different numbers of bins and angles.*84 The intensities averaged from 2D over different numbers of bins and angles. 85 85 86 86 Reference
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