Changeset fcb33e4 in sasmodels for sasmodels/models/barbell.py
- Timestamp:
- Jan 4, 2017 6:09:53 AM (7 years ago)
- Branches:
- master, core_shell_microgels, costrafo411, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
- Children:
- 473a9f1, b7e8b94
- Parents:
- 64614ad
- File:
-
- 1 edited
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sasmodels/models/barbell.py
r0d6e865 rfcb33e4 20 20 .. math:: 21 21 22 I(q) = \frac{\Delta \rho^2}{V} \left<A^2(q )\right>22 I(q) = \frac{\Delta \rho^2}{V} \left<A^2(q,\alpha).sin(\alpha)\right> 23 23 24 where the amplitude $A(q )$ is given as24 where the amplitude $A(q,\alpha)$ with the rod axis at angle $\alpha$ to $q$ is given as 25 25 26 26 .. math:: 27 27 28 28 A(q) =&\ \pi r^2L 29 \frac{\sin\left(\tfrac12 qL\cos\ theta\right)}30 {\tfrac12 qL\cos\ theta}31 \frac{2 J_1(qr\sin\ theta)}{qr\sin\theta} \\29 \frac{\sin\left(\tfrac12 qL\cos\alpha\right)} 30 {\tfrac12 qL\cos\alpha} 31 \frac{2 J_1(qr\sin\alpha)}{qr\sin\alpha} \\ 32 32 &\ + 4 \pi R^3 \int_{-h/R}^1 dt 33 \cos\left[ q\cos\ theta33 \cos\left[ q\cos\alpha 34 34 \left(Rt + h + {\tfrac12} L\right)\right] 35 35 \times (1-t^2) 36 \frac{J_1\left[qR\sin\ theta \left(1-t^2\right)^{1/2}\right]}37 {qR\sin\ theta \left(1-t^2\right)^{1/2}}36 \frac{J_1\left[qR\sin\alpha \left(1-t^2\right)^{1/2}\right]} 37 {qR\sin\alpha \left(1-t^2\right)^{1/2}} 38 38 39 39 The $\left<\ldots\right>$ brackets denote an average of the structure over 40 all orientations. $\left<A^2(q )\right>$ is then the form factor, $P(q)$.40 all orientations. $\left<A^2(q,\alpha)\right>$ is then the form factor, $P(q)$. 41 41 The scale factor is equivalent to the volume fraction of cylinders, each of 42 42 volume, $V$. Contrast $\Delta\rho$ is the difference of scattering length … … 85 85 * **Author:** NIST IGOR/DANSE **Date:** pre 2010 86 86 * **Last Modified by:** Paul Butler **Date:** March 20, 2016 87 * **Last Reviewed by:** Paul Butler **Date:** March 20, 201687 * **Last Reviewed by:** Richard Heenan **Date:** January 4, 2017 88 88 """ 89 89 from numpy import inf
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