# pringle¶

The Pringle model provides the form factor, \(P(q)\), for a ‘pringle’ or ‘saddle-shaped’ disc that is bent in two directions.

Parameter |
Description |
Units |
Default value |
---|---|---|---|

scale |
Scale factor or Volume fraction |
None |
1 |

background |
Source background |
cm |
0.001 |

radius |
Pringle radius |
Å |
60 |

thickness |
Thickness of pringle |
Å |
10 |

alpha |
Curvature parameter alpha |
None |
0.001 |

beta |
Curvature paramter beta |
None |
0.02 |

sld |
Pringle sld |
10 |
1 |

sld_solvent |
Solvent sld |
10 |
6.3 |

The returned value is scaled to units of cm^{-1} sr^{-1}, absolute scale.

**Definition**

The form factor for this bent disc is essentially that of a hyperbolic paraboloid and calculated as

where

and \(\Delta\rho\text{ is }\rho_{pringle}-\rho_{solvent}\), \(V\) is the volume of
the disc, \(\psi\) is the angle between the normal to the disc and the q vector,
\(d\) and \(R\) are the “pringle” thickness and radius respectively, \(\alpha\) and
\(\beta\) are the two curvature parameters, and \(J_n\) is the n^{th} order
Bessel function of the first kind.

**Source**

`pringle.py`

\(\ \star\ \) `pringle.c`

\(\ \star\ \) `gauss76.c`

\(\ \star\ \) `sas_JN.c`

\(\ \star\ \) `sas_J1.c`

\(\ \star\ \) `sas_J0.c`

\(\ \star\ \) `polevl.c`

**Reference**

Karen Edler, Universtiy of Bath, Private Communication. 2012. Derivation by Stefan Alexandru Rautu.

Onsager,

*Ann. New York Acad. Sci.*, 51 (1949) 627-659

**Authorship and Verification**

**Author:**Andrew Jackson**Date:**2008**Last Modified by:**Wojciech Wpotrzebowski**Date:**March 20, 2016**Last Reviewed by:**Andrew Jackson**Date:**September 26, 2016