-                      r38d4102
+                      r77cfcf0
 - CoreShellCylinderModel_
 - EllipticalCylinderModel_
 - FlexibleCylinderModel
 - FlexCylEllipXModel
 - CoreShellBicelleModel
 - BarBellModel
 - StackedDisksModel
 - PringleModel
+- FlexibleCylinderModel_
+- FlexCylEllipXModel_
+- CoreShellBicelleModel_
+- BarBellModel_
+- StackedDisksModel_
+- PringleModel_
 Ellipsoid-based
 …
 - EllipsoidModel
 - CoreShellEllipsoidModel
+- CoreShellEllipsoidXTModel
 - TriaxialEllipsoidModel
 …
 for a diagram and documentation.
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 Be careful! The SLDs and scale can be highly correlated. Hold as many of these parameters fixed as possible.
 …
 *2.1.16.1. Definition*
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 The Capped Cylinder geometry is defined as
 …
 **2.1.21 CoreShellBicelleModel**
 This model provides the form factor for a circular cylinder with a
+core-shell scattering length density profile. The form factor is
+normalized by the particle volume. This model is a more general case
+of core-shell cylinder model (seeabove and reference below) in that
+the parameters of the shell are separated into a face-shell and a rim-
+shell so that users can set different values of the thicknesses and
+slds.
+The returned value is scaled to units of |cm^-1| and the parameters of
+the core-shell cylinder model are the following:
+This model provides the form factor for a circular cylinder with a core-shell scattering length density profile. The
+form factor is normalized by the particle volume.
+This model is a more general case of core-shell cylinder model (see above and reference below) in that the parameters
+of the shell are separated into a face-shell and a rim-shell so that users can set different values of the thicknesses
+and SLDs.
+.. image:: img/image240.PNG
+*(Graphic from DOI: 10.1039/C0NP00002G)*
+The returned value is scaled to units of |cm^-1| and the parameters of the CoreShellBicelleModel are the following
 ==============  ========  =============
 …
 ==============  ========  =============
+The output of the 1D scattering intensity function for randomly
+oriented cylinders is then given by the equation above.
+The *axis_theta* and axis *_phi* parameters are not used for the 1D
+output. Our implementation of the scattering kernel and the 1D
+scattering intensity use the c-library from NIST.
+The output of the 1D scattering intensity function for randomly oriented cylinders is then given by the equation above.
+The *axis_theta* and *axis_phi* parameters are not used for the 1D output. Our implementation of the scattering kernel
+and the 1D scattering intensity use the c-library from NIST.
+.. image:: img/cscylbicelle_pic.jpg
 *Figure. 1D plot using the default values (w/200 data point).*
+Figure. Definition of the angles for the oriented Core-Shell Cylinder
+Bicelle Model.
+Figure. Examples of the angles for oriented pp against the detector
+plane.
+.. image:: img/image061.JPG
+*Figure. Definition of the angles for the oriented CoreShellBicelleModel.*
+.. image:: img/image062.JPG
+*Figure. Examples of the angles for oriented pp against the detector plane.*
 REFERENCE
+Feigin, L. A, and D. I. Svergun, "Structure Analysis by Small-Angle
+X-Ray and Neutron Scattering", Plenum Press, New York, (1987).
+L. A. Feigin and D. I. Svergun, *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, Plenum Press,
+New York, (1987)
 …
 **2.1.22. BarBellModel**
+Calculates the scattering from a barbell-shaped cylinder (This model
+simply becomes the DumBellModel when the length of the cylinder, L, is
+set to zero). That is, a sphereocylinder with spherical end caps that
+have a radius larger than that of the cylinder and the center of the
+end cap radius lies outside of the cylinder All dimensions of the
+barbell are considered to be monodisperse. See the diagram for the
+details of the geometry and restrictions on parameter values.
+*1.1. Definition*
+The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+Calculates the scattering from a barbell-shaped cylinder (This model simply becomes the DumBellModel when the length of
+the cylinder, *L*, is set to zero). That is, a sphereocylinder with spherical end caps that have a radius larger than
+that of the cylinder and the center of the end cap radius lies outside of the cylinder. All dimensions of the BarBell
+are considered to be monodisperse. See the diagram for the details of the geometry and restrictions on parameter values.
+*2.1.22.1. Definition*
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 The barbell geometry is defined as
+r is the radius of the cylinder. All other parameters are as defined
+in the diagram. Since the end cap radius R >= r and by definition for
+this geometry h > 0, h is then defined by r and R as
+h = sqrt(R^2 - r^2).
+The scattering intensity I(q) is calculated as:
+where the amplitude A(q) is given as:
+The < > brackets denote an average of the structure over all
+orientations. <A^2(q)> is then the form factor, P(q). The scale factor
+is equivalent to the volume fraction of cylinders, each of volume, V.
+Contrast is the difference of scattering length densities of the
+cylinder and the surrounding solvent.
+The volume of the barbell is:
+and its radius of gyration:
+The necessary conditions of R >= r is not enforced in the model. It is
+up to you to restrict this during analysis.
+REFERENCES
+H. Kaya, J. Appl. Cryst. (2004) 37, 223-230.
+H. Kaya and N-R deSouza, J. Appl. Cryst. (2004) 37, 508-509. (addenda
+and errata)
+TEST DATASET
+This example dataset is produced by running the Macro PlotBarbell(),
+using 200 data points, *qmin* = 0.001 -1, *qmax* = 0.7 -1 and the above
+default values.
+.. image:: img/image105.JPG
+where *r* is the radius of the cylinder. All other parameters are as defined in the diagram.
+Since the end cap radius
+*R* >= *r* and by definition for this geometry *h* < 0, *h* is then defined by *r* and *R* as
+*h* = -1 \* sqrt(*R*\ :sup:`2` - *r*\ :sup:`2`)
+The scattered intensity *I(q)* is calculated as
+.. image:: img/image106.PNG
+where the amplitude *A(q)* is given as
+.. image:: img/image107.PNG
+The < > brackets denote an average of the structure over all orientations. <*A* :sup:`2`\ *(q)*> is then the form
+factor, *P(q)*. The scale factor is equivalent to the volume fraction of cylinders, each of volume, *V*. Contrast is
+the difference of scattering length densities of the cylinder and the surrounding solvent.
+The volume of the barbell is
+.. image:: img/image108.JPG
+and its radius of gyration is
+.. image:: img/image109.JPG
+**The requirement that** *R* >= *r* **is not enforced in the model!** It is up to you to restrict this during analysis.
+This example dataset is produced by running the Macro PlotBarbell(), using 200 data points, *qmin* = 0.001 |Ang^-1|,
+*qmax* = 0.7 |Ang^-1| and the following default values
 ==============  ========  =============
 …
 ==============  ========  =============
+.. image:: img/image110.JPG
 *Figure. 1D plot using the default values (w/256 data point).*
+For 2D data: The 2D scattering intensity is calculated similar to the
+D cylinder model. At the theta = 45 deg and phi =0 deg with default
+values for other parameters,
+For 2D data: The 2D scattering intensity is calculated similar to the 2D cylinder model. For example, for
+|theta| = 45 deg and |phi| = 0 deg with default values for other parameters
+.. image:: img/image111.JPG
 *Figure. 2D plot (w/(256X265) data points).*
+Figure. Examples of the angles for oriented pp against the detector
+plane.
+.. image:: img/image061.JPG
+*Figure. Examples of the angles for oriented pp against the detector plane.*
+.. image:: img/image062.JPG
 Figure. Definition of the angles for oriented 2D barbells.
+REFERENCE
+H. Kaya, *J. Appl. Cryst.*, 37 (2004) 37 223-230
+H. Kaya and N-R deSouza, *J. Appl. Cryst.*, 37 (2004) 508-509 (addenda and errata)
 …
 **2.1.23. StackedDisksModel**
+This model provides the form factor, *P(q)*, for stacked discs
+(tactoids) with a core/layer structure where the form factor is
+normalized by the volume of the cylinder. Assuming the next neighbor
+distance (d-spacing) in a stack of parallel discs obeys a Gaussian
+distribution, a structure factor S(q) proposed by Kratky and Porod in
+is used in this function. Note that the resolution smearing
+calculation uses 76 Gauss quadrature points to properly smear the
+model since the function is HIGHLY oscillatory, especially around the
+q-values that correspond to the repeat distance of the layers.
+The 2D scattering intensity is the same as 1D, regardless of the
+orientation of the *q* vector which is defined as .
+The returned value is in units of [|cm^-1| |sr^-1|, on absolute scale.
+The scattering intensity I(q) is:
+where the contrast,
+N is the number of discs per unit volume, ais the angle between the
+axis of the disc and q, and Vt and Vc are the total volume and the
+core volume of a single disc, respectively.
+where d = thickness of the layer (layer_thick), 2h= core thickness
+(core_thick), and R = radius of the disc (radius).
+where n = the total number of the disc stacked (n_stacking), D=the
+next neighbor center to cent distance (d-spacing), and sD= the
+Gaussian standard deviation of the d-spacing (sigma_d).
+To provide easy access to the orientation of the stackeddisks, we
+define the axis of the cylinder using two angles and . Similarly to
+the case of the cylinder, those angles are defined on Figure 2 of
+CylinderModel.
+For P*S: The 2nd virial coefficient of the solid cylinder is calculate
+based on the (radius) and length = n_stacking*(core_thick
++2*layer_thick) values, and used as the effective radius toward S(Q)
+when P(Q)*S(Q) is applied.
+This model provides the form factor, *P(q)*, for stacked discs (tactoids) with a core/layer structure where the form
+factor is normalized by the volume of the cylinder. Assuming the next neighbor distance (d-spacing) in a stack of
+parallel discs obeys a Gaussian distribution, a structure factor *S(q)* proposed by Kratky and Porod in 1949 is used
+in this function.
+Note that the resolution smearing calculation uses 76 Gauss quadrature points to properly smear the model since the
+function is HIGHLY oscillatory, especially around the *q*-values that correspond to the repeat distance of the layers.
+The 2D scattering intensity is the same as 1D, regardless of the orientation of the *q* vector which is defined as
+.. image:: img/image008.PNG
+The returned value is in units of |cm^-1| |sr^-1|, on absolute scale.
+*2.1.23.1 Definition*
+.. image:: img/image079.GIF
+The scattering intensity I(q) is
+.. image:: img/image081.PNG
+where the contrast
+.. image:: img/image082.PNG
+and *N* is the number of discs per unit volume, |alpha| is the angle between the axis of the disc and *q*, and *Vt*
+and *Vc* are the total volume and the core volume of a single disc, respectively.
+.. image:: img/image083.PNG
+where *d* = thickness of the layer (*layer_thick*), 2\ *h* = core thickness (*core_thick*), and *R* = radius of the
+disc (*radius*).
+.. image:: img/image084.PNG
+where *n* = the total number of the disc stacked (*n_stacking*), *D* = the next neighbor center-to-center distance
+(*d-spacing*), and |sigma|\ D= the Gaussian standard deviation of the d-spacing (*sigma_d*).
+To provide easy access to the orientation of the stacked disks, we define the axis of the cylinder using two angles
+|theta| and |phi|. These angles are defined on Figure 2 of CylinderModel.
+NB: The 2nd virial coefficient of the cylinder is calculated based on the *radius* and *length* = *n_stacking* \*
+(*core_thick* + 2 \* *layer_thick*) values, and used as the effective radius for *S(Q)* when *P(Q)* \* *S(Q)* is applied.
 ==============  ========  =============
 …
 ==============  ========  =============
+.. image:: img/image085.JPG
 *Figure. 1D plot using the default values (w/1000 data point).*
+Figure. Examples of the angles for oriented stackeddisks against the
+detector plane.
+Figure. Examples of the angles for oriented pp against the detector
+plane.
+Our model uses the form factor calculations implemented in a c-library
+provided by the NIST Center for Neutron Research (Kline, 2006):
+.. image:: img/image086.JPG
+*Figure. Examples of the angles for oriented stackeddisks against the detector plane.*
+.. image:: img/image062.JPG
+*Figure. Examples of the angles for oriented pp against the detector plane.*
+Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research
+(Kline, 2006)
 REFERENCE
+Guinier, A. and Fournet, G., "Small-Angle Scattering of X-Rays", John
+Wiley and Sons, New York, 1955.
+Kratky, O. and Porod, G., J. Colloid Science, 4, 35, 1949.
+Higgins, J.S. and Benoit, H.C., "Polymers and Neutron Scattering",
+Clarendon, Oxford, 1994.
+A. Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, 1955
+O. Kratky and G. Porod, *J. Colloid Science*, 4, (1949) 35
+J. S. Higgins and H. C. Benoit, *Polymers and Neutron Scattering*, Clarendon, Oxford, 1994
 …
 **2.1.24. PringleModel**
+This model provides the form factor, *P(q)*, for a 'pringle' or
+'saddle-shaped' object (a hyperbolic paraboloid).
+This model provides the form factor, *P(q)*, for a 'pringle' or 'saddle-shaped' object (a hyperbolic paraboloid).
+.. image:: img/image241.PNG
+*(Graphic from Matt Henderson, matt@matthen.com)*
 The returned value is in units of |cm^-1|, on absolute scale.
 The form factor calculated is:
+The form factor calculated is
+.. image:: img/pringle_eqn_1.jpg
 where
+The parameters of the model and a plot comparing the pringle model
+with the equivalent cylinder are shown below.
+.. image:: img/pringle_eqn_2.jpg
+The parameters of the model and a plot comparing the pringle model with the equivalent cylinder are shown below.
 ==============  ========  =============
 …
 ==============  ========  =============
+.. image:: img/pringle-vs-cylinder.png
 *Figure. 1D plot using the default values (w/150 data point).*
 REFERENCE
 S. Alexandru Rautu, Private Communication.
 …
+.. _CoreShellEllipsoidXTModel:
+**2.1.27. CoreShellEllipsoidXTModel**
+An alternative version of *P(q)* for the core-shell ellipsoid (see CoreShellEllipsoidModel), having as parameters the
+core axial ratio *X* and a shell thickness, which are more often what we would like to determine.
+This model is also better behaved when polydispersity is applied than the four independent radii in
+CoreShellEllipsoidModel.
+*2.1.27.1 Definition*
+.. image:: img/image125.gif
+The geometric parameters of this model are
+  *equat_core* = equatorial core radius = *Rminor_core*
+  *X_core* = *polar_core* / *equat_core* = *Rmajor_core* / *Rminor_core*
+  *T_shell* = *equat_outer* - *equat_core* = *Rminor_outer* - *Rminor_core*
+  *XpolarShell* = *Tpolar_shell* / *T_shell* = (*Rmajor_outer* - *Rmajor_core*)/(*Rminor_outer* - *Rminor_core*)
+In terms of the original radii
+  *polar_core* = *equat_core* \* *X_core*
+  *equat_shell* = *equat_core* + *T_shell*
+  *polar_shell* = *equat_core* \* *X_core* + *T_shell* \* *XpolarShell*
+  (where we note that "shell" perhaps confusingly, relates to the outer radius)
+When *X_core* < 1 the core is oblate; when *X_core* > 1  it is prolate. *X_core* = 1 is a spherical core.
+For a fixed shell thickness *XpolarShell* = 1, to scale the shell thickness pro-rata with the radius
+*XpolarShell* = *X_core*.
+When including an *S(q)*, the radius in *S(q)* is calculated to be that of a sphere with the same 2nd virial
+coefficient of the **outer** surface of the ellipsoid. This may have some undesirable effects if the aspect ratio of
+the ellipsoid is large (ie, if *X* << 1 or *X* >> 1), when the *S(q)* - which assumes spheres - will not in any case
+be valid.
+If SANS data are in absolute units, and the SLDs are correct, then *scale* should be the total volume fraction of the
+"outer particle". When *S(q)* is introduced this moves to the *S(q)* volume fraction, and *scale* should then be 1.0,
+or contain some other units conversion factor (for example, if you have SAXS data).
+==============  ========  =============
+Parameter name  Units     Default value
+==============  ========  =============
+background      |cm^-1|   0.001
+equat_core      |Ang|     20
+scale           None      0.05
+sld_core        |Ang^-2|  2.0e-6
+sld_shell       |Ang^-2|  1.0e-6
+sld_solv        |Ang^-2|  6.3e-6
+T_shell         |Ang|     30
+X_core          None      3.0
+XpolarShell     None      1.0
+==============  ========  =============
+REFERENCE
+R. K. Heenan, Private communication
 .. _TriaxialEllipsoidalModel:
 **2.1.27. TriaxialEllipsoidModel***
+**2.1.28. TriaxialEllipsoidModel**
 This model provides the form factor, *P(q)*, for an ellipsoid (below)
 …
 .. _LamellarModel:
 **2.1.28. LamellarModel**
+**2.1.29. LamellarModel**
 This model provides the scattering intensity, I( *q*), for a lyotropic
 …
 .. _LamellarFFHGModel:
 **2.1.29. LamellarFFHGModel**
+**2.1.30. LamellarFFHGModel**
 This model provides the scattering intensity, I( *q*), for a lyotropic
 …
 .. _LamellarPSModel:
 **2.1.30. LamellarPSModel**
+**2.1.31. LamellarPSModel**
 This model provides the scattering intensity ( *form factor* \*
 …
 .. _LamellarPSHGModel:
 **2.1.31. LamellarPSHGModel**
+**2.1.32. LamellarPSHGModel**
 This model provides the scattering intensity ( *form factor* \*
 …
 .. _LamellarPCrystalModel:
 **2.1.32. LamellarPCrystalModel**
+**2.1.33. LamellarPCrystalModel**
 Lamella ParaCrystal Model: Calculates the scattering from a stack of
 …
 .. _SCCrystalModel:
 **2.1.33. SCCrystalModel**
+**2.1.34. SCCrystalModel**
 Calculates the scattering from a simple cubic lattice with
 …
 characterized by a Gaussian distribution.
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 The scattering intensity I(q) is calculated as
 …
 .. _FCCrystalModel:
 **2.1.34. FCCrystalModel**
+**2.1.35. FCCrystalModel**
 Calculates the scattering from a face-centered cubic lattice with
 …
 characterized by a Gaussian distribution.
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 The scattering intensity I(q) is calculated as:
 …
 .. _BCCrystalModel:
 **2.1.35. BCCrystalModel**
+**2.1.36. BCCrystalModel**
 Calculates the scattering from a body-centered cubic lattice with
 …
 Paracrystalline distortion is assumed to be isotropic and
 characterized by a Gaussian distribution.The returned value is scaled
 to units of [|cm^-1|\ |sr^-1|, absolute scale.
+to units of |cm^-1|\ |sr^-1|, absolute scale.
 The scattering intensity I(q) is calculated as:
 …
 .. _ParallelepipedModel:
 **2.1.36. ParallelepipedModel**
+**2.1.37. ParallelepipedModel**
 This model provides the form factor, *P(q)*, for a rectangular
 …
 .. _CSParallelepipedModel:
 **2.1.37. CSParallelepipedModel**
+**2.1.38. CSParallelepipedModel**
 Calculates the form factor for a rectangular solid with a core-shell
 …
 This example dataset is produced by running the Macro
 Plot_CSParallelepiped(), using 100 data points, *qmin* = 0.001 -1, *qmax*
+Plot_CSParallelepiped(), using 100 data points, *qmin* = 0.001 |Ang^-1|, *qmax*
 = 0.7 -1 and the below default values.
 …
 structures).
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 The scattering intensity I(q) is calculated by:
 …
 a low-Q signal and a high-Q signal
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 The scattering intensity I(q) is calculated by:
 …
 provided.
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 See each of these individual models for full documentation.
 …
 structures.
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 The scattering intensity I(q) is calculated as (eqn 5 from the
 …
 The returned value is P(Q) as written in equation (1), plus the
 incoherent background term. The result is in the units of [|cm^-1|\ |sr^-1|,
+incoherent background term. The result is in the units of |cm^-1|\ |sr^-1|,
 absolute scale.
 …
 molecular weight distribution.
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 …
 This example dataset is produced by running the Poly_GaussCoil, using
 data points, *qmin* = 0.001 -1, *qmax* = 0.7 -1 and the default values
+data points, *qmin* = 0.001 |Ang^-1|, *qmax* = 0.7 -1 and the default values
 below.
 …
 Calculates the scattering from polymers with excluded volume effects.
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 The returned value is P(Q) as written in equation (2), plus the
 incoherent background term. The result is in the units of [|cm^-1|\ |sr^-1|,
+incoherent background term. The result is in the units of |cm^-1|\ |sr^-1|,
 absolute scale.
 …
 a two Lorentzian functions.
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 The scattering intensity I(q) is calculated by:
 …
 two power laws.
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 …
 *3.25. UnifiedPower(Law and)Rg(Model)*
 The returned value is scaled to units of [|cm^-1|\ |sr^-1|, absolute scale.
+The returned value is scaled to units of |cm^-1|\ |sr^-1|, absolute scale.
 Note that the level 0 is an extra function that is the inverse

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