Calculation of small-angle scattering intensities from a model of subunits ^{
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Name of a data file for comparison (optional):

Optional:

The name of an experimental data file may be uploaded here.
Format: (q, I(q)) or (q, I(q), error). Textlines in the data file are ignored.
The result of the calculation below will be rescaled to match the data (using the first data points).
If no data file is entered the calculated intensity will be rescaled to 1.

Result is shown in a new window.

Subunits:

The model of the scatterer can be composed of several subunits to be defined below.
Overlapping subvolumes are automatically subtracted as described in the reference, unless the letter X is entered in the following box:
A total of 15000 points are used in this webversion of the program.
For a more detailed calculation the source code can be downloaded.
To start the calculation press "enter" on the keyboard when the cursor is in an input field
or press the "Submit"-button above.

Enter:
S (or s) for sphere.
E (or e) for ellipse (3 axis).
C (or c) for cylinder.
H (or h) for shell.

Enter:
For sphere: radius r (leave the two last boxes empty).
For ellipsoid: half-axis (a,b,c).
For cylinder: r,h (leave the last box empty). Height along z-axis.
For shell: r_outer, r_inner (leave the last box empty).
All have center of mass in (0,0,0).

Enter:
Center of (scattering) mass as (x,y,z).
If left empty (0,0,0) will be used.

Enter:
Rotation angles (psi, theta) in degrees where
psi is the rotation around the x-axis (first) and
theta is the rotation around the z-axis (second).
Plots will show the shape of the scatterer.
If left empty (0,0) will be used.

Enter:
The value for the scattering length (negative values are allowed).
The errorbars shown in I(q) correspond to uniform scattering density.
If left empty a scattering length of 1.0 will be used.
NB The calculated I(0) will be rescaled to 1 or to match a data file.

Enter volume fraction eta (default 0)
Using the Percus Yevick formula.

Enter a relative polydispersity (e.g. 0.1 - default 0)
Using a Gaussian distribution (number weighted).
NB The distance distribution function and the three figures of the shape
shown at the results page correspond to the single scatterer only.

Enter parameters for noise (will show noisy data at the results page):
No of data points in file with noisy data (default 50). Qmin and Qmax in file with noisy data (default 0 and some sensible large value respectively...).
Gaussian noise sd(q)=a*I(q)+b, where a is the relative noise and b is the absolute noise
(default 0.01 and 0.001 respectively). Smearing. Enter value for constant c as given by the expression (default c=0)
I_smear(q) = integrate P(t)*I(sqrt(q**2 + t**2)) dt with the
primary beam length profile: P(t) = c/sqrt(pi) * exp(-c**2*t**2).

The chi-square for the noisy data is written at the end of the file containing the noisy data.
The chi-square is calculated in the conventional way by comparison with the simulated intensity.

NB: The noisy data file is the default input for the indirect transformation in BayesApp (just press "submit" at www.BayesApp.org).