RDFCylinder normalisation is only valid for small ``bin_width``
name: RDFCylinder normalisation
about: normalisation is only valid for small ``bin_width``
At present, the normalisation done is incorrect g(r)= mean(dn/dV) where dn is the number of g2 around each element in g1 at a distance r subject to constraints. And dV is the volume explored around each element in g1, i.e., 4\pi r^2 dr for the case when there is no restriction.
Since in cylinder RDF, dV changes with the location of the element in g1, we normalise the RDF with \int dV dNg1, which effectively disintegrates mean(dn/dV) to \sum (dn)/ \sum (dV).
Solution We have to weight the histogram with the dV for each element. A 2D interpolation in dV(r,R) can be calculated where R is the radial position of the element in g1 in cylindrical coordinates. This can be used to calculate the weighing factors for the histogram in each frame.
Edited by Adyant Agrawal