INSPHERE
This is part of the volumes module

This quantity can be used to calculate functions of the distribution of collective variables for the atoms that lie in a particular, user-specified part of of the cell.

Each of the base quantities calculated by a multicolvar can can be assigned to a particular point in three dimensional space. For example, if we have the coordination numbers for all the atoms in the system each coordination number can be assumed to lie on the position of the central atom. Because each base quantity can be assigned to a particular point in space we can calculate functions of the distribution of base quantities in a particular part of the box by using:

\[ \overline{s}_{\tau} = \frac{ \sum_i f(s_i) \sigma(r) }{ \sum_i \sigma(r) } \]

where the sum is over the collective variables, \(s_i\), each of which can be thought to be at \( (x_i,y_i,z_i)\). The function \(\sigma\) is a switchingfunction that acts on the distance between the point at which the collective is located \((x_i,y_i,z_i)\) and the position of the atom that was specified using the ORIGIN keyword. In other words:

\[ r = sqrt{ ( x_i - x_0)^2 + ( y_i - y_0)^2 + ( z_i - z_0)^2} \]

In short this function, \(\sigma(r_{xy})\), measures whether or not the CV is within a sphere that is centered on the position of the atom specified using the keyword ORIGIN.

The function \((s_i)\) can be any of the usual LESS_THAN, MORE_THAN, WITHIN etc that are used in all other multicolvars.

When INCYLINDER is used with the DENSITY action the number of atoms in the specified region is calculated

Examples

The input below can be use to calculate the average coordination numbers for those atoms that are within a sphere of radius 1.5 nm that is centered on the position of atom 101.

Click on the labels of the actions for more information on what each action computes
tested on master