### Correlation function

This modifier calculates the spatial correlation function between two particle properties.

OVITO uses the FFT to compute the convolution. It then computes a radial average in reciprocal and real space. This gives the correlation function up to half of the cell size. The modifier can additionally compute the short-ranged part of the correlation function from a direct summation over neighbors.

For example, when both particle properties are constant and unity, the modifier returns the pair correlation function. The reciprocal space representation is then the structure factor.

#### Parameters

First property

First particle property for which to compute the correlation, P1.

Second property

Second particle property for which to compute the correlation, P2. If both particle properties are identical, the modifier computes the autocorrelation.

FFT grid spacing

This property sets the approximate size of the FFT grid cell. The actual size is determined by the distance of the cell faces which must contain an integer number of grid cells.

Apply window function to nonperiodic directions

This property controls whether nonperiodic direction have a Hann window applied to them. Applying a window function is necessary to remove spurios oscillations and power-law scaling of the (implicit) rectangular window of the nonperiodic domain.

Direct summation

If enabled, the real-space correlation plot will show the result of a direct calculation of the correlation function, obtaining by summing over neighbors. This short-ranged part of the correlation function is displayed as a red line.

This property determines the cutoff of the direct calculation of the real-space correlation function.

Number of neighbor bins

This property sets the number of bins for the direct calculation of the real-space correlation function.

Normalize correlation function

If set to "by covariance" for the real-space correlation, the correlation function is normalized to approach unity at small distances and zero at large distances, i.e. the plot shows (C(r)-〈P1〉〈P2〉)/(〈P1P2〉-〈P1〉〈P2〉) rather than the unnormalized C(r). If set to "by RDF" for the real-space correlation, the correlation function is divided by the radial distribution function. If activated for the reciprocal-space correlation function, the plot shows C(q)/〈P1P2〉 rather than the unnormalized C(q).

#### Acknowledgment

This modifier has been contributed by Lars Pastewka.