2. Filtering

The default grid-independent filter function used in HyMD is a Gaussian

$$H(x)=\frac{1}{\sqrt{2\pi }\sigma }\exp \left[\frac{-x^2}{2{\sigma }^2}\right]$$

with reciprocal space representation

$$\hat{H}(k)=\exp \left[\frac{-{\sigma }^2{k}^2}{2}\right].$$

The coarse-graining parameter $\sigma$ determines a length scale of particle extent and is given as configuration file input by

sigma = 0.75

2.1. Implementing new filters

Implementing new filter functions is straightforward by hijacking the setup method of the Hamiltonian superclass. The new filter is automatically applied and differentiated through the potential and interaction energy functional.