Influence Function

The influence function ω weights the contribution of each bond within the horizon. It can be defined either by selecting a predefined name or by providing a custom mathematical expression.

Predefined Functions

The following predefined options are available:

• 1/xi^2: Classical inverse-square influence function based on the bond length xi.
• 1: Constant influence function (all bonds weighted equally).

Custom Expression

Instead of a predefined name, an arbitrary mathematical expression can be provided as a string. The following variables are available inside the expression:

• xi: Bond length (Float64).
• xiX/xiY/xiZ: Bond direction components (Float64). xiZ is only meaningful in 3D and defaults to 0.0 in 2D.

Any valid Julia expression using these variables (e.g. +, -, *, /, ^, exp, sqrt, ...) can be used.

The yaml definition looks like this

Discretization:
  Influence Function: "1/xi^2"

or, using a custom expression

Discretization:
  Influence Function: "exp(-xi/3)"

or

Discretization:
  Influence Function: "xiX^2 + xiY^2"