Function Repository Resource:

PeriodicBoxDistance

Evaluate the shortest distance between two points in a box with periodic boundary conditions

Contributed by: Matt Kafker

ResourceFunction["PeriodicBoxDistance"][u,v,L]

gives the shortest distance between vectors u and v in a cubic box of side-length L centered on the origin with periodic boundary conditions.

Details

ResourceFunction["PeriodicBoxDistance"] works for boxes in any number of spatial dimensions.

Compute a 1D periodic box distance in the "box" represented by the interval [-1,1]:

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PeriodicBoxDistance reverts to Euclidean distance when points are close by within the box:

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Parallel points on the boundaries of the box have zero separation:

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PeriodicBoxDistance also works in higher dimensions:

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Compare PeriodicBoxDistance from the origin with Euclidean distance in two dimensions:

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