In mathematics, helical boundary conditions are a variation on periodic boundary conditions. Helical boundary conditions provide a method for determining the index of a lattice site's neighbours when each lattice site is indexed by just a single coordinate. On a lattice of dimension d where the lattice sites are numbered from 1 to N and L is the width (i.e. number of elements per row) of the lattice in all but the last dimension, the neighbors of site i are:
It is not necessary that N = Ld. Helical boundary conditions make it possible to use only one coordinate to describe arbitrary-dimensional lattices.
Famous quotes containing the words boundary and/or conditions:
“The boundary line between self and external world bears no relation to reality; the distinction between ego and world is made by spitting out part of the inside, and swallowing in part of the outside.”
—Norman O. Brown (b. 1913)
“Mankind always sets itself only such tasks as it can solve; since, looking at the matter more closely, we will always find that the task itself arises only when the material conditions necessary for its solution already exist or are at least in the process of formation.”
—Karl Marx (1818–1883)