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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: * * * *

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  • Helical boundary conditions (en)
  • ヘリカル境界条件 (ja)
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  • 数学においてヘリカル境界条件(ヘリカルきょうかいじょうけん、英: Helical boundary condition)とは、周期的境界条件を変化させたものである。ヘリカル境界条件は、各格子に単一の添え字が充てられている時に、一格子の近傍の添え字を決定する方法を提供する。格子サイトが 1 から N まで番号付けられ、長さ(すなわち、行毎の元の数)が L で次元 d の格子に対し、サイト i の近傍は次で与えられる: * * * * N = Ld である必要はない。ヘリカル境界条件により、任意の次元の格子を表現する上で唯一つの座標のみを使うことが可能となる。 (ja)
  • 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: * * * * (en)
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  • 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: * * * * where the modulo operator is used. It is not necessary that N = Ld. Helical boundary conditions make it possible to use only one coordinate to describe arbitrary-dimensional lattices. (en)
  • 数学においてヘリカル境界条件(ヘリカルきょうかいじょうけん、英: Helical boundary condition)とは、周期的境界条件を変化させたものである。ヘリカル境界条件は、各格子に単一の添え字が充てられている時に、一格子の近傍の添え字を決定する方法を提供する。格子サイトが 1 から N まで番号付けられ、長さ(すなわち、行毎の元の数)が L で次元 d の格子に対し、サイト i の近傍は次で与えられる: * * * * N = Ld である必要はない。ヘリカル境界条件により、任意の次元の格子を表現する上で唯一つの座標のみを使うことが可能となる。 (ja)
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