Primitive

class hoomd.md.manifold.Primitive(N, epsilon=0)

Bases: Manifold

Triply periodic primitive manifold.

Parameters:

• N (tuple [int, int, int] or int) – number of unit cells in all 3 directions. $[N_x, N_y, N_z]$. In case number of unit cells u in all direction the same ($[u, u, u]$), use N = u.

• epsilon (float) – defines CMC companion of the Primitive surface (default 0)

Primitive specifies a periodic primitive surface as a constraint. The primitive (or Schwarz P) belongs to the family of triply periodic minimal surfaces:

$$F(x,y,z) = \cos{\frac{2 \pi}{B_x} x} + \cos{\frac{2 \pi}{B_y} y} + \cos{\frac{2 \pi}{B_z} z} - \epsilon$$

is the nodal approximation of the diamond surface where $[B_x,B_y,B_z]$ is the periodicity length in the x, y and z direction. The periodicity length B is defined by the current box size L and the number of unit cells N. $B_i=\frac{L_i}{N_i}$

See also

• A. H. Schoen 1970)

• P. J.F. Gandy et. al. 2000

• H. G. von Schnering and R. Nesper 1991

Example:

primitive1 = manifold.Primitive(N=1)
primitive2 = manifold.Primitive(N=(1, 2, 2))