Gyroid

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

Bases: Manifold

Triply periodic gyroid 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 Gyroid surface (default 0)

Gyroid defines a periodic gyroid surface. The gyroid belongs to the family of triply periodic minimal surfaces:

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

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:

gyroid1 = manifold.Gyroid(N=1)
gyroid2 = manifold.Gyroid(N=(1, 2, 2))