Diamond

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

Bases: Manifold

Triply periodic diamond 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 Diamond surface (default 0)

Diamond defines a periodic diamond surface . The diamond (or Schwarz D) belongs to the family of triply periodic minimal surfaces:

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

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. 1999

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

Example:

diamond1 = manifold.Diamond(N=1)
diamond2 = manifold.Diamond(N=(1, 2, 2))