def pf_to_n(L, pf, R):
"""Returns the number of non-intersecting spheres required to achieve
as close to a given packing fraction as possible, along with the actual
achieved packing fraction. for a number of non-intersecting spheres.
Parameters
----------
L: float array, shape (d,)
System lengths.
pf: float
Fraction of space to be occupied by the spheres.
R: float
Sphere radius.
Returns
-------
n: integer
Number of spheres required to achieve a packing fraction `pf_actual`
pf_actual:
Fraction of space occupied by `n` spheres.
This is the closest possible fraction achievable to `pf`.
"""
dim = L.shape[0]
n = int(round(pf * np.product(L) / sphere_volume(R, dim)))
pf_actual = n_to_pf(L, n, R)
return n, pf_actual
def n_to_pf(L, n, R):
"""Returns the packing fraction for a number of non-intersecting spheres.
Parameters
----------
L: float array, shape (d,)
System lengths.
n: integer
Number of spheres.
R: float
Sphere radius.
Returns
-------
pf: float
Fraction of space occupied by the spheres.
"""
dim = L.shape[0]
return (n * sphere_volume(R=R, n=dim)) / np.product(L)
def V_1(self):
return sphere_volume(self.R, self.dim)
def vp_to_n(vp, R):
return ((vp / 100.0) * geom.sphere_volume(R, 3)) / dataset.Dataset.V_p
def n_to_vp(n, R):
return 100.0 * n * dataset.Dataset.V_p / geom.sphere_volume(R, 3)
def volume_sphere(self):
return geom.sphere_volume(self.R, self.dim)