3. Packing of Randomly Placed Overlapping Spheres Sample Data
The approach to reconstructing these domains is to randomly place spheres of given radii in a computational domain. The spheres are periodic in the sense that a sphere with a center near a given boundary will have part of the sphere on one side of the computational domain and part of the sphere on the opposite side of the computational domain. The spheres are allowed to overlap by a small amount to ensure continuity in the solid.
The algorithm works as follows:
1) An initial sphere center is chosen in the computational domain using a random number generator.
2) A random number generator is used to determine whether or not the next sphere is required to overlap with spheres which are already in the computational domain.
3) A random number generator is used to generate trial sphere centers. If the sphere is required to overlap with an existing sphere, the following two conditions must be met for a sphere center to be accepted: The trial sphere must overlap with an existing sphere and the overlapping portion of the spheres must not exceed the specified overlap tolerance. If the sphere is not required to overlap with an existing sphere, the following condition must be met: If the trial sphere center overlaps with any existing spheres, the overlapping portion of the spheres must not exceed the specified overlap tolerance.
4) Continue this process until the specified porosity has been reached.
(The full description of the algorithm can be found in [1])
To create these samples we selected the following parameters: mean diameter of solid sphere = 40 lu with an standard deviation of 3 lu; and a overlap tolerance of 0.4.
[1] Kyle J. Lange et al 2010 J. Electrochem. Soc. 157 B1434
