3. Further Development (Probabilistic Approach)
The complexity of the previous approach (which requires multiple simulations) can be addressed by a combinatorial count of clusters within a given grid.
Ergodicity allows us to consider the distribution of clusters within a single grid as related to the porosity distribution in the actual material.
Random grid generation allows us to introduce a probability distribution governing whether cells are open or closed.
The probability that a cell chosen at random from a grid is open is, of course, equal to p (the material’s intrinsic porosity).
The objective is to determine the probability of cluster formation around or originating from the specified cell.
Its neighboring cells (4 in total)...
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Further Development (Probabilistic Approach)