I'm currently working on mechanical modeling of microstructural samples and I have a question.
Can anyone tell me is there a way to mathematically express distribution of pores in a certain area. I would like to numerically express the distribution of pores - how "well" are the pores distributed with the use of some function.
The picture that I added represents two random microstructures. It is obvious that microstructure on the right has pores that are distributed in "more ordered" way, than the microstructure on the left.
Is there a way to express that distribution mathematically? Throughout the use of some function and coordinates of pores.
Here is a couple of suggestions.
Std dev(distance to nearest pore)/ mean(distance to nearest pore)
Std dev(distance to nearest pore/distance to second-nearest pore)
Std dev( number of pores within a distance $r$ of a random point ) / mean(number of ...) - this is a function of $r$
Measure the distance from each pore to its nearest pore. To do that, maybe find the distance between every pair of pores, and note the smallest distance for each pore.
1) Take the standard deviation of these distances, and divide by the mean of these distances. 2) also note the second-smallest distance for each pore. Divide the smallest distance by the the second smallest distance, to get a ratio for each pore. Find the mean and variance of these ratios.
3) Take a set distance, say 3mm, and count the number of pores within several random 3mm circles. Find the mean and standard deviation of these counts.