You can build a multi-scale model:

-your "voxel" cube or other geometric volume element repeated in your grid V(i)

-within the voxel V(i), consider a distribution of particles j with presence probability in Voxel V(i) p(j,i, t)dt. Assume position of particle j at time t to be x(j,t), with probability expressed as q(j,t).dx(j).dt

Then you can simulate whatever is relevant for you, e.g. particle motion inside V(i), and you can have a multi-level model:

-compute inside V(i), for all i in set I

-compute interaction between V(i) and V(j), for all pairs (i,j) of distinct i and j.

You may suppose attenuation/screening occurs and just do it for V(i) and V(j) where i and j are nearest neighbours in your voxel grid, with the other interactions negligible (depending on your model, and part of the physics you are looking at).

The challenge is:

-can you assume that what happens inside V(i) and what happens inside V(j) is independent? That is that the inside of V(i) is insulated from its outside ("Faraday cage" V(i)?)

-can you really build a multi-level model?

-can you aggregate the V(i)s, say by nearest neighbours, leading to a new grid of W(k) which is coarser (larger aggregated cells)?

-how do property interconnect at border (inside voxel, and outside.

I would go for simulations, in cases of increasing richness, starting with one dimensional line, segmented in intervals V(i)=[x(i), x(i+1)], and maybe springs (oscillators) constrained by -k(i).(x-x(i)) force to come back to x(i), intra voxel V(i).

Then think of an inter-voxel interaction (maybe springs again)...

But maybe you can give more details on your specific problem and we can fit something specific to it...

Thanks Renaud di Francesco

Sir I have put question on shape of electrons, could sub voxel volumetric analysis show the shape of electrons and electon holes