# Minimum box size in order for an object in the center to not 'see' duplications of itself under periodic boundary conditions?

I am working on developing a Dissipative Particle Dynamics (DPD) model of a colloid in a bulk fluid. I essentially want to ensure that the perturbations of my meshed colloid are completely uncoupled from the duplicated copies of itself that are present as a result of using periodic boundary condition. This includes any hierarchical interactions. For example, if fluid particles are disturbed from interacting with a duplicated version of the colloid, the propagation of these interactions should dissipate out enough such that by the time this propagation reaches the colloid of interest, that it essentially has a negligible effect on the behavior of the colloid. Unfortunately I myself am not certain about what 'negligible' means, but perhaps someone with more experience in the field could offer some advice on that point in particular.

As a starting point, I would assume the following:

$L-D > r_c$,

where $L$ is the box length, $D$ is the diameter of the colloid and $r_c$ is the largest cutoff for the bead-bead interactions forces. This ensures that the colloid will not interact with itself as a direct result of colloid-colloid interactions, but does not ensure the prevention of the hierarchical interactions I described earlier.

• Would Computational Science be a better home for this question? (Not that it's off-topic here.) If so, then flag for moderator attention asking for a migration. Oct 11 '17 at 11:26
• Thanks, @EmilioPisanty I did exactly that. Wasn't aware about the CS StackExchange! Always good to discover more resources, I appreciate your comment.
– cwm5412
Oct 12 '17 at 8:16
• As far as I can tell, there is not enough information here to allow for an answer. What is the condition you wish to enforce? And what does it mean to "see" something in this context? The answers to these questions should be equations (or, more likely, inequalities). Oct 12 '17 at 11:44
• Thanks for the reply. I updated the question to try to address your concerns. Although I don't have any equations, as you suggest, to add, hopefully it is a bit more clear with what I am asking. Oct 12 '17 at 15:01