Consider targets arranged in a regularly spaced array across a near-infinite X-Y plane (area of plane is large relative to area of a target). Each target is initially a unit distance from adjacent targets.
Targets exist initially as open. Targets progressively close. The fraction of closed targets is measurable, from 1 (all open) to 0 (all closed).
How can I model the average distance, D, separating an open target to the nearest open target as a function of the progressive fraction, f, of closed targets.
An approximation: Df = D/f
My question was tagged as 'biology' and 'unclear'; I am posting here to ask for the vocabulary to properly pose my question. I am confident the solution exists.
Biology: I am modelling photochemical properties of phytoplankton. Phytoplankton have reaction centres embedded in planar membranes. Photons hit reaction centres and the reaction centres are 'closed', or busy, for a period (~1 ms) until they can process another photon.
From the perspective of an individual reaction centre we can model the probability of closure as a poisson target function versus incident photons per unit area.
I need to estimate the average distance between open reaction centres, as a function of the fraction of closed reaction centres.
Geometrically I can approximate the system as an infinite array of points, with unit spacing between points. When all reaction centres are open, average distance between points = 1. Since all reaction centres are open, average distance between open reactions centres = 1.
When all reaction centres are closed (as happens under excess light), average distance between open reaction centres is infinite.
But what is the shape of the curve in between? I can readily measure the fraction of closed reaction centres, and I need to convert that to an average distance between open reaction centres.
If someone can point me towards the correct vocabulary to ask the question, I would be grateful.
