# problem in matching two sets of particles

I have been trying to simulate a simple system in which there are two set of particles. One kind of particles are localized on the boundary of a circle (shown in purple below), whereas the second kind can be either inside or outside of the boundary (delineated in blue).

I will post the simplified version of what is bugging me so as to avoid unnecessary confusion with detalied code and enable the readers to effectively answer my query.

Consider that I generate the two particles using the following commands:

particles = RandomReal[{0, 1}, {200, 2}, WorkingPrecision -> 2];

membrane = Table[SetAccuracy[RandomPoint[Circle[]], 3], 100];



we can see it visually:

Graphics[{Darker@Purple, Point@membrane, Blue, Point@particlemap}]


Now i can find the blue particle interacting with the purple particle using the following piece of code:

p = Reap[Function[{particle},

particleposition = particle[[2]];
Sow[particle[[1]],
Select[membrane, # === particleposition &]]] /@ particlemap
][[2]]

(* {{80}} was the index of the particle that was interacting with
the membrane for the example posted *)


Now I can also create an association to extract the coordinates of interacting particles

association = Association@Map[#[[1]] -> #[[2]] &, particlemap];

interactingParticlePos = association[#]&/@(Flatten@p)

(* {0.57, 0.83} was the interactingParticlePos *)


plugging this value back we can find that Position can get the index back

Position[particles, interactingParticlePos]
(* {{80}} as we expected *)


However the anomaly is that we do not find the position of the point in membrane,

Position[membrane, interactingParticlePos]
(* {} *)


This should not be the case because earlier the Select command found a match between the membrane and the particlemap

Moreover,

MemberQ[membrane, interactingParticlePos]
(*False*)
MemberQ[particles,interactingParticlePos]
(*True*)


Can someone Kindly let me know how I can get the index of the position shared by particles and membrane for the membrane. Furthermore, why is Position and MemberQ not able to find a match whereas Select could?

My hunch is that it has something to do with the way i am setting WorkingPrecision and SetAccuracy but not sure.

I am trying to do a reaction diffusion simulation but this seems to be the key step. If I do not use WorkingPrecision and SetAccuracy ** then the** RandomReal and RandomPoints are generated to machineprecision which makes it impossible for the two kinds of particles to find eachother

Many thanks in return for the help !

• Instead of messing with precisions, why not create a NearestFunction? Then use that, with some epsilon threshold, to determine when particles have in effect collided. – Daniel Lichtblau Nov 28 '16 at 15:50
• yeah actually that might do too. thanks :) but i am really interested in why the above mentioned problem is the case – Ali Hashmi Nov 28 '16 at 16:08
• It seems this falls into a gray area, where SameQ says one thing and whatever internals are in use by pattern matching for numbers says another. It is really not a reliable way to try to do this. Also it's slower than using a NearestFunction, which will matter if the size of these sets is scaled upward. – Daniel Lichtblau Nov 29 '16 at 2:00
• Thanks a lot for your advice Daniel. I have implemented using the NearestFunction approach as you suggested – Ali Hashmi Nov 29 '16 at 6:01
• Hi Daniel, could you kindly check this new post: its a different question regarding the same project. mathematica.stackexchange.com/questions/132525/… – Ali Hashmi Dec 1 '16 at 9:38

Position[particles, #] & /@ interactingParticlePos

MemberQ[membrane, #] & /@ interactingParticlePos