3
votes
1answer
131 views

“Trapping” of discs after random sequential adsorption

Imagine I perform Random Sequential Adsorption (RSA) of discs of some radius $r$ on $[0, 1]^2$, eventually covering the surface to some density $Q \leq 0.543$ with $N$ total discs (where $\approx ...
4
votes
2answers
98 views

Simulating random sequential adsorption in reverse

Please consider two processes: Process 1 - I simulate random sequential adsorption of discs on the unit square in the continuum limit, randomly selecting real number coordinates and rejecting the ...
0
votes
1answer
73 views

Random Sequential Adsorption of Discs on a Plane - What is the best known lowerbound for the number of circles (of some radius $r$) guaranteed to fit on $[0, 1]^2$?

Imagine I perform a random sequential adsorption (RSA) simulation for circles or discs of some radius $r \leq 1$ in $[0, 1]^2$ (I am open to changing this geometry to the unit circle). As a function ...
4
votes
5answers
606 views

Collisions between rooks taking random flights on an $N$ by $M$ chessboard

I randomly place $k$ rooks on an (arbitrarily sized) $N$ by $M$ chessboard. Until only one rook remains, for each of $P$ time intervals we move the pieces as follows: (1) We choose one of the $k$ ...
2
votes
2answers
490 views

Midpoint lattice polygons

Midpoint polygons (a.k.a Kasner polygons) have been studied, and their behavior is well understood. I am considering a variant, which I call midpoint lattice polygons. Start with a sequence of ...
2
votes
1answer
118 views

Inferring the location of a reflecting boundary in a toroidal cage with a Brownian particle

Let's say I have a Brownian particle of some radius $r_b$ and coefficient of diffusion $D$, freely moving about in a toroidal/doughnut-shaped chamber with inner and outer radius $R_{inner}$ and ...