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FloatingLantern
FloatingLantern
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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 of $r$, what is the best known lowerbound for the number of discs I can place on the surface s.t. all discs are guaranteed to fit? In other words, if I simulate RSA until I place all $N$ discs on the bounded surface, whenfor some value of $r$, what is the largest known $N$ s.t. my simulation guaranteed to halt?

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 of $r$, what is the best known lowerbound for the number of discs I can place on the surface s.t. all discs are guaranteed to fit? In other words, if I simulate RSA until I place all $N$ discs on the bounded surface, when is my simulation guaranteed to halt?

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 of $r$, what is the best known lowerbound for the number of discs I can place on the surface s.t. all discs are guaranteed to fit? In other words, if I simulate RSA until I place all $N$ discs on the bounded surface, for some value of $r$, what is the largest known $N$ s.t. my simulation guaranteed to halt?

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FloatingLantern
FloatingLantern
  • 47
  • 3

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 of $r$, what is the best known lowerbound for the number of discs I can place on the surface s.t. all discs are guaranteed to fit? In other words, if I simulate RSA until I place all $N$ discs on the bounded surface, when is my simulation guaranteed to halt?