Exact analytical expressions for mean hopping, disc-collision, and wall-collision times for two hard discs in a box, derived via a billiard model and Chernov's return-time formula, and verified numerically.
If w,h > 4r, then the limits of integration are unaffected by the radius of the circles
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Exact hopping and collision times for two hard discs in a box
Exact analytical expressions for mean hopping, disc-collision, and wall-collision times for two hard discs in a box, derived via a billiard model and Chernov's return-time formula, and verified numerically.