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This results in the following expression: Ahop = x1,x2=a y1,y2=b∫∫∫∫ x1,x2=−a y1,y2=−b dx 1dx 2dy 1dy 2 1{(x1−x2)2+(y1−y2)2≥(2r)2} δ (y1− y2√ 2 )

Alternatively, we can integrate directly in the (x,X,y,Y ) coordinates, where g(x,X,y,Y ) = y, then return to the original coordinates

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Exact hopping and collision times for two hard discs in a box

nlin.CD · 2019-08-13 · conditional · novelty 7.0

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.

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  • Exact hopping and collision times for two hard discs in a box nlin.CD · 2019-08-13 · conditional · none · ref 3

    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.