A Lower Bound for the Number of Elastic Collisions

We prove by example that the number of elastic collisions of n balls of equal mass and equal size in d -dimensional space can be greater than n 3 /27 for n ≥ 3 and d ≥ 2 . The previously known lower bound was of order n 2 .

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Veröffentlicht in:	Communications in mathematical physics 2019-12, Vol.372 (2), p.679-711
Hauptverfasser:	Burdzy, Krzysztof, Duarte, Mauricio
Format:	Artikel
Sprache:	eng
Schlagworte:	Classical and Quantum Gravitation Collisions Complex Systems Elastic scattering Lower bounds Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical
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Beschreibung
Zusammenfassung:	We prove by example that the number of elastic collisions of n balls of equal mass and equal size in d -dimensional space can be greater than n 3 /27 for n ≥ 3 and d ≥ 2 . The previously known lower bound was of order n 2 .
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-019-03399-3