Maximum number of collisions of elastic particles
1972 ◽
Vol 331
(1584)
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pp. 1-18
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Keyword(s):
Consider n point-particles, all of the same mass, moving freely in space and interacting only by elastic collisions. There are two degrees of freedom in the outcome of any collision. Let C(n) be the maximum number of collisions possible under Newtonian laws and C*(n) the maximum number possible in relativistic mechanics. This paper is directed towards finding those two functions but is far from achieving that. The following results are established: C(n) ≥1/2n ( n — 1), (C*(n) ≥ 1/2n( n — 1); C(3) = C*(3) = 3; C(4) = 6 (but only for a certain collision-topology) and C*(4)≥ 7. The problem of finding C(n) and C*(n) is of interest in kinetic theory and elsewhere.
Vestnik of Volga State University of Technology Ser Radio Engineering and Infocommunication Systems
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2016 ◽
Vol 31
(3)
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pp. 53-65
2019 ◽
Vol 139
(4)
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pp. 520-521
Keyword(s):
Enhanced Two-Degrees-of-Freedom Control Strategy for Second-Order Unstable Processes with Time Delay
2006 ◽
Vol 45
(10)
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pp. 3604-3614
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Keyword(s):