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TMF, 1988, Volume 77, Number 1, Pages 154–160 (Mi tmf5695)  

This article is cited in 6 scientific papers (total in 7 papers)

New mechanism of particle acceleration and relativistic analog of the Fermi–Ulam model

L. D. Pustyl'nikov


Abstract: An investigation is made of a relativistic analog of the Fermi–Ulam model in which a relativistic particle moves vertically and freely between parallel horizontal infinitely heavy walls that move in the vertical direction in accordance with a periodic law, the particle interacting with the walls in a collision in accordance with the law of elastic impact. The possibility of unlimited growth of the energy of the particle is proved; specifically, unbounded growth of the energy is realized for all initial data in some open set, and the asymptotic behavior of such growth is found.

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English version:
Theoretical and Mathematical Physics, 1988, 77:1, 1110–1115

Bibliographic databases:

Received: 27.03.1987

Citation: L. D. Pustyl'nikov, “New mechanism of particle acceleration and relativistic analog of the Fermi–Ulam model”, TMF, 77:1 (1988), 154–160; Theoret. and Math. Phys., 77:1 (1988), 1110–1115

Citation in format AMSBIB
\Bibitem{Pus88}
\by L.~D.~Pustyl'nikov
\paper New mechanism of particle acceleration and relativistic analog of the Fermi--Ulam model
\jour TMF
\yr 1988
\vol 77
\issue 1
\pages 154--160
\mathnet{http://mi.mathnet.ru/tmf5695}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=972488}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 77
\issue 1
\pages 1110--1115
\crossref{https://doi.org/10.1007/BF01028687}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1988AD89600014}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. D. Pustyl'nikov, “A new mechanism of particle acceleration and rotation numbers”, Theoret. and Math. Phys., 82:2 (1990), 180–187  mathnet  crossref  mathscinet  isi
    2. L. D. Pustyl'nikov, “A mechanism of irreversibility and unbounded growth of the energy in a model of statistical mechanics”, Theoret. and Math. Phys., 86:1 (1991), 82–89  mathnet  crossref  mathscinet  zmath  isi
    3. L. D. Pustyl'nikov, “Existence of invariant curves for maps close to degenerate maps, and a solution of the Fermi–Ulam problem”, Russian Acad. Sci. Sb. Math., 82:1 (1995), 231–241  mathnet  crossref  mathscinet  zmath  isi
    4. L. D. Pustyl'nikov, “Poincaré models, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism”, Russian Math. Surveys, 50:1 (1995), 145–189  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. L. D. Pustylnikov, “Dinamicheskie sistemy s uprugimi otrazheniyami i mekhanizm uskoreniya Fermi”, Matem. prosv., ser. 3, 8, Izd-vo MTsNMO, M., 2004, 164–180  mathnet
    6. L. D. Pustylnikov, M. V. Deryabin, “Chërnye dyry i obobschënnye relyativistskie billiardy”, Preprinty IPM im. M. V. Keldysha, 2013, 054, 36 pp.  mathnet
    7. L. D. Pustyl'nikov, M. V. Deryabin, “Nonequilibrium gas, entropy and generalized billiards”, Preprinty IPM im. M. V. Keldysha, 2014, 003, 10 pp.  mathnet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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