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The simple model of the Fermi–Pasta–Ulam problem

Keywords:

I.N. Aliev – Dr.Sc. (Phys.-Math.), Professor, Bauman Moscow State University (Moscow). E-mail: alievprof@yandex.ru P.P. Poluektov – Dr.Sc. (Phys.-Math.), Professor, Bochvara Russian Scientific Research Institute of Inorganic Materials (Moscow). E-mail: ppp@bochvar.ru


E. Fermi and colleagues have put forward the hypothesis of a nonlinear mechanism of thermalization in a spatially oscillating objects with nonlinear transfer of energy between modes. The conducted numerical experiments was observed asymptotic return of the energy in the original mode. In this work, on the example of a rather simple model, the result shows that there is a transfer between adjacent modes. As the model considers a set of mechanical collisions of the ball with a moving plane.
References:

 

  1. Fermi E., Pasta J., Ulam S. Los Alamos Report LA-1940, 1955; also in: Collection Papers of Enrico Fermi / Ed. E. Serge // University of Chicago Press. 1965. V. 2. P. 978. Many-Body Problems / Ed. MattisD.C. Singapore: WorldScientific. 1993.
  2. Ivanchenko M.V.Modovaja lokalizacija v cepochkakh Fermi–Pasta–Ulama s proizvolnym porjadkom nelinejjnosti // Izv. vuzov «PND». 2011. T.19. № 1. S. 55-61.

 

 

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