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Dissipative area-preserving one-dimensional Fermi accelerator model.

Edson D Leonel1, P V E McClintock

  • 1Departamento de Estatística, Matemática Aplicada e Computação, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista Av.24A, 1515, Bela Vista, CEP 13506-700, Rio Claro, São Paulo, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 16, 2006
PubMed
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Dissipation in the simplified Fermi-Ulam accelerator model (SFUM) creates unique phase space regions. These regions exhibit area preservation, a key characteristic of the system dynamics.

Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Mathematical physics

Background:

  • The Fermi-Ulam accelerator model explores particle acceleration dynamics.
  • Understanding dissipation's role is crucial for complex systems.
  • Nonlinear mappings are fundamental in describing dynamical systems.

Purpose of the Study:

  • To investigate the impact of dissipation on the simplified Fermi-Ulam accelerator model (SFUM).
  • To analyze the resulting phase space characteristics of a dissipative SFUM.

Main Methods:

  • Derivation of a two-dimensional nonlinear mapping from differential equations.
  • Analysis of the mapping to identify regions with specific phase space properties.

Main Results:

Related Experiment Videos

  • The dissipative SFUM exhibits distinct regions within its phase space.
  • These identified regions are characterized by the property of area preservation.
  • Dissipation does not universally destroy area-preserving properties in this model.

Conclusions:

  • The simplified Fermi-Ulam accelerator model with dissipation retains localized regions of area preservation.
  • This finding offers insights into the interplay between dissipation and conserved quantities in nonlinear systems.
  • Further research can explore the extent and implications of these area-preserving regions.