## In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas

- Some dynamical properties for a time dependent Lorentz gas considering both the dissipative and non dissipative dynamics are studied. The model is described by using a four-dimensional nonlinear mapping. For the conservative dynamics, scaling laws are obtained for the behavior of the average velocity for an ensemble of non interacting particles and the unlimited energy growth is confirmed. For the dissipative case, four different kinds of damping forces are considered namely: (i) restitution coefficient which makes the particle experiences a loss of energy upon collisions; and in-flight dissipation given by (ii) F = −ηV2; (iii) F = −ηVμ with μ ≠ 1 and μ ≠ 2 and; (iv) F = −ηV, where η is the Some dynamical properties for a time dependent Lorentz gas considering both the dissipative and non dissipative dynamics are studied. The model is described by using a four-dimensional nonlinear mapping. For the conservative dynamics, scaling laws are obtained for the behavior of the average velocity for an ensemble of non interacting particles and the unlimited energy growth is confirmed. For the dissipative case, four different kinds of damping forces are considered namely: (i) restitution coefficient which makes the particle experiences a loss of energy upon collisions; and in-flight dissipation given by (ii) F = −ηV2; (iii) F = −ηVμ with μ ≠ 1 and μ ≠ 2 and; (iv) F = −ηV, where η is the dissipation parameter. Extensive numerical simulations were made and our results confirm that the unlimited energy growth, observed for the conservative dynamics, is suppressed for the dissipative case. The behaviour of the average velocity is described using scaling arguments and classes of universalities are defined.…

Author: | Diego Fregolente Mendes de Oliveira, Edson D. Leonel |
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URN: | urn:nbn:de:bvb:29-opus-38343 |

Document Type: | Article |

Language: | English |

Date of Publication (online): | 2012/11/08 |

Publishing Institution: | Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) |

Release Date: | 2012/11/08 |

Tag: | chaos; damping; nonlinear dynamical systems; scaling phenomena |

SWD-Keyword: | - |

Original publication: | Chaos 22.2 (2012): 07.11.2012 <http://chaos.aip.org/resource/1/chaoeh/v22/i2/p026123_s1> |

Institutes: | Naturwissenschaftliche Fakultät -ohne weitere Spezifikation- |

Dewey Decimal Classification: | 500 Naturwissenschaften und Mathematik |

PACS-Classification: | 05.45.Ac Low-dimensional chaos |

05.45.Pq Numerical simulations of chaotic systems | |

Collections: | Allianzlizenzen 2012 |