Non-uniform drag force on the Fermi accelerator model |
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Authors: | Danila F Tavares Edson D Leonel RN Costa Filho |
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Institution: | 1. Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil;2. Universidade da Integração Internacional da Lusofonia Afro-Brasileira–UNILAB, Campus da Liberdade Avenida da Abolição, 3–Centro–Redenção–CE, Brazil;3. Departamento de Estatística, Matemática Aplicada e Computação–UNESP–Univ. Estadual Paulista, Av. 24A, 1515–CEP: 13506-900–Rio Claro–SP, Brazil |
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Abstract: | Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F∝−vγ. The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton’s second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for γ=1; (ii) exponential for γ=2; and (iii) second-degree polynomial type for γ=1.5. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems. |
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Keywords: | Fermi accelerator model Damping forces |
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