Publication: Non-uniform drag force on the Fermi accelerator model
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Undergraduate course
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Elsevier B.V.
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Article
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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 alpha -nu(gamma). 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 gamma = 1; (ii) exponential for gamma = 2; and (iii) second-degree polynomial type for gamma = 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
Language
English
Citation
Physica A-statistical Mechanics and Its Applications. Amsterdam: Elsevier B.V., v. 391, n. 22, p. 5366-5374, 2012.
