Dissipative area-preserving one-dimensional Fermi accelerator model.

The influence of dissipation on the simplified Fermi-Ulam accelerator model (SFUM) is investigated. The model is described in terms of a two-dimensional nonlinear mapping obtained from differential equations. It is shown that a dissipative SFUM possesses regions of phase space characterized by the property of area preservation.

[1]  P. J. Holmes.  The dynamics of repeated impacts with a sinusoidally vibrating table , 1982 .

[2]  Kwok Yeung Tsang,et al.  Dynamics of relaxing systems subjected to nonlinear interactions , 1997 .

[3]  Richard M. Everson,et al.  Chaotic dynamics of a bouncing ball , 1986 .

[4]  Gunther Karner.  The simplified Fermi accelerator in classical and quantum mechanics , 1994 .

[5]  Edson D. Leonel,et al.  LETTER TO THE EDITOR: A crisis in the dissipative Fermi accelerator model , 2005 .

[6]  Jain.  Fractal-like quasienergy spectrum in the Fermi-Ulam model. , 1993, Physical review letters.

[7]  Michael A. Lieberman,et al.  Transient chaotic distributions in dissipative systems , 1986 .

[8]  R. H. Cohen,et al.  Fermi acceleration revisited , 1980 .

[9]  Seba.  Quantum chaos in the Fermi-accelerator model. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[10]  A. Lichtenberg,et al.  Regular and Chaotic Dynamics , 1992 .

[11]  Michael A. Lieberman,et al.  Stochastic and Adiabatic Behavior of Particles Accelerated by Periodic Forces , 1972 .

[12]  Edson D. Leonel,et al.  A hybrid Fermi–Ulam-bouncer model , 2005 .

[13]  Mehta,et al.  Novel temporal behavior of a nonlinear dynamical system: The completely inelastic bouncing ball. , 1990, Physical review letters.

[14]  Luna-Acosta.  Regular and chaotic dynamics of the damped Fermi accelerator. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[15]  Badii,et al.  Coexistence of conservative and dissipative behavior in reversible dynamical systems. , 1986, Physical review. A, General physics.

[16]  Edson D. Leonel,et al.  On the dynamical properties of a Fermi accelerator model , 2004 .

[17]  J. K. D. da Silva,et al.  Time-dependent properties of a simplified Fermi-Ulam accelerator model. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Warr,et al.  Energy input and scaling laws for a single particle vibrating in one dimension. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Mehta,et al.  Bouncing ball with a finite restitution: Chattering, locking, and chaos. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Kowalik,et al.  Self-reanimating chaos in the bouncing-ball system. , 1988, Physical review. A, General physics.

[21]  Tsang,et al.  Transient chaos in dissipatively perturbed near-integrable Hamiltonian systems. , 1985, Physical review letters.

[22]  Jonathan M. Huntley,et al.  Probability distribution functions for a single-particle vibrating in one dimension: experimental study and theoretical analysis , 1996 .

[23]  Enrico Fermi,et al.  On the Origin of the Cosmic Radiation , 1949 .

[24]  M. Berry,et al.  Classical billiards in magnetic fields , 1985 .

[25]  P V E McClintock,et al.  Fermi-Ulam accelerator model under scaling analysis. , 2004, Physical review letters.

[26]  Paul Sánchez,et al.  Chaotic dynamics of an air-damped bouncing ball. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Gerald J. Sussman,et al.  Structure and interpretation of classical mechanics , 2001 .

[28]  José,et al.  Study of a quantum fermi-acceleration model. , 1986, Physical review letters.