%0 Journal Article %1 WOS:000308050000008 %A Tavares, Danila F %A Leonel, Edson D %A Filho, R N Costa %C PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS %D 2012 %I ELSEVIER SCIENCE BV %J PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS %K Damping accelerator forces} model; {Fermi %N 22 %P 5366-5374 %R 10.1016/j.physa.2012.06.044 %T Non-uniform drag force on the Fermi accelerator model %V 391 %X 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. (C) 2012 Elsevier B.V. All rights reserved.

@article{WOS:000308050000008, 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. (C) 2012 Elsevier B.V. All rights reserved.}, added-at = {2022-05-23T20:00:14.000+0200}, address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}, author = {Tavares, Danila F and Leonel, Edson D and Filho, R N Costa}, biburl = {https://www.bibsonomy.org/bibtex/2f0d03a9364ac8fb0883b1ae936af7b25/ppgfis_ufc_br}, doi = {10.1016/j.physa.2012.06.044}, interhash = {bcfe36b7c592c5c33a7b4e4d7deb374d}, intrahash = {f0d03a9364ac8fb0883b1ae936af7b25}, issn = {0378-4371}, journal = {PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS}, keywords = {Damping accelerator forces} model; {Fermi}, number = 22, pages = {5366-5374}, publisher = {ELSEVIER SCIENCE BV}, pubstate = {published}, timestamp = {2022-05-23T20:00:14.000+0200}, title = {Non-uniform drag force on the Fermi accelerator model}, tppubtype = {article}, volume = 391, year = 2012 }