Non-uniform drag force on the Fermi accelerator model
Non-uniform drag force on the Fermi accelerator model
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DOI：
10.1016/j.physa.2012.06.044
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发表时间：
2012-11
影响因子：
3.3
通讯作者：
Danila F. Tavares;E. Leonel;R. N. C. Filho
中科院分区：
文献类型：
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作者：
Danila F. Tavares;E. Leonel;R. N. C. Filho
在耗散费米加速模型下，得到了粒子在一般阻力作用下的动力学性质。耗散是通过粘性阻力引入的，就像气体一样，并假设与速度的幂F −vγ成正比。动力学描述通过牛顿第二运动定律的解决方案获得的二维非线性面积收缩映射。我们证明了高能量的衰变是由一个连分数给出的，它恢复了以下表达式：（i）γ=1时的线性;（ii）γ=2时的指数;（iii）γ=1.5时的二次多项式型。我们的结果进行了讨论的完整版本和简化版本。本文所用的方法可以推广到许多不同类型的系统，包括一类台球问题。
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.