一维有耗散碰撞系统的统计研究和热性质
Statistical investigation and thermal properties for a 1-D impact system with dissipation
摘要：
用三种方法对一维耗散碰撞系统的平均速度、平均速度偏差和平均速度平方进行了表征。该系统-粒子，或非相互作用粒子的合奏，在恒定的引力场中运动，并与变化的平台碰撞-由非线性映射描述。平均平方速度允许描述粒子系综的温度作为参数的函数，使用：（i）直接的数值模拟;（ii）从动力学方程解析;（iii）使用概率分布函数。比较这三种技术的分析和数值结果，可以检查所开发的形式主义的鲁棒性，在那里我们能够估计统计变量的数值，而无需进行大量的数值模拟。此外，扩展到其他动力系统是立即的，包括时间依赖台球。
英文摘要：
The behavior of the average velocity, its deviation and average squared velocity are characterized using three techniques for a 1-D dissipative impact system. The system -- a particle, or an ensemble of non interacting particles, moving in a constant gravitation field and colliding with a varying platform -- is described by a nonlinear mapping. The average squared velocity allows to describe the temperature for an ensemble of particles as a function of the parameters using: (i) straightforward numerical simulations; (ii) analytically from the dynamical equations; (iii) using the probability distribution function. Comparing analytical and numerical results for the three techniques, one can check the robustness of the developed formalism, where we are able to estimate numerical values for the statistical variables, without doing extensive numerical simulations. Also, extension to other dynamical systems is immediate, including time dependent billiards.
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