Motion of a Rigid Body in a Special Lorentz Gas: Loss of Memory Effect
Motion of a Rigid Body in a Special Lorentz Gas: Loss of Memory Effect
复制标题
刚体在特殊洛伦兹气体中的运动：记忆效应丧失
DOI：
10.1007/s10955-018-2072-3
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发表时间：
2018
影响因子：
1.6
通讯作者：
Kai Koike
中科院分区：
文献类型：
--
作者：
岩崎悟;Kai Koike
对一类特殊洛伦兹气体中刚体的直线运动进行了数学分析。根据牛顿方程，刚体在气体阻力下运动。气体模型是由气体分子和背景障碍物组成的特殊洛伦兹气体，由Tsuji和Aoki （J Stat Phys 146:620-645, 2012）提出。在得到的动力学方程上施加镜面边界条件。本研究补充了上述引用的Tsuji和Aoki的数值研究，尽管本文的设置与他们的略有不同，但定性地证明了相同的渐近行为：当障碍物发生热运动时，刚体的速度v (t)呈指数衰减；如果障碍物不动，则速度v (t)以与空间维度无关的速率代数衰减。这证明了分子与背景障碍物的相互作用破坏了由于回忆而产生的记忆效应。
Linear motion of a rigid body in a special kind of Lorentz gas is mathematically analyzed. The rigid body moves against gas drag according to Newton’s equation. The gas model is a special Lorentz gas consisting of gas molecules and background obstacles, which was introduced in Tsuji and Aoki (J Stat Phys 146:620–645, 2012). The specular boundary condition is imposed on the resulting kinetic equation. This study complements the numerical study by Tsuji and Aoki cited above—although the setting in this paper is slightly different from theirs, qualitatively the same asymptotic behavior is proved: The velocityV(t) of the rigid body decays exponentially if the obstacles undergo thermal motion; if the obstacles are motionless, then the velocityV(t) decays algebraically with a rateindependent of the spatial dimension. This demonstrates the idea that interaction of the molecules with the background obstacles destroys the memory effect due to recollision.