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Nonlinear behavior of a many-body one-dimensional plasma sheet model and its transport phenomena

多体一维等离子体片模型的非线性行为及其输运现象

基本信息

批准号：
11837018
负责人：
KITAHARA Kazuo
金额：
$ 2.05万
依托单位：
International Christian University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

项目摘要

A one-dimenslonal plasma sheet model, which consists of negatively charged sheets in a uniformly distributed positive charges, is equivalent to a system of harmonic oscillators around equilibrium positions equally separated from each other, neighboring oscillators colliding elastically. Therefore, if the motion of each sheet is described in terms of action and angle variables, the action variables are constants of motion and the motion is regular until collision of oscillators occurs. When collisionof neighboring pair of oscillators, their action variables undergo discontinuous jumps due to exchange of momenta between neighboring pair. Numerical calculation can be done by connecting analytical solutions before and after each collision. First, we investigated thermal conductivity of this system by imposing boundary condition of heat baths of different temperatures and calculate energyflow from one boundary to the other. The size dependence of the conductivity coefficient is normal as long as the system is at low temperature. However, at higher temperature, there is size-dependence of the coefficient, which is due to ballistic motion of sheets as observed in the phase space. Namely there are ballistic sheets(free particle motion) and trapped sheets in potential wells. The tendencyto Maxwell distribution of velocities is quick at lower temperature, where orbital instability is enhanced due to chaos. We succeeded to explain these behavior by the usage of escape rate formalism which implies that Green-Kubo formula works at least at low temperature. In order to under stand these observations, we are now developing a kinetic theory based up on action and angle variables for the evolution of distribution function of angle variables. We have also investigated effect of particle transport (diffusion) on non-linear chemical reaction, which may create spatial correlation under nonequilibrium conditions,

一个由正电荷均匀分布的负电荷片组成的一维等离子体片模型，相当于一个在平衡位置周围均匀分离的谐振子系统，相邻的谐振子进行弹性碰撞。因此，如果用作用变量和角度变量来描述每个薄片的运动，则作用变量是运动常数，运动是规则的，直到振子发生碰撞。当相邻振子对发生碰撞时，由于相邻振子对之间的动量交换，它们的作用变量发生不连续的跳跃。数值计算可以通过连接每次碰撞前后的解析解来完成。首先，我们通过施加不同温度的热浴边界条件来研究该系统的导热性，并计算了从一个边界到另一个边界的能量流。只要系统处于低温状态，电导率系数的尺寸依赖性是正常的。然而，在较高的温度下，由于在相空间中观察到薄片的弹道运动，该系数存在尺寸依赖性。也就是说，有弹道片（自由粒子运动）和势阱中的捕获片。在较低的温度下，轨道的不稳定性由于混沌而增强，速度向麦克斯韦分布的趋势很快。我们成功地用逃逸率公式解释了这些行为，这意味着Green-Kubo公式至少在低温下是有效的。为了理解这些观察结果，我们现在正在发展一个基于作用和角度变量的动力学理论，用于角度变量分布函数的演化。我们还研究了粒子输运（扩散）对非线性化学反应的影响，这可能在非平衡条件下产生空间相关性。