A simulation of hydrodynamics on non-commutative space
A simulation of hydrodynamics on non-commutative space
复制标题
非交换空间上的流体动力学模拟
DOI：
10.1093/ptep/pty061
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发表时间：
2016
影响因子：
3.5
通讯作者：
A. Sugamoto
中科院分区：
文献类型：
--
作者：
T. Kawamura;A. Kuwana;Y. Nagata;Mayumi Saitou;A. Sugamoto
在二维非对易空间上进行了流体动力学模拟，其中空间坐标$（x，y）$是非对易的，满足对易关系$[x，y]=i \theta$. Navier-Stokes方程有一个额外的力项，它反映了空间的非对易性，与$\θ ^2 $成比例。这个参数$\theta$与流体粒子的最小尺寸有关，这是由不确定性原理所暗示的，$\Delta x \Delta y \ge \theta/2$。为了了解该参数对流动的影响，考虑以下情况。在水流中间放置一个障碍物，将水流分成小缝和大缝，但水流随后在下游汇合。对于雷诺数700，与没有$\theta$的流动的行为被观察到不同的，和差异被认为是相关的下游的旋涡的活动的差异。在通常的流动中，当出现“两个附着涡”时，小缝处流量的振荡在一定时间后减弱。在非对易流动中，这两个附着涡从一开始就出现，流动的行为没有很大的波动。开始时存在的流动不规则性在一定时间后消失。
A simulation of the hydrodynamics on the two dimensional non-commutative space is performed, in which the space coordinates $(x, y)$ are non-commutative, satisfying the commutation relation $[x, y]=i \theta$. The Navier-Stokes equation has an extra force term which reflects the non-commutativity of the space, being proportional to $\theta^2$. This parameter $\theta$ is related to the minimum size of fluid particles which is implied by the uncertainty principle, $\Delta x \Delta y \ge \theta/2$. To see the effect of this parameter on the flow, following situation is considered. An obstacle placed in the middle of the stream, separates the flow into small slit and large slit, but the flow is joined afterwards in the down stream. For the Reynolds number 700, the behavior of the flows with and without $\theta$ is observed to differ, and the difference is seen to be correlated to the difference of the activity of vortices in the down stream. The oscillation of the flow rate at the small slit diminishes after the certain time in the usual flow when the "two attached eddies" appear. In the non-commutative flow this two attached eddies appear from the beginning and the behavior of the flows does not fluctuate largely. The irregularity in the flow existing in the beginning disappears after the certain time.