Kinetic-theoretic studies of the effect of sharp edges of the boundary in low-pressure gases

1. 均匀冷却或加热板边缘诱导稀薄气体流动的研究：在我们之前的论文中，我们通过直接模拟蒙特卡罗方法的数值分析表明，放置在稀薄气体中的均匀冷却或加热板的边缘诱导了相当强的气体流动。在本研究中，为了获得更高可靠性的结果，我们采用精确的动力学方程有限差分分析来研究流动。从而全面地澄清了气体的行为。特别是，在近连续介质情况下，流动比热蠕变流动和热应力引起的流动具有更强的影响。壁面温度不连续引起的稀薄气体流动的研究：我们研究了壁面温度不连续分布时在容器内引起的稀薄气体流动。应用1中提出的有限差分法，在较宽范围内精确地得到了气体稀薄度较大范围内的流动。我们发现，随着连续极限的逼近，虽然有明显流动的区域缩小到壁面温度的不连续线，但最大流动速度趋于有限值。此外，我们在具有气体动力学方程特征的简单输运方程的基础上，从数学上阐明了由边界数据中的奇点引起的奇点的传播。其他一些基本问题的研究：考虑到众所周知的由温度场引起的流动（热蒸腾流）的另一个方面，我们研究了通过设计温度分布和管道结构来控制管道内的流动（例如，引起单向流动）。我们还研究了气体混合物的连续统极限的基本特征，对它的理解有助于将1和2的分析推广到混合物的情况。少

1. Study of a rarefied gas flow induced around edges of a uniformly cooled or heated plate :In our previous paper, we showed, by means of a numerical analysis using the direct simulation Monte Carlo method, that a fairly strong gas flow is induced around the edges of a uniformly cooled or heated plate placed in a rarefied gas. In the present study, in order to obtain the result with higher reliability, we investigated the flow by an accurate finite-difference analysis of a kinetic equation. As a result, the behavior of the gas was clarified comprehensively. In particular, it was confirmed that the flow has a stronger effect than the thermal creep flow and the flow induced by the thermal stress in the near continuum case.2. Study of a rarefied gas flow caused by a discontinuous wall temperature :We have investigated a rarefied gas flow induced in a container when the temperature of the wall of the container has a discontinuous distribution. The flow was obtained accurately for a wide ra … More nge of the degree of gas rarefaction by applying the finite-difference method developed in 1. We showed that, as the continuum limit is approached, though the region with an appreciable flow shrinks to the discontinuity line of the wall temperature, the maximum speed of the flow tends to approach a finite value. In addition, we have clarified the propagation of singularities, caused by the singularities in the boundary data, mathematically on the basis of a simple transport equation that possesses the feature of the equations in kinetic theory of gases.3. Studies of some other fundamental problems :Paying attention to another aspect of a well-known flow induced by a temperature field (thermal transpiration), we studied the control of the flow in a pipe (e. g., causing a one-way flow) by devising the temperature distribution as well as the configuration of the pipe. We have also investigated the fundamental features of the continuum limit for gas mixtures, the understanding of which facilitates the extension of the analyses of 1 and 2 to the case of the mixtures. Less