论文标题
随机台球中的诺德森扩散率：光谱，几何和计算
Knudsen diffusivity in random billiards: spectrum, geometry, and computation
论文作者
论文摘要
我们开发了一种分析框架和数值方法，以获得自扩散率的系数，以在较大的诺德森数量的限制中稀有气体运输。该框架提供了一种确定通道表面微观结构对扩散率值的影响的方法，当微结构表现出相对较低的粗糙度时，这特别有效。该方法基于这样的观察结果，即在弱表面散射的条件下，由微观结构确定的马尔可夫过渡（散射）操作员具有由经典的legendre差异算子给出的通用形式，最多可达乘法常数。我们还展示了系统的特征数字 - 微观结构的几何参数，马尔可夫操作员的光谱间隙以及一个常用的表面散射模型的切向动量适应系数 - 都是相关的。研究了微观结构的示例，以在数值和分析上说明这些数量的关系。
We develop an analytical framework and numerical approach to obtain the coefficient of self-diffusivity for the transport of a rarefied gas in channels in the limit of large Knudsen number. This framework provides a method for determining the influence of channel surface microstructure on the value of diffusivity that is particularly effective when the microstructure exhibits relatively low roughness. This method is based on the observation that the Markov transition (scattering) operator determined by the microstructure, under the condition of weak surface scattering, has a universal form given, up to a multiplicative constant, by the classical Legendre differential operator. We also show how characteristic numbers of the system -- namely geometric parameters of the microstructure, the spectral gap of a Markov operator, and the tangential momentum accommodation coefficient of a commonly used model of surface scattering -- are all related. Examples of microstructures are investigated to illustrate the relation of these quantities numerically and analytically.
