The transport coefficients for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal ($\alpha$) and tangential ($\beta$) restitution are obtained in a unified framework as functions of the number of translational ($d_t$) and rotational ($d_r$) degrees of freedom. The derivation is carried out by means of the Chapman–Enskog method with a Sonine-like approximation in which, in contrast to previous approaches, the reference distribution function for angular velocities does not need to be specified. The well-known case of purely smooth $d$-dimensional particles is recovered by setting $d_t=d$ and formally taking the limit $d_r\to 0$. In addition, previous results [G. M. Kremer, A. Santos, and V. Garzó, Phys. Rev. E 90, 022205 (2014)] for hard spheres are reobtained by taking $d_t=d_r=3$, while novel results for hard-disk gases are derived with the choice $d_t=2, d_r=1$. The singular quasismooth limit ($\beta \to -1$) and the conservative Pidduck's gas ($\alpha =\beta =1$) are also obtained and discussed.

中文翻译：

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非弹性和粗糙的硬盘或球体的颗粒气体的流体动力学。一、运输系数

非弹性和粗糙的硬盘或球体的稀颗粒气体的输运系数，其法向系数为常数（$\alpha$) 和切线 ($\beta$) 在统一框架中获得恢复原状作为翻译数量的函数 ($d_{吨}$) 和旋转 ($d_r$） 自由程度。推导是通过使用类 Sonine 近似的 Chapman-Enskog 方法进行的，与以前的方法相比，不需要指定角速度的参考分布函数。纯光滑的著名案例$d$-维粒子通过设置回收 $d_{吨}=d$ 并正式采取极限 $d_r\to 0$. 此外，之前的结果 [GM Kremer, A. Santos, and V. Garzó, Phys. Rev. E 90 , 022205 (2014)] 用于硬球体通过取$d_{吨}=d_r=3$，而硬盘气体的新结果是通过选择获得的 $d_{吨}=2, d_r=1$. 奇异准光滑极限 ($\beta \to -1$) 和保守的 Pidduck 气体 ($\alpha =\beta =1$) 也得到并讨论。