Comparison of hydrodynamic calculations with experimental data inevitably requires a model for converting the fluid to particles. For shear viscous fluids, several different conversion models have been proposed, such as the quadratic Grad corrections, the Strickland-Romatschke (SR) ansatz, self-consistent shear corrections from linearized kinetic theory, or corrections from the relaxation time approach. We show, via comparison to nonlinear $2\to 2$ kinetic theory evolution, that even for low specific shear viscosities $0.03\lesssim \eta /s\lesssim 0.2$, these four models have varying accuracy and still significant errors in reproducing particle phase space densities from hydrodynamic fields. Moreover, we demonstrate that the overall reconstruction error of additive shear viscous $f=f_{\mathrm{eq}}+\delta f$ models dramatically reduces by up to one order of magnitude, if one ensures through exponentiation that $f$ is always positive. We also illustrate how even more accurate viscous $\delta f$ models can be constructed by incorporating the first time derivatives of hydrodynamic fields to account for the past evolution of the system. Such time derivatives are readily available in hydrodynamic simulations, though usually not included in the output. Though our comparisons are limited to a one-component massless system undergoing a $(0+1)$-dimensional $(0+1\mathrm{D})$ longitudinal boost-invariant expansion, we expect that the improved models will be useful in $2+1\mathrm{D}$ and $3+1\mathrm{D}$ hydrodynamic studies as well.

中文翻译：

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相对论重离子碰撞的粘性流体动力学模型的改进单粒子相空间分布

流体力学计算与实验数据的比较不可避免地需要一个将流体转化为颗粒的模型。对于剪切粘性流体，已经提出了几种不同的转换模型，例如二次Grad校正，Strickland-Romatschke（SR）ansatz，线性动力学理论的自洽剪切校正或弛豫时间方法的校正。通过与非线性比较$2\to 2$ 动力学理论的演变，即使对于低比剪切粘度 $0.03\lesssim \eta /s\lesssim 0.2$，这四个模型在从水动力场再现粒子相空间密度时具有不同的精度，并且仍然存在很大的误差。此外，我们证明了附加剪切粘性的整体重建误差$F=F_{\mathrm{当量}}+\delta F$ 如果通过幂运算确保模型可以最大程度地减少一个数量级 $F$永远是积极的。我们还说明了粘性如何更加精确$\delta F$可以通过合并水动力场的第一时间导数来构建模型，以说明系统的过去演变。尽管通常不包括在输出中，但这些时间导数在流体动力学仿真中很容易获得。尽管我们的比较仅限于经历了$（0+\mathrm{1个}）$尺寸 $（0+\mathrm{1个}\mathrm{d}）$ 纵向助推不变膨胀，我们期望改进的模型将对 $2+\mathrm{1个}\mathrm{d}$ 和 $3+\mathrm{1个}\mathrm{d}$ 流体力学研究也是如此。