In the context of event-by-event hydrodynamic description, we analyze the implications of two models characterized by distinct initial conditions. The initial energy density of the first model adopts a Gaussian-type distribution, while those of the second one are features by high energy peripheral tubes. We calibrate the initial conditions of both models so that their initial probability distribution of eccentricity are mostly identical. Subsequently, the resultant scaled probability distributions of collective flow and the correlations between flow harmonic and eccentricity coefficients are investigated. Besides, the calculations are carried out for particle correlations regarding the symmetric cumulant, mixed harmonics, and nonlinear response coefficients. Although the resultant two-particle correlations possess similar shapes, numerical calculations indicate a subtle difference between the two models. To be specific, the difference resides in more detailed observables such as the probability distributions of elliptic flow as well as Pearson correlation coefficient regarding higher-order harmonics. We discuss several essential aspects concerning the linearity and nonlinearity between initial eccentricities and final state anisotropies. Further implications are addressed.

中文翻译：

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相对论重离子碰撞中流体动力学对初始几何的非线性响应

在逐个事件的流体动力学描述的背景下，我们分析了以初始条件不同为特征的两个模型的含义。第一个模型的初始能量密度采用高斯型分布，而第二个模型的初始能量密度则是高能外围管的特征。我们校准两个模型的初始条件，以使它们的初始偏心率分布基本相同。随后，研究了集体流动的最终定标概率分布以及流动谐波与偏心系数之间的相关性。此外，还针对与对称累积量，混合谐波和非线性响应系数有关的粒子相关性进行了计算。尽管最终的两粒子相关具有相似的形状，数值计算表明两个模型之间存在细微的差异。具体而言，差异在于更详细的可观察性，例如椭圆流的概率分布以及与高次谐波有关的皮尔逊相关系数。我们讨论了有关初始偏心率和最终状态各向异性之间的线性和非线性的几个基本方面。解决了进一步的影响。