论文标题
不均匀的随机性对平均场理论的伪造性的影响，并产生了积聚盘建模的示例
Influence of inhomogeneous stochasticity on the falsifiability of mean-field theories and examples from accretion disc modeling
论文作者
论文摘要
尽管湍流天体物理系统中的空间和时间波动，但平均场理论仍可以用来描述其世俗的进化。但是，随时间尺度的观测比动态时间尺度短得多。与平均场理论相比，只有当该理论还以量化精度提供时，才能伪造后者。仅当波动对可观察到的恒定相干尺度线性贡献时，中心极限定理才能对精度进行适当的估计。在这里，我们引入了一个误差传播公式，该公式将放宽这两个局限性，从而允许可观察到的非线性功能形式和不均匀的相干尺度和波动的振幅。该方法在积聚盘理论的背景下进行了例证，在积聚盘理论的背景下，表面温度中的不均匀波动传播到圆盘发射谱 - 后者是前者的非线性和非局部功能。派生的精度非单调取决于发射频率。使用相同的方法，我们研究了望远镜数据中的bin频谱波动如何随频谱分辨能力而变化。我们讨论了对平均场理论的伪造性的更广泛含义。
Despite spatial and temporal fluctuations in turbulent astrophysical systems, mean-field theories can be used to describe their secular evolution. However, observations taken over time scales much shorter than dynamical time scales capture a system in a single state of its turbulence ensemble. Comparing with mean-field theory can falsify the latter only if the theory is additionally supplied with a quantified precision. The central limit theorem provides appropriate estimates to the precision only when fluctuations contribute linearly to an observable and with constant coherent scales. Here we introduce an error propagation formula that relaxes both limitations, allowing for nonlinear functional forms of observables and inhomogeneous coherent scales and amplitudes of fluctuations. The method is exemplified in the context of accretion disc theories, where inhomogeneous fluctuations in the surface temperature are propagated to the disc emission spectrum--the latter being a nonlinear and non-local function of the former. The derived precision depends non-monotonically on emission frequency. Using the same method, we investigate how binned spectral fluctuations in telescope data change with the spectral resolving power. We discuss the broader implications for falsifiability of a mean-field theory.
