We model astrophysical disk surface brightness fluctuations as an inhomogeneous, anisotropic, time-dependent Gaussian random field. The field locally obeys the stochastic partial differential equation of a Mat\'ern field, which has a power spectrum that is flat at large scales and falls off as a power law at small scales. We provide a series of pedagogical examples and along the way provide a convenient parameterization for the local covariance. We then consider two applications to disks. In the first we generate a movie of a disk. In the second, by integrating over a movie of a disk, we generate synthetic light curves and show that the high frequency slope of the resulting power spectrum depends on the local covariance model. We finish with a summary and a brief discussion of other possible astrophysical applications.

中文翻译：

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作为非均匀、各向异性高斯随机场的圆盘

我们将天体物理磁盘表面亮度波动建模为非均匀、各向异性、时间相关的高斯随机场。该场局部服从 Mat\'ern 场的随机偏微分方程，其功率谱在大尺度上是平坦的，在小尺度下作为幂律下降。我们提供了一系列教学示例，并在此过程中为局部协方差提供了方便的参数化。然后我们考虑两个磁盘应用程序。首先，我们生成一个磁盘电影。在第二个中，通过对磁盘的电影进行积分，我们生成合成光曲线并表明所得功率谱的高频斜率取决于局部协方差模型。我们以总结和对其他可能的天体物理学应用的简要讨论结束。