O'Malley Daniel, Cushman John H
Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette, Indiana 47906, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 1):011126. doi: 10.1103/PhysRevE.86.011126. Epub 2012 Jul 24.
Renormalization-group operators are used to classify stochastic processes on two time scales. Repeated application of one operator is associated with the long-time behavior of the process while the other is associated with the short-time behavior of the process. This approach is shown to be robust even in the presence of nonstationary increments and infinite second moments. Fixed points of the operators can be used for further subclassification of processes when appropriate limits exist. Several processes are classified using the renormalization-group scheme. The processes to be classified include advection-diffusion in an ergodic velocity field, and a model of diffusion in the human bronchial tree.
重整化群算子用于对两个时间尺度上的随机过程进行分类。一个算子的重复应用与过程的长期行为相关，而另一个算子与过程的短期行为相关。即使存在非平稳增量和无穷二阶矩，这种方法也被证明是稳健的。当存在适当的极限时，算子的不动点可用于对过程进行进一步的子分类。使用重整化群方案对几个过程进行了分类。要分类的过程包括遍历速度场中的平流扩散，以及人类支气管树中的扩散模型。
