Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy.
CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy.
PLoS One. 2019 Feb 22;14(2):e0212135. doi: 10.1371/journal.pone.0212135. eCollection 2019.
A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a Langevin-type stochastic equation from a time series of empirical data. Even if the protocol is based upon the introduction of drift and diffusion terms in stochastic differential equations, its implementation involves subtle conceptual problems and, most importantly, requires some prior theoretical knowledge about the system. Here we apply this approach to the data obtained in a rotational granular diffusion experiment, showing the power of this method and the theoretical issues behind its limits. A crucial point emerged in the dense liquid regime, where the data reveal a complex multiscale scenario with at least one fast and one slow variable. Identifying the latter is a major problem within the Langevin derivation procedure and led us to introduce innovative ideas for its solution.
预测物理系统的行为和理解其性质，即在某种期望的抽象层次上了解其工作方式。一种有前途的建模方法是从经验数据的时间序列中推导出朗之万型随机方程。即使协议基于在随机微分方程中引入漂移和扩散项，其实现也涉及微妙的概念问题，最重要的是，需要对系统有一些预先的理论知识。在这里，我们将这种方法应用于旋转颗粒扩散实验中获得的数据，展示了这种方法的威力及其局限性背后的理论问题。在密集液体状态下出现了一个关键点，数据显示出一个复杂的多尺度场景，至少有一个快变量和一个慢变量。在朗之万推导过程中，识别后者是一个主要问题，这促使我们提出了一些创新性的解决方案。
