标题： 直接相互作用近似在湍流问题中的广义随机模型的应用 显示英文标题

标题： Application of the Direct Interaction Approximation to generalized stochastic models in the turbulence problem

摘要： 本文的目的是考虑Kraichnan开发的直接相互作用近似（DIA）在湍流问题中的广义随机模型的应用。 以前的发展（Kraichnan，Shivamoggi等，Shivamoggi和Tuovila）基于Boltzmann-Gibbs对底层熵度量的假设，该度量表现出可扩展性，并适用于遍历系统。 在这里，我们考虑引入一种影响偏差，明确区分罕见事件和频繁事件，这适用于非遍历系统。 更具体地说，我们考虑将DIA应用于一个线性阻尼随机振子系统，使用具有底层非可扩展熵度量的Tsallis类型自相关模型，并描述由此产生的随机过程。 我们还推导了一些与本次研究相关的随机模型似乎新颖的数学性质——伽马分布和Tsallis非可扩展熵。 显示英文摘要

摘要： The purpose of this paper is to consider the application of the direct interaction approximation (DIA) developed by Kraichnan to generalized stochastic models in the turbulence problem. Previous developments (Kraichnan, Shivamoggi et al., Shivamoggi and Tuovila) were based on the Boltzmann-Gibbs prescription for the underlying entropy measure, which exhibits the extensivity property and is suited for ergodic systems. Here, we consider the introduction of an influence bias discriminating rare and frequent events explicitly, as behooves non-ergodic systems. More specifically, we consider the application of the DIA to a linear damped stochastic oscillator system using a Tsallis type autocorrelation model with an underlying non-extensive entropy measure, and describe the resulting stochastic process. We also deduce some apparently novel mathematical properties of the stochastic models associated with the present investigation -- the gamma distribution and the Tsallis non-extensive entropy.