论文标题
路径积分描述和弹性板湍流的直接相互作用近似
Path integral description and direct interaction approximation for elastic plate turbulence
论文作者
论文摘要
在这项工作中，我们将Martin-Siggia-Rose路径积分形式形式应用于薄弹性板的方程。使用示意技术，我们获得了直接相互作用近似（DIA）方程，以描述相关函数的演变和磁场的响应函数。与先前的结果一致，我们表明弹性板的DIA方程可以从非巨摩夫的随机过程中得出，并且在弱非线性极限中，DIA方程导致波湍流理论的动力学方程。我们预计这种方法将可以更好地理解波湍流的统计特性，并且DIA方程可以为理解弹性板的弱非线性湍流的细分开放新途径。
In this work, we apply the Martin-Siggia-Rose path integral formalism to the equations of a thin elastic plate. Using a diagrammatic technique, we obtain the direct interaction approximation (DIA) equations to describe the evolutions of the correlation function and the response function of the fields. Consistent with previous results, we show that DIA equations for elastic plates can be derived from a non-markovian stochastic process and that in the weakly nonlinear limit, the DIA equations lead to the kinetic equation of wave turbulence theory. We expect that this approach will allow a better understanding of the statistical properties of wave turbulence and that DIA equations can open new avenues for understanding the breakdown of weakly nonlinear turbulence for elastic plates.
