Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension
Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension
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DOI：
10.1088/1742-5468/2016/09/093211
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
V. Popkov;A. Schadschneider;Johannes Schmidt;Gunter M. Schutz
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文献类型：
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作者：
V. Popkov;A. Schadschneider;Johannes Schmidt;Gunter M. Schutz
在一维空间非线性脉动流体力学的框架内，对于特征速度不同的严格双曲情形，我们得到了动力结构函数的单圈模态耦合方程的精确解。所有的解决方案的特点是动态指数是开普勒比连续Fibonacci数，其中包括黄金平均值作为一个极限情况。所有高阶斐波那契模的标度形式都是非对称的Lévy分布。这样就建立了一个新的动力学普适类的层次结构。我们还计算了精确的数值的Prähofer-Spohn标度常数，从模式耦合理论得到的标度函数是敏感的。
We obtain the exact solution of the one-loop mode-coupling equations for the dynamical structure function in the framework of non-linear fluctuating hydrodynamics in one space dimension for the strictly hyperbolic case where all characteristic velocities are different. All solutions are characterized by dynamical exponents which are Kepler ratios of consecutive Fibonacci numbers, which includes the golden mean as a limiting case. The scaling form of all higher Fibonacci modes are asymmetric Lévy-distributions. Thus a hierarchy of new dynamical universality classes is established. We also compute the precise numerical value of the Prähofer–Spohn scaling constant to which scaling functions obtained from mode coupling theory are sensitive.