稀释聚合物流中动量闭合与非线性变分近似福克-普朗克方程的等价性
An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow
AI总结：
本文研究了稀释聚合物流中动量闭合与非线性变分近似的等价性，通过变分框架实现了宏观构型张量的精确演化，并为非线性强迫定律下的简化近似方案提供了理论基础。
摘要：
我们严格建立了经典动量闭合与稀释聚合物流中线性化霍克弹簧链设定下福克-普朗克方程的非线性变分近似的等价性。变分公式基于狄拉克-弗兰克尔原理应用于一个高斯近似流形上，该流形配备了费舍尔-劳信息度量。我们证明了该流形在线性构型动力学下的不变性导致宏观构型张量的精确演化，恢复了经典的扩散Oldroyd-B闭合。虽然等价性仅在线性化设定下成立，但相关的变分框架提供了一个抽象的误差表示，并为具有非线性强迫定律的聚合物流的系统构造简化近似方案提供了起点。
英文摘要：
We establish the equivalence between a classical moment closure and a nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow in the linearized Hookean spring chain setting. The variational formulation is based on the Dirac-Frankel principle applied to a Gaussian approximation manifold endowed with the Fisher-Rao information metric. We show that the invariance of this manifold under the linear configurational dynamics yields an exact evolution for the macroscopic conformation tensor, recovering the classical diffusive Oldroyd-B closure. While the equivalence only holds in the linearized setting, the associated variational framework provides an abstract error representation. Thus it can serve in future work as a starting point for the systematic construction of reduced approximation schemes for polymeric flows with nonlinear forcing laws.
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