Lemaître Anaël
Laboratoire Navier (UMR 8205), Université Paris-Est, CNRS, ENPC, IFSTTAR, 2 allée Képler, F-77420 Marne-la-Vallée, France.
J Chem Phys. 2015 Oct 28;143(16):164515. doi: 10.1063/1.4933235.
It was recently proposed that the local rearrangements governing relaxation in supercooled liquids impress on the liquid medium long-ranged (Eshelby) stress fluctuations that accumulate over time. From this viewpoint, events must be characterized by elastic dipoles, which are second order tensors, and Eshelby fields are expected to show up in stress and stress increment correlations, which are fourth order tensor fields. We construct here an analytical framework that permits analyzing such tensorial correlations in isotropic media in view of accessing Eshelby fields. Two spherical bases are introduced, which correspond to Cartesian and spherical coordinates for tensors. We show how they can be used to decompose stress correlations and thus test such properties as isotropy and power-law scalings. Eshelby fields and the predicted stress correlations in an infinite medium are shown to belong to an algebra that can conveniently be described using the spherical tensor bases. Using this formalism, we demonstrate that the inherent stress field of 3D supercooled liquids is power law correlated and carries the signature of Eshelby fields, thus supporting the idea that relaxation events give rise to Eshelby stresses that accumulate over time.
最近有人提出，在过冷液体中控制弛豫的局部重排会在液体介质中产生随时间累积的长程（埃舍尔比）应力涨落。从这个观点来看，事件必须由弹性偶极子来表征，弹性偶极子是二阶张量，并且预计埃舍尔比场会出现在应力和应力增量关联中，而应力和应力增量关联是四阶张量场。我们在此构建一个分析框架，以便在考虑到获取埃舍尔比场的情况下分析各向同性介质中的此类张量关联。引入了两个球基，它们分别对应于张量的笛卡尔坐标和球坐标。我们展示了如何用它们来分解应力关联，从而检验诸如各向同性和幂律标度等性质。无限介质中的埃舍尔比场和预测的应力关联被证明属于一个代数，该代数可以方便地用球张量基来描述。使用这种形式体系，我们证明了三维过冷液体的固有应力场具有幂律相关性，并带有埃舍尔比场的特征，从而支持了弛豫事件会产生随时间累积的埃舍尔比应力这一观点。
