多衰减通道模式耦合理论的标度方程
Scaling equations for mode-coupling theories with multiple decay channels
摘要：
多个弛豫通道经常出现在液体动力学中，其中与粒子守恒定律相关的动量流分成不同的贡献。例子是强烈限制的液体，在横向和纵向方向的电流的墙壁是非常不同的，或流体的非球形粒子与不同的松弛模式的平移和旋转自由度。在这里，我们进行了渐近分析的缓慢的结构弛豫动力学逮捕所描述的模式耦合理论（MCT）与几个松弛通道。与标准MCT相比，多个弛豫通道的存在显著改变了基本运动方程的结构，并导致渐近解中的额外的非平凡项。我们表明，解决方案可以重新缩放，从而证明了著名的$ β$标度方程的MCT仍然有效，即使在存在多个弛豫通道。渐近处理验证使用一种新的示意性模型。我们证明，这个示意性模型的数值解确实可以描述的渐近标度律接近动力学逮捕。此外，在低频磁化率谱中发现了两个不同衰变通道存在的清晰痕迹，这表明在受限或分子液体的模拟或实验中原则上可以检测到额外弛豫通道的清晰足迹。
英文摘要：
Multiple relaxation channels often arise in the dynamics of liquids where the momentum current associated to the particle-conservation law splits into distinct contributions. Examples are strongly confined liquids for which the currents in lateral and longitudinal direction to the walls are very different, or fluids of nonspherical particles with distinct relaxation patterns for translational and rotational degrees of freedom. Here, we perform an asymptotic analysis of the slow structural relaxation close to kinetic arrest as described by mode-coupling theory (MCT) with several relaxation channels. Compared to standard MCT, the presence of multiple relaxation channels significantly changes the structure of the underlying equations of motion and leads to additional, non-trivial terms in the asymptotic solution. We show that the solution can be rescaled, and thus prove that the well-known $ β$-scaling equation of MCT remains valid even in the presence of multiple relaxation channels. The asymptotic treatment is validated using a novel schematic model. We demonstrate that the numerical solution of this schematic model can indeed be described by the derived asymptotic scaling laws close to kinetic arrest. Additionally, clear traces of the existence of two distinct decay channels are found in the low-frequency susceptibility spectrum, suggesting that clear footprints of the additional relaxation channels can in principle be detected in simulations or experiments of confined or molecular liquids.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
