慢动力学与堵塞堆积的几何结构
Slow Dynamics and the Geometry of Jammed Packings
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中文总结 AI 辅助
本研究比较颗粒堆积与p-自旋模型的最速下降路径，发现颗粒堆积受鞍点吸引且形状参数不变，而p-自旋参数更大，差异原因成谜。
中文摘要 AI 辅助
颗粒堆积能量景观中的鞍点主导着离散最速下降动力学，并最终决定了一个偏离力学平衡的堆积将遵循的路径以及它最终找到的稳定极小值。最终决定所得极小值的鞍点往往是低指数鞍点。对于具有解析能量景观的模型，如$p$-自旋模型，最速下降最小化路径受到高指数鞍点的影响，这些鞍点将系统拉向指数递减的鞍点，然后才到达极小值。在这里，我们考察了颗粒堆积的最速下降最小化路径，并将其与$p$-自旋模型进行比较。我们表明，颗粒堆积的最速下降最小化路径的行为类似于其光滑能量景观对应物，并被鞍点吸引。所有模型的指数随时间变化的曲线都遵循一个平移的、拉伸的指数函数。我们进一步表明，当能量景观被修改为解析的（谐振子阱中的高斯势）或非局域的（Mari-Krzakala-Kurchan）时，颗粒堆积的形状参数保持不变。另一方面，$p$-自旋具有显著更大的形状参数。其原因并非由于模型的维度、堆积分数、非解析性或哈密顿量的局域性。形状参数差异的确切原因\b{仍然}是一个未解之谜。
英文摘要
Saddle points in the energy landscape of granular packings dominate the discrete steepest descent dynamics and ultimately determine the path that an out of mechanical equilibrium packing will follow and the resulting stable minimum that it will find. The saddle points that ultimately determine the resulting minima tend to be low-index saddle points. For models with an analytic energy landscape, such as the $p$-spin model, the steepest descent minimization path is affected by higher-index saddle points, which pull the system towards saddle points of decreasing index before arriving at the minima. Here, we examine the steepest descent minimization path of granular packings and compare them to the $p$-spin model. We show that the granular packing steepest descent minimization paths act like their smooth energy landscape counterparts and get attracted by saddle points. The index versus time curves for all models follow a shifted, stretched exponential. We further show that the shape parameter for the granular packings is unchanged when the energy landscape is modified to become analytic (Gaussian potential in a harmonic well) or non-local (Mari-Krzakala-Kurchan). The $p$-spin, on the other hand, has a significantly larger shape parameter. The reason is not due to the dimensionality, packing fraction, nonanalyticity, or the locality of the Hamiltonian of the models. The exact reason for the discrepancy in the shape parameter is \st{still} an unsolved mystery.
发表机构
- University of Oregon（俄勒冈大学）
机构由 AI 辅助整理，请以论文原文为准。
