空间随机关联势诱发内禀摩擦的微观机制研究

The problems in reality have a high degree of complexity, and a reaction process is often accompanied by the presence of impurities. As a non-ideal mode, the spatial random correlated potential is often used to reflect the effect of micro-spatial structure on system particles. In this project, the motion behavior of experimental particles is studied by superposing that with different external potential fields. The specific contents include: Based on the Monte Carlo simulation and the double-statistical-averaging approach, the increasing damping of experimental particles in rough potential fields has been confirmed; further more, the analytical expressions for the damping is deduced and the influence factors are analyzed correspondingly; more importantly, the physical mechanism of advantageous friction caused by the roughness is studied;in addition, a spectrum method will be developed for simulating space and time correlated noise sources, which is used to simulate the inherent spatio-temporal disorder in biological and physical systems. The purpose of this project is to find out the micro-mechanism of intrinsic friction induced by spatial random correlation potential in the disorder media, to understand the origin of friction force on particles to the greatest extent, and ultimately to reveal the new mechanism of abnormal diffusion. It is confident that this project will provide theoretical and methodological help for the experiments of related disciplines.

真实的反应过程常常伴随着缺陷、杂质或者其他形式的无序结构的产生，空间随机关联势作为一个非理想模型，可以用来体现微观空间结构对系统粒子的作用。本项目通过将其与不同外部势场进行叠加，对实验粒子的运动行为进行了研究。具体内容包括：基于蒙特卡罗模拟及双统计平均方法，证实不同粗糙势场中实验粒子受到的阻尼增加；解析推导得到势场不光滑时粒子受到的阻尼表达式，分析影响粒子阻尼的因素；研究较大系统中随机关联势形成有利摩擦的物理机制；发展谱方法产生任意时间与空间关联噪声，模拟生物及物理系统中固有的时空无序。本项目旨在搞清破缺媒介中由空间随机关联势诱发内禀摩擦的微观机制，最大程度地弄清楚粒子受到摩擦力的起源，从而进一步地揭示引起反常扩散的新机制，并为相关学科的实验提供理论和方法的帮助。

本项目采用空间随机关联势描述介质破缺程度，对破缺环境中实验粒子的运动行为进行了研究。基于蒙特卡罗模拟及双统计平均方法，证实了不光滑的空间势场会导致实验粒子受到的阻尼增加。若将空间随机关联势与亚稳势这样的小系统叠加，势场的不光滑使得粒子扩散变慢。但在倾斜周期势系统中，势场的不光滑更容易使粒子的“锁态”与“跑态”分离，导致粒子分布波包的包络线变宽甚至出现“输运改变扩散规律”的现象。通过研究不光滑倾斜周期势中莱维粒子的运动行为，发现与反常扩散对应的外力值区域发生后移，并且有效扩散指数被放大的现象。对粒子速度分布进行统计，可直观体现出不同偏压下“跑态”和“锁态”的转换。若将OU噪声驱动的粒子置于以上环境中，粒子的有效扩散系数显著增强。并且伴随势场不光滑程度的增加，扩散增强效果越发明显。此外，若噪声关联时间增加，粒子运动加快进入“跑态”，而关联时间足够大时，粒子空间分布的宽度急剧下降，使得粒子处于“锁态”。为了更加准确理解不光滑势场中粒子所受摩擦的机制，我们考虑有限势垒高度修正，利用改进的反应流理论，得到了一维倾斜周期势中粒子所受阻尼和逃逸速率的解析表达式。再将其应用到确定形式的空间关联随机势上，试图得到速度概率密度满足的福克—普朗克方程，以用来解析地表示粒子所受阻尼。另外，我们对具有时空关联特性的随机势也进行了一定的研究，观察有限势垒中逃逸速率出现了非单调行为，具体位置与空间关联长度和关联时间有关。相信我们的研究能为相关学科的实验提供理论和方法的帮助。