Collective and tracer dynamics in single-file transport through periodic structures

单列输运是指多粒子系统中的运动，其中粒子由于相互作用和空间限制而不能相互超越。在本课题中，我们考虑了具有单列特征的扩散介质的随机布朗运动。这种类型的运动在自然界和技术中随处可见，每当颗粒被迫通过直径仅略大于颗粒大小的狭窄孔洞时。最主要的例子是在晶态铝硅酸盐(沸石)、膜通道、纳米管、微纳流体设备中的通道中的扩散，以及在使用先进的光学和磁操纵技术的实验中的胶体运动。虽然这些和其他例子通常涉及周期结构，但到目前为止，理论工作主要集中在相对于单个标记粒子(示踪物)的反常次扩散的空间均匀系统，或者关于集体输运性质的过于简化的离散系统。对于通过周期结构的单列布朗运动中的示踪物和集体动力学的理解仍然是空白。在这个双边项目中，我们的目标是通过开发用于分析它们的范例模型和方法来填补这一空白。这既包括分析方法，也包括有效的模拟技术。我们的具体目标是发展一个完整的粒子行为类似坚硬球体的理论，这将作为进一步研究其他类型的短程粒子相互作用和具有不同类型粒子的系统的基础。特别强调通过观察示踪剂在周期结构中位置之间的跃迁动力学来探索集体行为的不同阶段的可能性。对于理想化的一维单文件传输的结果，将就其对相应的全三维孔隙结构的有效性进行检验。

Single-file transport refers to the motion in a many-particle system,where the particles cannot overtake each other because of theirinteractions and spatial confinements. In this project the stochasticBrownian motion of diffusion agents with single-file character isconsidered. This type of motion occurs ubiquitously in nature andtechnology whenever particles are forced to move through narrow poreswith diameters only slightly larger than the particle size. Prominentexamples are diffusion in crystalline aluminosilicates (zeolites),membrane channels, nanotubes, channels in micro- and nanofluidicdevices, as well as colloid motions in experiments with advancedoptical and magnetic manipulation techniques. While these and otherexamples typically involve periodic structures, theoretical work hasmainly focused so far on spatially homogeneous systems with respect tothe anomalous subdiffusion of a single tagged particle (tracer), or onoversimplified discrete systems with respect to collective transportproperties. An understanding of tracer and collective dynamics insingle-file Brownian motion through periodic structures is stillmissing. In this bilateral project, we aim to fill this gap bydeveloping paradigmatic models and methods for their analysis. Thisincludes both analytical approaches and efficient simulationtechniques. Our specific objectives are to develop a full theory forparticles behaving like hard spheres, which will serve as a basis forfurther investigations of other types of short-range particleinteractions and systems with different types of particles.Particular emphasis will be put on the possibility to probe differentphases of collective behavior by observing a tracer's transitionkinetics between sites in the periodic structures. Resultsobtained for idealized one-dimensional single-file transport will bechecked with respect to their validity for corresponding fullthree-dimensional pore structures.