Lane formation in restricted geometries

对于特殊的二维和三维系统，已经从理论上预测了两组分粒子系统中粒子沿相反方向运动的通道的形成。到目前为止，对这一现象的实验证明只在很短的时间尺度上完成。因此，这种现象可以看作是一种瞬时现象，而不是一种真正的相变。基于密度泛函理论的模拟证实了这一实验结果。在这里，我们建议从实验和理论上研究表示周期边界条件的受限运动中的粒子运动。我们将研究运动的周期性对粒子相行为的影响，并期望找到稳定的车道形成区域。此外，相互作用粒子的单组分系统将形成层，这已在静止和运动系统中进行了研究。因此，我们将对类似的整体系统进行测量和模拟，然后将其作为周期性边界条件下颗粒流行为的参考系统。模拟和实验的结合使我们能够涵盖广泛的可能场景，并同时使我们有可能检查真实物理条件下模拟的假设和近似。通过这些研究，我们打算对统计物理中的一种现象给予理解，这种现象似乎存在于许多不同的系统中，但由于许多虚假效应可能会阻碍纯形式的出现，因此在其纯形式下极难识别。这种理解反过来将有助于更好地理解许多系统中传输过程中的有序现象，从生物细胞中的传输到管道中颗粒介质的传输。

The formation of lanes in a two-component system of particles, in which the components move in opposite directions, has been predicted theoretically for special 2d and 3d systems. Experimental proof of this phenomenon has so far been achieved on short timescales, only. Thus, the phenomenon can be regarded as a transient phenomenon and not as a real phase transition. Simulations based on density functional theory have confirmed this experimental result. Here we suggest studies of particle motion in restricted motion which represent periodic boundary conditions experimentally and theoretically. We will investigate the influence of the periodicity of the motion on the phase behaviour of the particles and expect to find stable regions of lane formation. In addition, single component systems of interacting particles will form layers, which have been investigated in resting and moving systems. Therefore, we will perform measurements and simulations of similar monolithic systems which then serve as reference systems for the behaviour of particle flow under periodic boundary conditions. The combination of simulation and experiments allows us to cover a wide range of possible scenarios and gives at the same time the possibility to check the assumptions and approximations of the simulations under real physical conditions. With these studies we intend to give understanding of a phenomenon in statistical physics, which seems to be present in a large variety of systems but is extremely difficult to identify in its pure form due to the fact that many spurious effects can hinder the occurrence of the pure form. This understanding, in turn, will provide better understanding of order phenomena in transport processes in many systems, ranging from transport in biological cells to transport of granular media in pipes