Large Scale Lattice-Boltzmann Simulation of Liquid Crystals

在简单的流体中，原子或分子是无序的，可以自由流动。在晶体中，它们排列在晶格上，不能彼此移动，形成一种刚性材料。液晶介于两者之间：它们在某种意义上是有序的，而在另一些意义上是无序的。一个例子是当一块肥皂留在一片水中时，你会得到粘糊糊的东西：这是一个“微晶”液晶，其中的分子堆积成层。在晶体堆叠中，每一层都与下一层排列，但在层的平面上，材料是流动的。这就是它的“粘稠”感的原因。细度可以通过测量材料的“流变性”来量化。（流变学是研究流动行为的科学。）液晶包括许多用于笔记本电脑显示器、平板电视和其他设备的高科技材料。在许多这样的设备中，材料的流动（例如对电场的响应）是使设备工作或不工作的一部分。许多这样的设备使用“向列”液晶，其中棒状分子沿同一方向排列，但不是在晶格上；另一些则涉及“胆甾相”或（潜在的）“蓝相”液晶，其结构更为复杂。由于科学和技术的原因，正确理解液晶在应力和/或电场和磁场下的流动是非常重要的。这是一项非常艰巨的任务，原因有二。首先，需要考虑复杂的部分有序结构。其次，由于所谓的“缺陷”的存在，这种结构在实际材料中变得更加复杂。这些缺陷的类型非常具体，在每种类型的液晶中都有所不同。对向列方程来说，缺陷是奇怪的蠕虫状结构。（事实上，“向列”这个名字来自希腊语，意思是蠕虫。）在最简单的情况下，可以用笔和纸来求解描述纯液晶流动的方程，但当存在缺陷时，这几乎总是不可能的。该项目的目的是开发和使用在非常大的计算机上求解相关方程的方法。只有最大的计算机才能提供解决缺陷问题所需的高分辨率研究，因为这些是扩展的对象，与分子尺度相比很大。这项工作需要将简化方程本身的技巧（从描述中删除所有不必要的细节）与如何使大型计算机有效地求解此类方程的深入知识相结合。对于每种类型的液晶，我们计划解决缺陷影响流动行为的方式，以及流动影响缺陷组织的方式。这种影响循环导致了在实验室中看到的相当复杂的行为，如果理解了，可能会在下一代液晶技术中得到利用。

In simple fluids, the atoms or molecules are disordered and can flow freely. In a crystal, they are arranged on a lattice, and cannot move past one another, creating a rigid material. Liquid crystals are in between: they are ordered in some senses and disordered in others. An example is the slimy mess you get when a bar of soap is left in a patch of water: this is a 'smectic' liquid crystal, in which the molecules pack into layers. Each layer lines up with the next in a crystalline stack, but in the plane of the layers the material is fluid. This is responsible for its 'slimy' feel. The sliminess can be quantified by measuring the material's 'rheology'. (Rheology is the science of flow behaviour.) Liquid crystals include many high tech materials used in laptop displays, flat-screen TVs, and other devices. In many of these devices, the flow of the material (for example in response to an electric field) is part of what makes the device work or not work. Many of these devices use 'nematic' liquid crystals in which rod-shaped molecules are lined up in the same direction but are not on a lattice; others involve 'cholesteric' or (potentially) 'blue phase' liquid crystals whose structure is more complex.For both scientific and technological reasons it is very important to understand properly the flow of liquid crystals in response to stresses and/or electric and magnetic fields. This is a very difficult task for two reasons. Firstly, there is the complicated, partially ordered structure to consider. Secondly, this structure is made even more complex in real materials by the presence of so-called 'defects'. These defects are of quite specific types, different in each type of liquid crystal. For nematics the defects are strange worm-like structures. (In fact, the name 'nematic' comes from the greek word for a worm.) In the simplest cases it is possible to solve using pen and paper the equations that describe the flow of pure liquid crystals, but when defects are present this is almost always impossible. The aim of the project is to develop and use methods for solving the relevant equations on very large computers. Only the biggest computers can provide the high resolution studies needed to address the problem of defects, since these are extended objects, large compared to the molecular scale. The work involves combining skill in simplifying the equations themselves (removing all inessential details from the description) with in-depth knowledge of how to make large computers solve such equations efficiently. For each type of liquid crystal, we plan to address both the way defects influence the flow behaviour, and the way a flow affects the organization of defects. This circle of influence is responsible for quite complex behaviour that is seen in the laboratory and, if understood, might be exploited in the next generation of liquid crystal technologies.