RUI: Interfacial Pattern Formation

凝聚态系统中界面的宏观形式通常由微观效应决定（如晶体的各向异性，原子与表面的结合能，或由非均质性引起的界面的随机固定）。因此，对界面形状的研究可以带来基本的见解。这个项目特别关注非平衡系统中的界面。它的目的是建立(a)为平衡系统开发的经过验证的概念在理解那些远离平衡的系统方面的有用程度，以及(b)对界面模式的宏观连续统解释的可能程度。计划研究三个主要领域：(1)多面晶体的动力学粗化，其中晶体形状在生长过程中变得圆润；(2)枝晶（雪花状结构）等复杂界面的生长，特别是晶体各向异性的作用和复杂图案的发展；(3)在随机多孔介质中运动的流体界面的形式和动力学。这些实验将利用哈弗福德在之前的资助期间开发的高精度数字图像处理方法。该RUI项目将采用研究生和本科生之间的合作，以提高本科研究的效率，并帮助解决对本科教育感兴趣的有能力的研究人员严重短缺的问题。

The macroscopic forms of interfaces in condensed matter systems are often determined by microscopic effects (such as crystalline anisotropy, the binding energy of atoms to the surface, or random pinning of the interface by inhomogeneities). Therefore, studies of interfacial shapes can lead to fundamental insights. This project is especially concerned with interfaces in non- equilibirum systems. It is intended to establish (a) the degree to which proven concepts developed for equilibrium systems are useful in understanding those driven away from equilibrium and (b) the degree to which a macroscopic continuum explanation of interfacial patterns is possible. Three major areas of investigation are planned: (1) the kinetic roughening of faceted crystals, in which crystal shapes become rounded during growth; (2) the growth of dendritic crystals (snowflake-like structures) and other complex interfaces, especially the role of crystalline anistropy and the development of complex patterns; and (3) the form and dynamics of a fluid interface moving in a random porous medium. The experiments will utilize high precision digital image processing methods developed at Haverford during the previous grant period. This RUI project will employ collaborations between graduate and undergraduate students, both to enhance the effectiveness of undergraduate research and to help address the severe shortage of capable researchers interested in undergraduate education.