Computational Methods for Problems in Material Science

这个项目涉及到材料科学相关问题的有效数值方法的发展。研究了薄膜生长连续介质模型数值解的计算问题。这些模型中许多都包含了表面扩散效应，这是非线性的四阶项。因此，从计算的角度来看，这些模型是非常僵硬的。由于表面扩散项是非线性的，使用隐式方法比较困难。提出了一种求解表面扩散运动的半隐式水平集新方法。他使用这种新方法将表面扩散的影响纳入多晶薄膜的模型中。他还开发了一种计算岛屿动力学的新方法，其中梯田上的原子被视为连续场，而岛屿边缘的原子被离散地处理。这种方法保留了连续体方法的潜在优势，但同时保留了岛屿动力学中存在的离散和随机效应。研究者包括边缘扩散，表面张力，成核和弹性的影响。这个问题的一个重要的计算方面是在复域中扩散方程的数值解。研究者研究了有效解决这个问题的新方法。薄膜有很多应用，从轴承涂层到半导体器件。在许多情况下，这些薄膜不是单晶，而是多晶，薄膜的质量取决于它的结构。例如，具有良好双轴结构的薄膜接近于单晶，可用于制造超导磁带。决定织构演变的一个重要物理效应是表面扩散，但这很难在数值上实现，研究人员计划开发一种半隐式水平集方法来研究多晶薄膜的生长。这项工作可以帮助提高对这些电影的基本理解。制备薄膜的另一个重要过程是分子束外延。精确模拟这一过程的标准方法是动力学蒙特卡罗。在许多情况下，这种方法可能很慢，而连续统模型有可能大大提高这种计算的速度。然而，连续模型忽略了离散和随机效应。研究者开发了混合模型，具有良好的物理保真度，但提供相当大的计算速度。

This project concerns the development of efficient numericalmethods for problems related to material science. Theinvestigator studies computational issues concerning thenumerical solution of continuum models for thin film growth. Manyof these models include effects for surface diffusion, which is anonlinear 4th order term. Consequently, these models are verystiff from a computational point of view. Because the surfacediffusion term is nonlinear, it is difficult to use implicitmethods. The investigator introduces a new semi-implicit levelset method for solving motion by surface diffusion. He uses thisnew method to incorporate the effects of surface diffusion intomodels of polycrystalline thin films. He also develops a newapproach for computing island dynamics, where the adatoms on theterraces are considered as a continuum field and the atoms on theedge of the island are treated discretely. This approach retainsthe potential advantage of continuum methods but at the same timepreserves the discrete and stochastic effects present in islanddynamics. The investigator includes effects of edge diffusion,surface tension, nucleation, and elasticity. An importantcomputational aspect of this problem is the numerical solution ofthe diffusion equation in a complex domain. The investigatorexamines new methods for the efficient solution of this problem. Thin films occur in a large number of applications, fromcoatings on bearings to semi-conductor devices. In many casesthese films are not single crystals but instead arepolycrystalline and the quality of the film can depend on itstexture. Films with good biaxial texture are close to being asingle crystal and have applications in the manufacture ofsuper-conducting tapes, for example. One important physicaleffect in determining the evolution of the texture is surfacediffusion, but this is difficult to implement numerically and theinvestigator plans to develop a semi-implicit level set method tostudy the growth of polycrystalline thin films. The work herecould help improve the fundamental understanding of these films.Another important process by which thin films are made ismolecular beam epitaxy. The standard method for accuratesimulation of this process is kinetic Monte Carlo. In manysituations this method can be slow, and continuum models have thepotential to greatly increase the speed of such computations.However, continuum models ignore discrete and stochastic effects.The investigator develops hybrid models that have good physicalfidelity but offer considerable computational speed.