Intrinsic Equations of Motion for Interfaces in Models of Solidification

提出了一种在小扩散渐近极限下推导两相过渡界面运动方程的方法，例如液体凝固成固体。研究者将证明界面的速度是其局部几何的函数，由所谓的固有量如曲率来描述。该模型可以计算球形颗粒在生长过程中变得不稳定的半径，并且可以更深入地了解凝固过程中所见的复杂枝晶结构。液体凝固的问题有许多工业应用，例如从熔体中生长出用于计算机芯片等半导体器件的石英晶体。对于这些应用，需要生长光滑、规则的晶体。不幸的是，许多物质往往会长成不规则的雪花状树突。在这项研究中，研究者提出了一种方法，以减少复杂的方程控制凝固相对简单的几何描述。这种还原可以预测从规则凝固到枝晶凝固的转变。它还可能对不规则树突结构形成和生长的过程提供一些见解。

A methodology is proposed for deriving equations of motion for interfaces in transition between two phases, such as the solidification of a liquid into a solid, in the asymptotic limit of small diffusion. The investigator will show that the velocity of the interface is a function of its local geometry, described by so-called intrinsic quantities such as the curvature. This model allows the computation of the radius at which a growing spherical particle becomes unstable and may allow a deeper understanding of the complex dendritic structures seen in solidification. The problem of the solidification of a liquid has many industrial applications, such as the growing of a quartz crystal from a melt for use in semiconductor devices like computer chips. For these applications it is desirable to grow smooth, regular crystals. Unfortunately, many substances tend to grow into irregular snowflake-like dendrites. In this study the investigator proposes a methodology for reducing the complex equations governing solidification to a relatively simple geometric description. This reduction should allow the prediction of the transition from regular to dendritic solidification. It may also give some insight into the process by which irregular dendritic structures form and grow.