Numerical and mathematical analysis of diffusion induced grain boundary motion

本研究旨在利用数学和计算技术研究扩散诱导晶界运动(DIGM)现象。晶界，通常是由不同结构组成的金属中非常薄的独立区域。当一块薄薄的金属片被放在含有不同金属的蒸汽中时，就会发生DIGM。蒸气中的原子扩散到板材中，但只扩散到晶界所在的区域。薄板中蒸汽原子的存在在金属中引起应力，作为这些应力的结果，晶界在薄板内移动。拟议研究的目的是分析这些晶界运动的数学模型，并产生可靠和有效的计算机代码，使计算机能够在三维空间模拟DIGM。

This research intends to use mathematical and computational techniques to study the phenomenon of diffusion induced grain boundary motion (DIGM). Grain boundaries, that are typically very thin, separate regions in metals that are made up of different structures. DIGM occurs when a thin sheet of metal is placed in a vapour that contains a different metal. The atoms from the vapour diffuse into the sheet but only in the areas where the grain boundaries are situated. The presence of the vapour atoms in the sheet causes stresses in the metal and as a result of these stresses the grain bounadies move within the sheet. The objective of the proposed research is to analyse mathematical models for the motion of these grain boundaries and to produce reliable and efficient computer codes that will enable computer simulations of DIGM in three space dimensions.