50 MS10 Abstracts IP1 because of physical requirements like objectivity and plas- Diffusion Generated Motion for Large Scale Simu- tic indifference. The latter leads to the multiplicative de- lations of Grain Growth and Recrystallization composition of the strain tensor and asks to consider the plastic tensor as elements of multiplicative matrix group, A polycrystalline material consists of many crystallites which leads to strong geometric nonlinearities. We show called grains that are differentiated by their varying ori- how polyconvexity and time-incremental minimization can entation. These materials are very common, including be used to establish global existence for elastoplastic evo- most metals and ceramics. The properties of the network lutionary systems. of grains making up these materials influence macroscale properties, such as strength and conductivity. Hence, un- Alexander Mielke derstanding the statistics of the grain network and how it Weierstrass Institute for Applied Analysis and Stochastics evolves is of great interest. We describe new, efficient nu- Berlin merical algorithms for simulating with high accuracy on
[email protected] uniform grids the motion of grain boundaries in polycrys- tals. These algorithms are related to the level set method, but generate the desired geometric motion of a network IP4 of curves or surfaces (along with the appropriate bound- Gels and Microfluidic Devices ary conditions) by alternating two very simple operations for which fast algorithms already exist: Convolution with a Gels are materials that consist of a solid, crosslinked sys- kernel, and the construction of the signed distance function tem in a fluid solvent. They are over-whelmingly present to a set. Motions that can be treated with these algorithms in biological systems and also occur in many aspects of include grain growth under misorientation dependent sur- materials applications.