TY - GEN A1 - Dreyer, Wolfgang A1 - Kimmerle, Sven-Joachim T1 - Mean field diffusion models for precipitation in crystalline GaAs including surface tension and bulk stresses N2 - Based on a thermodynamically consistent model for precipitation in gallium arsenide crystals including surface tension and bulk stresses by Dreyer and Duderstadt, we propose different mathematical models to describe the size evolution of liquid droplets in a crystalline solid. The first class of models treats the diffusion-controlled regime of interface motion, while the second class is concerned with the interface-controlled regime of interface motion. Our models take care of conservation of mass and substance. We consider homogenised models, where different length scales of the experimental situation have been exploited in order to simplify the equations. These homogenised models generalise the well-known Lifshitz-Slyozov-Wagner model for Ostwald ripening. Mean field models capture the main properties of our system and are well adapted for numerics and further analysis. Numerical evidence suggests in which case which one of the two regimes might be appropriate to the experimental situation. KW - mean field approximation KW - homogenisation KW - semi-insulating GaAs KW - Ostwald ripening including mechanics Y1 - 2010 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/674 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6749 ER -