Renormalization Group Approach to Multiscale Modelling in Materials Science

摘要: Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range length scales from atomic up to sample dimensions. The phase field approach Langer, enhanced by optimal asymptotic methods adaptive mesh refinement, copes with this scales, provides an effective way move boundaries. However, it fails preserve memory underlying crystallographic anisotropy, thus is ill-suited for problems involving defects or elasticity. crystal (PFC) equation—a conserving analogue Swift-Hohenberg equation—is equation periodic solutions that represent density. It can natively model elasticity, solid phases, accurately reproduces nonequilibrium dynamics transitions real materials. PFC models matter at scale, rendering unsuitable coping serious interest. Here, we show computationally-efficient multiscale be developed systematically using renormalization group equivalent techniques derive appropriate coarse-grained coupled amplitude equations, which are suitable solution refinement algorithms.