caa a22 4500 467893233 CHVBK 20180406152755.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s10955-005-9013-7 doi (NATIONALLICENCE)springer-10.1007/s10955-005-9013-7 Renormalization Group Approach to Multiscale Modelling in Materials Science [Elektronische Daten] [Nigel Goldenfeld, Badrinarayan Athreya, Jonathan Dantzig] Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range of length scales from the atomic up to sample dimensions. The phase field approach of Langer, enhanced by optimal asymptotic methods and adaptive mesh refinement, copes with this range of scales, and provides an effective way to move phase boundaries. However, it fails to preserve memory of the underlying crystallographic anisotropy, and thus is ill-suited for problems involving defects or elasticity. The phase field crystal (PFC) equation—a conserving analogue of the Swift-Hohenberg equation—is a phase field equation with periodic solutions that represent the atomic density. It can natively model elasticity, the formation of solid phases, and accurately reproduces the nonequilibrium dynamics of phase transitions in real materials. However, the PFC models matter at the atomic scale, rendering it unsuitable for coping with the range of length scales in problems of serious interest. Here, we show that a computationally-efficient multiscale approach to the PFC can be developed systematically by using the renormalization group or equivalent techniques to derive appropriate coarse-grained coupled phase and amplitude equations, which are suitable for solution by adaptive mesh refinement algorithms. Springer Science + Business Media, Inc., 2006 multiscale nationallicence pattern formation nationallicence renormalization group nationallicence grain growth nationallicence Goldenfeld Nigel Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, 61801-3080, Urbana, Illinois, USA aut Athreya Badrinarayan Department of Mechanical and Industrial Engineering, 1206 West Green Street, 61801, Urbana, IL, USA aut Dantzig Jonathan Department of Mechanical and Industrial Engineering, 1206 West Green Street, 61801, Urbana, IL, USA aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/5-6(2006-12-01), 1015-1023 0022-4715 125:5-6<1015 2006 125 10955 https://doi.org/10.1007/s10955-005-9013-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-9013-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goldenfeld Nigel Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, 61801-3080, Urbana, Illinois, USA aut NATIONALLICENCE 700 1- Athreya Badrinarayan Department of Mechanical and Industrial Engineering, 1206 West Green Street, 61801, Urbana, IL, USA aut NATIONALLICENCE 700 1- Dantzig Jonathan Department of Mechanical and Industrial Engineering, 1206 West Green Street, 61801, Urbana, IL, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/5-6(2006-12-01), 1015-1023 0022-4715 125:5-6<1015 2006 125 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer