Athreya Badrinarayan P, Goldenfeld Nigel, Dantzig Jonathan A
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, Illinois 61801, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jul;74(1 Pt 1):011601. doi: 10.1103/PhysRevE.74.011601. Epub 2006 Jul 17.
We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time.
