On Power Law Scaling Dynamics for Time-Fractional Phase Field Models During Coarsening
Document Type
Article
Journal/Book Title/Conference
Communications in Nonlinear Science and Numerical Simulation
Volume
70
Publisher
Elsevier BV
Publication Date
10-24-2018
Award Number
NSF, Division of Mathematical Sciences 1816783
Funder
NSF, Division of Mathematical Sciences
First Page
257
Last Page
270
Abstract
In this paper, the energy scaling behavior of the time-fractional phase field models is investigated. We report a seminal observation that the effective free energy of the time-fractional phase field models obeys a general power-law scaling dynamics during coarsening. Mainly, the effective free energy and roughness in the time-fractional phase field models scale by following a similar power law as the integer phase field models, where the power is linearly proportional to the fractional order. This general scaling law is verified numerically against several classes of phase field models, including the Cahn–Hilliard equation with different types of variable mobilities and the molecular beam epitaxy models. This new finding opens potential paths of applying time-fractional phase field models in studying anomalous coarsening dynamics.
Recommended Citation
Zhao, Jia, et al. “On Power Law Scaling Dynamics for Time-Fractional Phase Field Models during Coarsening.” Communications in Nonlinear Science and Numerical Simulation, vol. 70, May 2019, pp. 257–70. DOI.org (Crossref), doi:10.1016/j.cnsns.2018.10.019.
