Computational and analytical studies of a new nonlocal phase-field crystal model in two dimensions

Du, Qiang1,2; Wang, Kai3; Yang, Jiang4,5

2024-09-01

10.1142/S0218202524500441

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   影响因子和分区

0218-2025

1793-6314

A nonlocal phase-field crystal (NPFC) model is presented as a nonlocal counterpart of the local phase-field crystal (LPFC) model and a special case of the structural PFC (XPFC) derived from classical field theory for crystal growth and phase transition. The NPFC incorporates a finite range of spatial nonlocal interactions that can account for both repulsive and attractive effects. The specific form is data-driven and determined by a fitting to the materials structure factor, which can be much more accurate than the LPFC and previously proposed fractional variant. In particular, it is able to match the experimental data of the structure factor up to the second peak, an achievement not possible with other PFC variants studied in the literature. Both LPFC and fractional PFC (FPFC) are also shown to be distinct scaling limits of the NPFC, which reflects the generality. The advantage of NPFC in retaining material properties suggests that it may be more suitable for characterizing liquid-solid transition systems. Moreover, we study numerical discretizations using Fourier spectral methods, which are shown to be convergent and asymptotically compatible, making them robust numerical discretizations across different parameter ranges. Numerical experiments are given in the two-dimensional case to demonstrate the effectiveness of the NPFC in simulating crystal structures and grain boundaries.

Nonlocal phase-field crystal models Fourier spectral methods asymptotically compatible schemes crystal lattices structure factor grain boundary

SCI

英语

通讯

NSF["DMS 2309245","DMS-1937254"] ; National Science Foundation of China[NSFC-12271240] ; Shenzhen Natural Science Fund[RCJC20210609103819018]

Mathematics

Mathematics, Applied

WOS:001310073800002

WORLD SCIENTIFIC PUBL CO PTE LTD

Web of Science

1.Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA
2.Columbia Univ, Data Sci Inst, New York, NY 10027 USA
3.Cent South Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China
4.Southern Univ Sci & Technol, Shenzhen Int Ctr Math, Dept Math, Shenzhen NCAMS, Shenzhen, Peoples R China
5.Southern Univ Sci & Technol, Natl Ctr Appl Math, Shenzhen NCAMS, Shenzhen, Peoples R China

Du, Qiang,Wang, Kai,Yang, Jiang. Computational and analytical studies of a new nonlocal phase-field crystal model in two dimensions[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES,2024.

Du, Qiang,Wang, Kai,&Yang, Jiang.(2024).Computational and analytical studies of a new nonlocal phase-field crystal model in two dimensions.MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES.

Du, Qiang,et al."Computational and analytical studies of a new nonlocal phase-field crystal model in two dimensions".MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2024).