2023/10/11 by Gang Cui, Kai Jiang, Cui, Gang +3 · 2 citations
Materials Science · #37M05 #37N30 #49K35 #Crystallization and Solubility Studies #FOS: Mathematics #Numerical Analysis (math.NA) #Quasicrystal Structures and Properties #X-ray Diffraction in Crystallography
paper · pdf · doi:10.48550/arxiv.2310.07108
openalex publication_date 2023/10/11 · openalex created_date 2023/10/13 · openalex updated_date 2026/07/28
In this work, we propose an efficient nullspace-preserving saddle search (NPSS) method for a class of phase transitions involving translational invariance, where the critical states are often degenerate. The NPSS method includes two stages, escaping from the basin and searching for the index-1 generalized saddle point. The NPSS method climbs upward from the generalized local minimum in segments to overcome the challenges of degeneracy. In each segment, an effective ascent direction is ensured by keeping this direction orthogonal to the nullspace of the initial state in this segment. This method can escape the basin quickly and converge to the transition states. We apply the NPSS method to the phase transitions between crystals, and between crystal and quasicrystal, based on the Landau-Brazovskii and Lifshitz-Petrich free energy functionals. Numerical results show a good performance of the NPSS method.