振幅展开相场晶体（APFC）建模中基于傅里叶伪谱法的高效位错模拟
Amplitude Expansion Phase Field Crystal (APFC) Modeling based Efficient Dislocation Simulations using Fourier Pseudospectral Method
AI总结：
本文提出一种基于傅里叶伪谱法的高效数值方法求解振幅展开相场晶体（APFC）方程，利用周期性和解析性精确施加边界条件，在2D三角和3D体心立方晶格上准确复现刃型位错应变场，验证了APFC模型模拟介观缺陷的潜力。
摘要：
晶体缺陷对材料性能有重要影响，因此需要精确的模拟方法。现有方法从原子尺度构型到连续弹性理论，在模拟位错引起的晶格变形方面均存在固有局限性。相场晶体（PFC）模型的振幅展开（APFC）通过介观描述弥补了这一差距。本文提出了一种计算高效的傅里叶伪谱法来求解APFC方程。该方法利用系统的周期性和解的解析性——其中解析性的严格证明仍是一个开放问题，本文对此进行了讨论——从而实现了周期边界条件的精确施加。在二维三角晶格和三维体心立方晶格上的数值实验表明，该方法能准确再现刃型位错的应变场，与连续介质理论的预测相符。这些结果证实了APFC模型在介观尺度上捕捉复杂缺陷结构的潜力，为模拟更复杂的缺陷动力学铺平了道路。
英文摘要：
Crystalline defects critically influence material properties, necessitating accurate simulation methods. Existing approaches, from atomic-scale configurations to continuum elasticity, face inherent limitations in modeling dislocation-induced lattice deformation. The amplitude expansion of the phase field crystal (APFC) model bridges this gap with a mesoscopic description. This paper introduces a computationally efficient Fourier pseudospectral method for solving the APFC equations. The method exploits system periodicity and solution analyticity--the latter's rigorous proof remaining an open question, as discussed herein--to enable precise implementation of periodic boundary conditions. Numerical experiments on 2D triangular and 3D body-centered cubic lattices demonstrate that the method accurately reproduces the strain fields of edge dislocations, matching continuum theory predictions. These results confirm the APFC model's potential for capturing complex defect structures at the mesoscale, paving the way for simulating more intricate defect dynamics.
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