7 papers
Accurately computing quasiperiodic parabolic equations within finite-size domains via modeling quasiperiodic boundary conditions
Xiaofang Han, Kai Jiang, Meng Li
Quasiperiodic systems exhibit long-range order without decay and are naturally posed on the whole space. However, in practical applications, computations are performed on finite do…
Geometric construction of superintegrable Poisson projection chains via Poisson centralizers
Kai Jiang, Guorui Ma, Ian Marquette +2
We introduce a geometric framework for constructing superintegrable systems from Poisson centralizers (commutants) in the Lie-Poisson algebra of a complex semisim…
Quasiperiodic Elliptic Operators: Projection Method and Convergence Analysis
Kai Jiang, Jiaqi Tang, Qilong Zhai +1
Quasiperiodic elliptic operators (QEOs) serve as fundamental models in both mathematics and physics, as exemplified by their role in the numerical modeling of one-dimensional photo…
Amplitude Expansion Phase Field Crystal (APFC) Modeling based Efficient Dislocation Simulations using Fourier Pseudospectral Method
Xinyi Wei, Yangshuai Wang, Kai Jiang +1
Crystalline defects critically influence material properties, necessitating accurate simulation methods. Existing approaches, from atomic-scale configurations to continuum elastici…
Projection method for quasiperiodic elliptic equations and application to quasiperiodic homogenization
Kai Jiang, Meng Li, Juan Zhang +1
In this study, we address the challenge of solving elliptic equations with quasiperiodic coefficients. To achieve accurate and efficient computation, we introduce the projection me…
Convergence analysis of PM-BDF2 method for quasiperiodic parabolic equations
Kai Jiang, Meng Li, Juan Zhang +1
Numerically solving parabolic equations with quasiperiodic coefficients is a significant challenge due to the potential formation of space-filling quasiperiodic structures that lac…