A Hamiltonian System Solution Method for Planar Problems of 2D Quasicrystals

LI Tong; QU Jianlong; WANG Wei; WANG Chenlong; XU Xinsheng

doi:10.21656/1000-0887.450204

Volume 45 Issue 11

Nov. 2024

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LI Tong, QU Jianlong, WANG Wei, WANG Chenlong, XU Xinsheng. A Hamiltonian System Solution Method for Planar Problems of 2D Quasicrystals[J]. Applied Mathematics and Mechanics, 2024, 45(11): 1359-1371. doi: 10.21656/1000-0887.450204

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A Hamiltonian System Solution Method for Planar Problems of 2D Quasicrystals

doi: 10.21656/1000-0887.450204

School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China

Received Date: 2024-07-10
Rev Recd Date: 2024-08-16

Available Online: 2024-12-02

Abstract

Abstract

Aimed at the planar problem of 2D quasicrystals, the problem was transformed into one of symplectic eigenvalues and symplectic eigensolutions through introduction of the Hamiltonian system. In the Hamiltonian system, the solution to this problem was expressed by a series of symplectic eigensolutions. With the symplectic conjugate orthogonality relationship between symplectic eigensolutions, the solving problem satisfying boundary conditions can be reduced to a problem of solving algebraic equations, thus to form an analytical solution method. The proposed method can be directly extended to solve the problems of mixed boundary conditions and segmented boundary conditions.
- 2D quasicrystal,
- Hamiltonian system,
- symplectic conjugate orthogonality,
- symplectic method,
- planar problem

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References(30)

References

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