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Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

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Chinese Physics B 2024年第1期33卷 581-590页

作者：孙志强侯国林乔艳芬刘金存 School of Mathematical Sciences Inner Mongolia UniversityHohhot 010021China

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

关键词： Hamiltonian system symplectic elasticity quasicrystals analytic solution state function

Topological states in quasicrystals

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Frontiers of physics 2022年第1期17卷 123-142页

作者： Jiahao Fan Huaqing Huang School of Physics Peking UniversityBeijing100871China Center for High Energy Physics Peking UniversityBeijing100871China Collaborative Innovation Center of Quantum Matter Beijing100871China

With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart.

关键词： topological states quasicrystals quantum Hall effect topological insulator topological superconductor

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quasicrystals

Open Journal of Physical Chemistry 2012年第1期2卷 7-14页

作者： Feridoun Samavat Mohammad Hossein Tavakoli Safdar Habibi Babak Jaleh Parisa Taravati Ahmad Department of Physics Bu-Ali Sina University Hamedan Iran

quasicrystals are material with perfect long-range order, but with no three-dimensional translation periodicity. They are typically binary and ternary metallic alloys. quasicrystals have characteristic physical properties. Some resemble those of periodic crystals while others have similar properties to amorphous alloys. Many of their mechanical physical prop- erties are quite unusual by the standards of common metals. The peculiar physical properties of quasicrystals certainly give rise to the hope that they may become of some practical importance in the future. Some of these properties are surface related. This provides the main motivation for surface scientists to study this material. In this paper;quasicrystals, types of them, physical properties, surface science and potential applications of them have been discussed.

关键词： Quasicrstals Icosahedral quasicrystals Polygonal quasicrystals Aperiodic Intermetallics

Elastic analysis of an elliptic notch in quasicrystals of point group 10 subjected to shear loading

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Chinese Physics B 2010年第4期19卷 322-327页

作者：李联和 College of Mathematics Science Inner Mongolia Normal University

Based on the stress potential and complex variable function method, this paper makes an elastic analysis of an elliptic notch subjected to uniform shear stress at infinity in quasicrystals with point group 10. With the aid of conformal transformation, an exact solution for the elliptic notch of the quasicrystals is obtained. The solution of the mode II Griffith crack as a special case is constructed. The stress intensity factor and energy release rate have been also obtained as a direct result of the crack solution.

关键词： quasicrystals plane elasticity elliptic notch stress potential

Linear and Nonlinear Optical Properties of quasicrystals

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Chinese Physics Letters 2004年第1期21卷 140-142页

作者：周详胡承正龚平朱家昆 DepartmentofPhysics WuhanUniversityWuhan430072

An investigation is carried out on the linear and nonlinear optical properties of quasicrystals. The linear and nonlinear susceptibilities are determined for two- and three-dimensional quasicrystals. The results show that for optical linearity, two-dimensional quasicrystals are uniaxial, while icosahedral quasicrystals are optically isotropic. Meanwhile all quasicrystals, except those with 5, 5m, N, Nmm (N = 8, 10, 12) symmetries, have no the first-order optical nonlinearity. The tensor scheme of the first order nonlinear susceptibility is the same for these eight exceptional kinds of quasicrystals.

关键词： quasicrystals

Complex variable method for an anti-plane elliptical cavity of one-dimensional hexagonal piezoelectric quasicrystals

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Chinese Journal of Aeronautics 2015年第4期28卷 1287-1295页

作者： Yu Jing Guo Junhong Xing Yongming School of Science Inner Mongolia University of Technology College of General Education Inner Mongolia Normal University

Based on the fundamental equations of piezoelasticity of quasicrystal media, using the symmetry operations of point groups, the linear piezoelasticity behavior of one-dimensional（1D）hexagonal quasicrystals is investigated and the piezoelasticity problem of 1D hexagonal quasicrystals is decomposed into two uncoupled problems, i.e., the classical plane elasticity problem of conventional hexagonal crystals and the phonon–phason-electric coupling elasticity problem of1 D hexagonal quasicrystals.The final governing equations are derived for the phonon–phasonelectric coupling anti-plane elasticity of 1D hexagonal quasicrystals.The complex variable method for an anti-plane elliptical cavity in 1D hexagonal piezoelectric quasicrystals is proposed and the exact solutions of complex potential functions, the stresses and displacements of the phonon and the phason fields, the electric displacements and the electric potential are obtained explicitly.Reducing the cavity into a crack, the explicit solutions in closed forms of electro–elastic fields,the field intensity factors and the energy release rate near the crack tip are derived.

关键词： Complex variable methodElliptical cavity Fracture mechanics Piezoelasticity quasicrystals

Elliptic holes in octagonal quasicrystals

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Chinese Physics B 2013年第1期22卷 411-414页

作者：李联和 College of Mathematical Science Inner Mongolia Normal University

The stress potential function theory for the plane elasticity of octagonal quasicrystals is developed. By introducing stress functions, a large number of basic equations involving the elasticity of octagonal quasicrystals are reduced to a single partial differential equation. Furthermore, we develop the complex variable function method （Lekhnitskii method） for anisotropic elasticity theory to that for quasicrystals. With the help of conformal transformation, an exact solution for the elliptic hole of quasicrystals is presented. The solution of the Griffith crack problem, as a special case of the results, is obtained. As a consequence, the phonon stress intensity factor is derived analytically.

关键词： quasicrystals plane elasticity elliptic hole stress potential

Complex variable method for plane elasticity of icosahedral quasicrystals and elliptic notch problem

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Science China(Physics,Mechanics & Astronomy) 2008年第7期51卷 773-780页

作者： LI LianHe1,2 & FAN TianYou1 1 Department of Physics, Beijing Institute of Technology, Beijing 100081, China 2 College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China Department of Physics Beijing Institute of Technology Beijing China College of Mathematics Science Inner Mongolia Normal University Hohhot China

The complex variable method for the plane elasticity theory of icosahedral quasicrystals is developed. Based on the general solution obtained previously, complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an analytic solution for the elliptic notch problem of the material is presented. The solution of the Griffith crack problem can be observed as a special case of the results. The stress intensity factor and energy release rate of the crack are also obtained.

关键词： icosahedral quasicrystals plane elasticity elliptic notch complex variable method

Evaluation of Some Fourier Integrals in N-Dimensional Space for the Theory of Dislocations in quasicrystals

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Wuhan University Journal of Natural Sciences 2001年第4期6卷 787-790页

作者： Yao Duan-zheng Ding Di-hua Wang Ren-hui Hu Cheng-zheng School of Physics and Technology Wuhan University Wuhan 430072 China

A method to evaluate some Fourier integrals is extended from two-dimensional (2-D) and three dimensional (3-D) spaces ton-dimensional (n-D) space, which are often used in the elasticity theory of dislocations in quasi... 详细信息

关键词： quasicrystals dislocation Fourier integral elasticity theory