Group-theoretical method for physical property tensors of quasicrystals

In addition to the phonon variable there is the phason variable in hydrodynamics for quasicrystals. These two kinds of hydrodynamic variables have different transformation properties. The phonon variable transforms under the vector representation, whereas the phason variable transforms under another related representation. Thus, a basis (or a set of basis functions) in the representation space should include such two kinds of variables. This makes it more difficult to determine the physical property tensors of quasicrystals. In this paper the group-theoretical method is given to determine the physical property tensors of quasicrystals. As an illustration of this method we calculate the third-order elasticity tensors of quasicrystals with five-fold symmetry by means of basis functions. It follows that the linear phonon elasticity is isotropic, but the nonlinear phonon elasticity is anisotropic for pentagonal quasicrystals. Meanwhile, the basis functions are constructed for all noncrystallographic point groups of quasicrystals.     

Thermodynamics of equilibrium properties of quasicrystals

Thermodynamics of equilibrium properties of crystals has been generalized to the case of quasicrystals. Based on it, relations between direct and converse effects, and some relations between the coefficients measured under different conditions have been derived. By group representation theory, physical property tensors have been derived for two-dimensional pentagonal, octagonal, decagonal and dodecagonal, and three-dimensional icosahedral and cubic quasicrystals.     

Isotropic and anisotropic physical properties of quasicrystals

Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.     

Topological states in quasicrystals

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.     

含相变材料玻璃类围护结构传热系数分析

建立太阳辐射加热下含半透明相变材料类玻璃围护结构的一维相变导热和辐射耦合稳态传热模型,采用控制容积法结合布格尔定律,数值求解含相变材料玻璃围护结构内部的能量传递,分析相变材料的辐射物性参数和室内外环境因素对其传热系数的影响.结果表明,计算相变材料类玻璃围护结构传热系数需要考虑其半透明性;传热系数不仅受物性参数和环境因素的影响,还与材料的液相率与透光率等因素有关.     

准晶结构的激光全息人工制作

报道了用激光全息刻写技术结合感光聚合材料体系制作介观尺度二维准周期结构(准晶). 并在前期工作的基础上，研究了不同曝光量对二维空气柱孔径的影响，不同偏振对准晶结构花样的影响. 实验结果显示，可以制作的二维准晶的空气柱孔径可达100nm，而且结构均匀，无缺陷面积大. 用此实验系统可以制作多种花样二维甚至是三维准晶结构. 目前，除激光全息刻写技术外，用其他传统精密机械加工技术来人工制作介观准晶体尚存在很大挑战性. 关键词： 准晶结构 光子晶体 激光全息技术     

非中性电解液的光子相关光谱

本文研究了非中性电解液光散射动态特性问题,导出了一元非中性电解液和二元非中性电解液的光子相关光谱。结果表明:它们的光子相关光谱是时间衰减谱,衰减系数同扩散系数只差因子q~2,微弱的非中性使利用光子相关光谱测得的扩散系数显著增加,且与散射角的关系更为密切。对于10~(-3)molar的稀薄电解液,1%的非中性就使扩散系数增大10~2～10~3倍以上。最后,本文对造成非中性效应的物理机制进行了分析。     

Uphill anomalous transport in a deterministic system with speed-dependent friction coefficient

We investigate the transport of a deterministic Brownian particle theoretically, which moves in simple onedimensional, symmetric periodic potentials under the influence of both a time periodic and a static biasing force. The physical system employed contains a friction coefficient that is speed-dependent. Within the tailored parameter regime, the absolute negative mobility, in which a particle can travel in the direction opposite to a constant applied force, is observed.This behavior is robust and can be maximized at two regimes upon variation of the characteristic factor of friction coefficient. Further analysis reveals that this uphill motion is subdiffusion in terms of localization(diffusion coefficient with the form D(t) ~t~(-1) at long times). We also have observed the non-trivially anomalous subdiffusion which is significantly deviated from the localization; whereas most of the downhill motion evolves chaotically, with the normal diffusion.     

动态冰浆传热特性的研究

动态冰浆由于具有较强的蓄能和传热能力,日益受到人们的重视。文中建立了动态冰浆传热特性的数理模型,并利用已知的载流溶液和冰晶的物性参数,得到了动态冰浆在水平直管、等热流加热条件下的传热系数,根据计算结果,分析了传热系数随着冰浆浓度的变化的规律和冰浆流速和管径对动态冰浆传热性能的影响。     

二维Fibonacci准晶电子能谱

基于重整化群技术,我们用分解-消元方法研究二维Fibonacci准晶电子能谱性质,得到了具有多种分支结构的能谱,这与一维Fibonacci的单一分支结构完全不同。同时,利用晶格的四重旋转对称性将哈密顿量化简,然后进行数值模拟计算,计算结果与分析结果完全一致。 关键词：     

一维对心碰撞恢复系数的讨论

本文深入讨论了两球对心碰撞时,速度恢复系数、冲量恢复系数、能量恢复系数3种恢复系数的不同定义,并且讨论了3种定义之间的关系,总结了影响恢复系数的各种因素;同时,分析了恢复系数不同取值时的物理意义.研究这3种定义时,我们发现了一个共同特点是经典理论中都将恢复系数看作只与材料有关的常数.但是实际碰撞过程恢复系数不是仅仅依赖于材料的一种固有属性,它还与摩擦、撞击物和被撞击物的材料、接触面的几何性质以及碰撞的位形、初始速度等因素有关.本文仅限于考虑与材料特性有关的经典理论研究.     

十二重准晶光子结构中的负折射与成像

最近实验证明周期性的光子晶体中存在电磁波的负折射现象，并且观测到亚波长成像．然而，这些研究主要集中在剧期性结构中，对非周期结构的研究还没有相关的报道。文章报道了一种新的理论和实验结果：非周期性十二重准晶光子结构同样存在负折射，并且可以实现超透镜的远场成像。具有这些特性的光子准晶可以广泛的应用于光集成器件中。     

General solutions of plane elasticity of one-dimensional orthorhombic quasicrystals with piezoelectric effect

By introducing four potential functions, the governing equations of plane problems in 1D orthorhombic quasicrystals with piezoelectric effect are composed of four second-order partial differential equations, in which the quasi-harmonic functions are the essential unknowns. The general solution of these equations is further established, and all expressions are expressed in terms of the potential functions. As an application of the general solution, the closed-form solutions are obtained for wedge problems or half-plane problems of 1D orthorhombic piezoelectric quasicrystals.     

Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect

In this paper, a set of 3D general solutions to static problems of 1D hexagonal piezoelectric quasicrystals is obtained by introducing two displacement functions and utilizing the rigorous operator theory. All the physical quantities are expressed by five quasi-harmonic functions. Based on the general solutions and with the help of the superposition principle, fundamental solutions for infinite/half-infinite spaces are presented by trial-and-error technique. The general solutions can be conveniently used to solve the boundary value problems regarding dislocations, cracks and inhomogeneities. The fundamental solutions are of primary significance to development of numerical codes such as boundary element method.     

海面冰层对声波的反射和散射特性

北极海面冰层复杂多变,其对声波的反射和散射严重影响冰下水声信道的传输特性,建立海面冰层的声波反射和散射模型对冰下水声通信研究具有重要意义.假设海面冰层为多层固体弹性介质且冰-水界面粗糙,满足微扰边界条件,导出声波从海水介质入射到海面冰层时相干反射系数满足的线性方程组.对相干反射系数随声波频率、掠射角、冰层厚度的变化进行数值分析.进一步引入根据散射声场功率谱密度计算散射系数的方法,改变掠射角,对冰层厚度、散射掠角对散射系数的影响进行研究.     

Local rules for quasicrystals

The relationship of local ordering and long-range order is studied for quasicrystalline tilings of plane and space. Two versions of the concept of local rules are introduced: strong and weak. Necessary conditions of the existence of strong local rules are found. They are mainly reduced to the constraints for irrational numbers related to incommensurabilities of the quasicrystals. For planar quasicrystals the quadratic irrationalities play an important role. For three-dimensional quasicrystals not only quadratic but also cubic irrationalities are allowed. The existence of weak local rules is established for almost all two-dimensional quasicrystals based on quadratic irrationalities and for the three-dimensional quasicrystal having icosahedral symmetry.     

Magnetotransport in simple metals. An exactly soluble model

The magnetoconductivity tensors of a metal with a weakly anisotropic Fermi surface are determined from analytic solutions to the Boltzmann equation without any restrictions on the magnitude of the cyclotron frequency compared to the collision rate. Results are given for both a two- and a three-dimensional model, the former being analytically simpler to handle. The Hall coefficient and magnetoresistance are obtained as functions of the magnetic field, and we show by explicit calculation how the thermoelectric coefficients at high magnetic fields are determined by the thermodynamic entropy.     

On dynamic plane elasticity problems of 2D quasicrystals

In this Letter, the dynamic plane elasticity problems of 2D quasicrystals is considered. By use of the Fourier transform and matrix transformations the system is reduced to uncoupled ordinary differential equations. Fourier images of Green's functions for dynamic plane elasticity problems of 2D dodecagonal, pentagonal and decagonal quasicrystals are obtained explicitly by the suggested method.     

PERTURBATION METHOD SOLVING ELASTIC PROBLEMS OF ICOSAHEDRAL QUASICRYSTALS CONTAINING A CIRCULAR CRACK

Perturbation method for solving elastic three-dimensional (3D) problems for 3D icosahedral quasicrystals is proposed. Considering an infinite 3D icosahedral quasicrystal weakened by a circular crack, we obtain the uniformly valid asymptotic solutions up to O(R²) for the mode I loading, where R is the elastic constant of phonon-phason coupling.