Quasi-Periodic Structures Based on Symmetrical Lucas Function of (2+1)-Dimensional Modified Dispersive Water-Wave System

By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riecati equation that the symmetrical Lucas functions satisfy. From the variable separation sohition and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated.

Carbon Material with Fibonacci Parastichy Structure

The curd of Romanesco broccoli was carbonized at 900°C under argon atmosphere in a gold furnace chamber. The carbonization afforded a carbon material with a fine logarithmic spiral on the surface, resembling the Fibonacci parastichy structure of the Romanesco broccoli flower bud. The carbonized “flower bud” structure was observed under scanning electron microscopy. Infrared absorption spectra and X-ray photoelectron spectroscopy measurements confirmed the chemical structure and component of the carbon material.

The Two-dimensional Electromagnetic Scattering from Periodic Chiral Structures and Its Finite Element Approximation

In this paper, we consider the electromagnetic scattering from periodic chiral structures. The structure is periodic in one direction and invariant in another direction. The electromagnetic fields in the chiral medium are governed by the Maxwell equations together with the Drude-Born-Fedorov equations. We simplify the problem to a two-dimensional scattering problem and we show that for all but possibly a discrete set of wave numbers, there is a unique quasi-periodic weak solution to the diffraction problem. The diffraction problem can be solved by finite element method. We also establish uniform error estimates for the finite element method and the error estimates when the truncation of the nonlocal transparent boundary operators takes place.

基于Fibonacci序列准周期结构的小角度低通空间滤波器

利用常规材料构造了Fibonacci序列准周期结构,运用传输矩阵法研究了该结构的空间传输特性,并基于该结构优良的空间传输特性设计了小角度低通空间滤波器.数值模拟结果表明,该小角度空间滤波器的角域带宽可通过改变序列的结构类型和序列数来调谐,其调谐规律为:随着Fibonacci序列F(m,1)中m值的增加,对应空间滤波器的角域带宽减小;随着序列数的增大,对应角域带宽也减小.在调谐的基础上,还可通过改变构成准周期结构的介质折射率参量来精确调节其角域带宽.相比于基于超材料的小角度空间滤波器而言,基于Fibonacci序列的小角度空间滤波器制备更简单,且有望应用于新一代的高功率激光系统中.

新型Fibonacci准周期结构一维等离子体光子晶体的全方位带隙特性研究

以二元Fibonacci准周期结构的一维等离子体光子晶体为对象,在系统研究不同初始序列及周期数的该结构光子晶体带隙特性的基础上,给出了一种新颖的一维等离子体光子晶体结构,用于扩大全方位光子带隙.相比文献中的结构,该结构更简单(层数大大减少,且属于二元结构),全方位光子带隙宽度也更宽.此外,讨论了等离子体材料参数,如等离子厚度、等离子体频率、碰撞频率对该结构全方位带隙的影响,并与文献结构情况进行了对比.研究结果可为新型全方位反射器的设计提供重要的理论指导.

The twoscale asymptotic error analysis for piezoelectric problems in the quasi-periodic structure

Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of twoscale asymptotic expansions for solutions to the electrical potential and the displacement in quasi-periodic structure under coupled piezoelectric effect are derived, and the homogenization constants of piezoelectric materials are presented. The coupled twoscale relation between the electrical potential and the displacement is set up, and some improved asymptotic error estimates are analyzed.

A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures

This paper develops a second-order multiscale asymptotic analysis and numerical algorithms for predicting heat transfer performance of porous materials with quasi-periodic structures.In these porousmaterials,they have periodic configurations and associated coefficients are dependent on the macro-location.Also,radiation effect at microscale has an important influence on the macroscopic temperature fields,which is our particular interest in this study.The characteristic of the coupled multiscale model between macroscopic scale and microscopic scale owing to quasi-periodic structures is given at first.Then,the second-ordermultiscale formulas for solving temperature fields of the nonlinear problems are constructed,and associated explicit convergence rates are obtained on some regularity hypothesis.Finally,the corresponding finite element algorithms based on multiscale methods are brought forward and some numerical results are given in detail.Numerical examples including different coefficients are given to illustrate the efficiency and stability of the computational strategy.They show that the expansions to the second terms are necessary to obtain the thermal behavior precisely,and the local and global oscillations of the temperature fields are dependent on the microscopic and macroscopic part of the coefficients respectively.

在转移-混合模型下Fibonacci点阵的电子性质

在转移模型基础上，考虑格点间的相互作用对座能量的影响，提出转移－ 混合模型在该模型下 Ｆｉｂｏｎａｃｃｉ 点阵有与座模型、转移模型等明显不同的电子能谱结构，随座能量的差异，可以是４ 主带和５ 主带结构，并稳定于５ 主带结构，还找到了主带进一步分裂为子带的规则点阵电子波函数广泛存在自相似性。

一类广义 Fibonacci 准晶电子能谱分析

讨论一类广义Ｆｉｂｏｎａｃｃｉ准周期链ｏｎ＿ｓｉｔｅ模型的电子能谱，其原子排列由Ｂ→Ａ，Ａ→ＡＢＢ产生。重整化群方法分析表明，一级近似时能谱为五主支结构；二级近似时每个主支又有三分支。数值计算结果证实了以上的分析，但并未发现有明显的连续谱，这与ｔｒａｎｓｆｅｒ模型的谱不同。

含液晶缺陷层Fibonacci结构局域模的电控可调特性

利用传输矩阵法研究含一向列相液晶缺陷层的一维Fibonacci第八代准周期结构局域模的电控可调特性.首先建立含一向列相液晶缺陷层的一维Fibonacci第八代准周期结构的物理模型;然后利用传输矩阵法数值计算该结构的透射谱,发现在禁带中存在局域模;最后讨论该局域模及其品质因子随外加电场方向与入射光方向间的夹角θ的变化关系.结果表明:局域模波长随夹角θ的增大而向短波方向移动,局域模的品质因子随夹角θ的减小而增大.

Nonreciprocal properties of 1D magnetized plasma photonic crystals with the Fibonacci sequence

In this paper, the nonreciprocal properties of a novel kind of 1D magnetized plasma photonic crystals(MPPCs) with the Fibonacci sequence are investigated. The isolation of the proposed 1D MPPCs is also used to analyze the nonreciprocal properties. Compared to the conventional 1D MPPCs with periodic structure, the nonreciprocal performance can be significantly improved.The effects of several parameters of the proposed 1D MPPCs on the nonreciprocal properties are studied by the transfer matrix method, which includes the incident angle, order of the Fibonacci sequence, plasma frequency, plasma cyclotron frequency and plasma filling factor. The obtained results show that the nonreciprocal propagation properties can be improved by increasing the values of the plasma cyclotron frequency and incident angle, but they will worsen by blindly increasing the order of the Fibonacci sequence, plasma frequency and filling factor of plasma.The peaks of transmittance also are obviously reduced. In addition, the value of isolation will increase with increasing the incident angle, order of Fibonacci sequence, plasma frequency and plasma filling factor. However, when the plasma cyclotron frequency is increased, the value of isolation will be increased at lower frequencies, but is almost unchanged at higher frequencies.

一维Fibonacci准晶的电子能谱结构

用格林函数——重整化群方法数值计算了一维Fibonacci准晶在位模型和组合模型的平均局域电子态密度。对于在位模型,谱结构是清晰的四子带全局结构,但每一子带未见明显的三分支结构。对于组合模型,则对于参数变化时的各种典型情况给出了数值结果和解释。

液晶缺陷阶梯型Fibonacci第七代结构的特性研究

设计了一种向列相液晶染料缺陷一维阶梯型Fibonacci第七代光子晶体结构,利用传输矩阵法数值仿真了该结构的电场方向及增益特性。计算了引入缺陷前后的透射谱,分析了有增益和无增益时,缺陷模随外加电场方向的夹角θ的变化关系和增益系数对缺陷模透射率大小的影响。结果表明:引入缺陷后,该结构的光子禁带范围变宽,并且在禁带区域两端的波长分别向短波和长波方向移动。引入增益系数后,当夹角θ的变大时,缺陷模的空间位置会向短波方向一侧偏移,但是,缺陷模波长的空间位置并没有发生改变,仅仅改变了其大小;在夹角θ为(0°~90°)时,该结构缺陷模波长的空间位置的变化量为13.1nm。当增益系数Co变大时,不同缺陷模波长对应的透射率大小都是先增大后减小的过程。

Microwave Transmission Through One-Dimensional Hybrid Quasi-Regular （Fibonacci and Thue-Morse）/ Periodic Structures

The transmission properties of hybrid quasi-periodic photonic systems （HQPS） made by the combination of one-dimensional periodic photonic crystals （PPCs） and quasi-periodic photonic crystals （QPCs） were theoretically studied. The hybrid quasi-periodic photonic lattice based on the hetero-structures was built from the Fibonacci and Thue-Morse sequences. We addressed the microwave properties of waves through the one-dimensional symmetric Fibonacci, and Thue-Morse system i.e., a quasi-periodic structure was made up of two different dielectric materials （Rogers and air）, in the quarter wavelength condition. It shows that controlling the Fibonacci parameters permits to obtain selective optical filters with the narrow passband and polychromatic stop band filters with varied properties which can be controlled as desired. From the results, we presented the self-similar features of the spectra, and we also presented the fractal process through a return map of the transmission coefficients. We extracted powerfully the band gaps of hybrid quasi-periodic multilayered structures, called ＂pseudo band gaps＂, often containing resonant states, which could be considered as a manifestation of numerous defects distributed along the structure. The results of transmittance spectra showed that the cutoff frequency could be manipulated through the thicknesses of the defects and the type of dielectric layers of the system. Taken together, the above two properties provide favorable conditions for the design of an all-microwave intermediate reflector.

Photonic bandgap structure and long-range periodicity of a cumulative Fibonacci lattice

In this work, we study the photonic band of cumulative Fibonacci lattices, of which the structure is composed of all generated units in a Fibonacci sequence. The results are compared with distributed Bragg reflector(DBR)structures with the same numbers of layers. Photonic bandgaps are found at two characteristic frequencies, symmetrically separated from the central bandgap in the DBR counterpart. Field amplitude and phase distribution in the Fibonacci lattice indicates an interferential origin of the bandgaps. Fourier transform on the refractive index profile is carried out, and the result confirms a determinate long-range periodicity that agrees well with the photonic band structure.

薄壁管轴向冲击的数值模拟与吸能优化

从抗撞性角度观察车辆设计,薄壁构件具有良好的吸能性能,为了深入探讨车辆吸能元件抗撞的性能,应用LS-DYNA对不同正多边形截面薄壁管进行计算机数值模拟,旨在获得工程抗撞设计中对某些抗撞部位具有借鉴性的吸能元件。采用斐波那契(Fibonacci)搜索对正多边形截面薄壁管吸能最大对应的最佳边数的搜索求解,得在正多边形截面薄壁管冲击压缩相同长度时,正十一边形截面薄壁管的吸能最大。

多边形电阻网络等效电阻的统一建构

采用网络分析构建差分方程模型的方法,实现了多边形电阻网络等效电阻的统一建构,获得了简洁的通用公式,并且给出了用费波那契数列表达的结果,同时将多边形概念拓展到非平直空间的二边形(二角形).最后,将所得结果与相关结果进行了比较.所得结论也适用于规则联接的多边形电容网络.

Fluctuation characteristics and topological interface states in the quasi-periodic structures of shallow-water waves

Compared with periodic structures,quasi-periodic structures have superior band gap properties and topological interface states.In this paper,a one-dimensional quasi-periodic Fibonacci water wave metamaterial model that can be used to apply quasi-periodic structures to shallow-water wave systems is presented.The fluctuation characteristics of periodic and quasi-periodic structures are examined using finite element numerical calculations based on the shallow-water wave equation.The research results show that the band characteristics of quasi-periodic structures are complex,enabling flexible control of the propagation of shallow-water waves.Furthermore,the mirror-symmetrical design of Fibonacci quasi-periodic water wave metamaterials was created to engineer the topological interface states in shallow-water wave systems,ultimately achieving successful localization of wave energy.This research will greatly enrich our understanding of topology,expand the potential applications of quasi-periodic structures,and provide new insights for manipulating water waves and harvesting energy.

离散变量结构优化的斐波那契算法

根据工程实际,充分考虑规范规定的约束条件和各项技术标准要求,建立了建筑结构优化模型。利用斐波那契数列的规律,提出了离散变量结构优化设计的斐波那契算法。算例结果表明,该方法能直接计算具有应力约束和截面尺寸约束的离散变量结构优化问题,也能处理同时具有稳定约束和位移约束的多工况、多约束、多变量的离散变量结构优化设计问题。是一种理想建筑结构优化设计方法。

一维准晶系统中具有套层结构的局域性

在研究一维准晶的电子性质时，发现了一种特殊的局域性。该模型是生长规则为Ａ→ＡＢＢ，Ｂ→Ａ的广义Ｆｉｂｏｎａｃｃｉ链，其能谱具有三分支的自相似结构，且在任一层的任一子带中，处于能谱中间的态是扩展态，两边的是局域态，而在它们之间存在中间态，即该系统具有规则套层结构的局域性。由此可预言多个迁移率边的存在。