黄金数与Fibonacci数列

本文用美学的观点研究了黄金数和与之有密切关系的Fibonacci数列,并给出了大量应用Fibonacci数列的例子,说明了它在优选法上的重要意义.     

具有最小应力的裴波纳契螺旋结构

裴波纳契（Fibonacci）数列是一种整数数列，其中每数等于前面两数之和，这种数列在自然界中广泛存在．例如雏菊每一圈花瓣的个数，树干自下而上分枝的密度等等．最近中国科学院理论物理研究所在实验室中通过一种“应力机制”在微观结构上形成了符合裴波纳契数列的螺旋．他们认为找到了这个数列广泛存在于自然界的原因．     

太赫兹波在一维反铁磁/电介质准周期光子晶体的传输性质

本文利用传递矩阵方法研究了电磁波倾斜入射时,一维反铁磁/电介质准周期光子晶体的透射性质.反铁磁层和电介质层按Fibonacci数列排列构成准周期光子晶体.通过数值模拟发现光子禁带中有透射峰出现, 而且随着准周期光子晶体级数的增加透射峰的数目也在增加.此外,透射峰受电介质层的介电常数、入射角度和电磁波偏振影响明显. 关键词： 反铁磁层 准周期光子晶体 太赫兹波传输性质     

广义Fibonacci准周期结构声子晶体透射性质的研究

提出了一维广义Fibonacci准周期结构的声子晶体模型. 对弹性波通过该一维准周期结构声子晶体的透射系数进行数值计算,并与周期结构和标准Fibonacci准周期结构声子晶体的透射系数进行比较. 结果表明,利用一维广义Fibonacci准周期结构的声子晶体可获得比周期结构和标准Fibonacci准周期结构声子晶体更大的带隙范围,同时在带隙内有更丰富的局域模式存在. 对局域模性质的研究有助于声波或弹性波滤波器的制作. 关键词： 广义Fibonacci准周期结构 声子晶体 局域化     

“0.618”法、Fibonacci法、抛物线法搜寻复摆周期极值点

在实验室条件下,用"0.618"法、Fibonacci法和抛物线法来搜寻钟摆复摆周期极值点位置.通过实验发现,Fibonacci法在搜索精度上比"0.618"法高,但在搜寻速度上不占优势,而抛物线法在搜寻速度和精度上比"0.618"法和Fibonacci法都好.     

广义Fibonacci时间准周期量子行走波包扩散的动力学特性

本文通过数值计算的方法研究了一维离散时间准周期量子行走的动力学特性,主要研究了两个自旋空间C算符按照广义Fibonacci准周期排列的量子行走,发现对两类广义Fibonacci准周期序列,波包扩散都是超扩散(即标准方差σ约为t~γ,0.5γ1),而且在给定的两个C算符下,第二类广义Fibonacci准周期序列的幂指数γ大于第一类广义Fibonacci准周期序列.通过对波包扩散的概率分布情形和标准方差的研究发现,第一类广义Fibonacci准周期序列的波包扩散更接近于经典随机行走(γ=0.5),而第二类广义Fibonacci准周期序列的波包扩散更接近于均匀量子行走(γ=1),这与两类广义Fibonacci准周期量子自旋链中量子相变时的特性相反.     

Quantum diffusion in semi-infinite periodic and quasiperiodic systems

This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.     

一维压电Fibonacci类准周期声子晶体传输特性

基于传输矩阵法研究了一维压电Fibonacci类准周期声子晶体的传输特性, 比较了一维Fibonacci序列压电准周期声子晶体与非压电准周期声子晶体以及压电周期性声子晶体的透射性. 计算结果表明:弹性波通过一维准周期结构压电声子晶体时与周期性声子晶体一样会有带隙的出现, 且发现具有压电性的Fibonacci序列准周期声子晶体禁带宽度发生了展宽. 进一步讨论了入射角度对固定频率下声子透射系数的影响,结果表明一维压电Fibonacci序列准周期结构声子透射性依赖于入射角度的选取.     

Fibonacci序列的统计属性和电子输运系数

对按膨胀规律A→AB和B→A生成的Fibonacci序列,采用一维随机行走模型数值计算了序列的自相关函数以及自行定义的准标准偏差.利用Hurst分析法研究了序列的再标度范围函数及其Hurst指数,并将结果与一维随机二元序列进行了对比.发现这些统计量有奇特的准周期振荡行为以及小于05的Hurst指数,直接论证了Fibonacci序列具有关联、标度不变及自相似等性质.从Anderson紧束缚模型出发,采用传输矩阵方法研究了Fibonacci序列的电子输运特性,讨论了输运系数对能量及其序列长度的依赖关系.研究 关键词： Fibonacci序列 统计属性 电子输运系数     

缺陷对准周期磁超晶格输运性质的影响

研究了缺陷结构的Fibonacci磁超晶格的输运性质.结果表明,缺陷结构对纳米准周期链的电子输运性质有重要影响,特别是低能区电子输运 关键词： 缺陷 Fibonacci链 磁纳米结构 输运性质     

Omnidirectional Single-negative Gap and in Fibonacci Sequences Composed of Single-negative Materials

The band structures of Fibonacci sequence composed of single-negative materials are studied with a transfer matrix method. A new type of omnidirectional single-negative gaps is found in the Fibonacci sequence. In contrast to the Bragg gaps, such an omnidirectional single-negative gap is insensitive to the incident angles and polarization, and is invariant upon the change of the ratio of the thicknesses of two media. It is found that omnidirectional single-negative gap exists in the other Fibonacci sequence, and it is rather stable and independence of the structure sequence.     

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.     

光学波段菲波纳契序列一维光子晶体纳米膜传输特性研究

为了研究光学波段菲波纳契序列一维光子晶体纳米膜的传输特性,应用传输矩阵方法数值模拟各种情况下的透射率即传输函数随频率的变化.数值结果表明在正入射时,菲波纳契序列一维光子晶体中的禁带宽度、中心位置、数目都与构成序列的项数、组元物理厚度、组成序列组元初始次序、组元折射率差值都对传输特性有较大影响,在可见光区组元折射率差值越大越易形成较宽禁带,进一步研究广义菲波纳契序列一维光子晶体纳米膜的传输特性,发现比典型情况更易在可见光区形成禁带.     

Transverse elastic waves in Fibonacci superlattices

We study the transverse elastic waves propagating in 6-mm class hexagonal crystals forming Fibonacci superlattices. These are formed by repetitions of CdS and ZnO slabs in A and B constituent blocks following the Fibonacci sequence. We study the periodic superlattices formed by the infinite repetition of a given Fibonacci generation together with the finite Fibonacci generations having stress-free surfaces, in order to compare the effects introduced by the different boundary conditions. We have also considered the effects of piezoelectricity when all the interfaces are metallized and kept at a fixed potential. We use the surface Green function matching method forNnonequivalent interfaces to obtain the dispersion relations and the density of states of these systems. We have studied the influence of the increasing order of the Fibonacci generations on the dispersion relation of the transverse elastic modes. The Fibonacci spectrum is clearly seen even for low-order Fibonacci generations and is almost not modified by the piezoelectric coupling when the interfaces are metallized.     

Fibonacci order in the period-doubling cascade to chaos

In this contribution, we describe how the Fibonacci sequence appears within the Feigenbaum scaling of the period-doubling cascade to chaos. An important consequence of this discovery is that the ratio of successive Fibonacci numbers converges to the golden mean in every period-doubling sequence and therefore the convergence to ϕ, the most irrational number, occurs in concert with the onset of deterministic chaos.     

规则连接的电阻、电容网络的数学模型

从网络基本单元数学模型出发，用费玻那数列和另外建立的类费玻那契数列，建立了规则连接的电阻网络的数学模型。     

Multi-wavelength photonic band gaps based on quasi-periodically poled lithium niobate ordered in Fibonacci sequences

We demonstrate a quasi-periodic structure exhibiting multiple photonic band gaps （PBGs） based on sub- micron-period poled lithium niobate （LN）. The structure consists of two building blocks, each containing a pair of antiparallel poled domains, arranged as a Fibonacci sequence. The gap wavelengths are analyzed with the Fibonacci sequence parameters such as the quasiperiodic indices and the average lattice parameter. The transmission properties are investigated by a traditional 4×4 matrix method. It has also been proved that the gap depth can be tuned by the lengths of poled domains.     

Fibonacci quasi-periodic superstructure fiber Bragg gratings

Superstructure fiber Bragg gratings constructed following the Fibonacci sequence are proposed and simulated by using the transfer matrix method. The reflection spectrum has a multi-fractal structure as a function of the wavelength and is symmetric to the center. The reflectivity has self-similarity and scaling with respect to the Fibonacci sequence order at the central wavelength. For the transmission spectrum, the interaction of the core-cladding mode is investigated and the particular wavelengths for which the resonance condition is satisfied are located by varying the grating parameters. The potential application of the quasi-periodic structure as fiber sensors is also proposed.