非自治Kadomtsev-Petviashvili方程的自相似变换和二维怪波构造

首先给出非自治Kadomtsev-Petviashvili方程转换为Kadomtsev-Petviashvili方程的一个自相似变换,然后基于Kadomtsev-Petviashvili方程的Lump解构造了非自治Kadomtsev-Petviashvili方程的有理函数表示的二维单、双、三怪波解,最后通过合适选取变参数,用图示说明了它们的演化特征,并利用快速傅里叶变换算法数值模拟测试了二维单怪波的动力学稳定性.本文方法对寻找(2+1)维非线性波动模型的怪波激发提供了启迪.     

自相似结构的谱函数

本文设计了两种自相似平面结构,制成相应的衍射屏,获得夫琅和费衍射图样。理论上以逐代繁衍的眼光看待自相似结构,导出频谱递推公式,并给出了总频谱函数与谱函数曲线,讨论了谱函数曲线的某些特征与能量转移性质。本文提出了一种研究实际自相似问题的光学模拟方法。 关键词：     

自相似Euler方程的数值方法

Euler方程某些问题的解具有自相似特点，可以使用更准确的方法求解.提出了两种数值方法，分别称为自相似和准自相似方法，新方法可以使用现有守恒律方程的数值格式，无须设计特殊方法.对一维激波管问题、二维Riemann问题、激波反射以及激波折射问题进行了数值计算.对自相似Euler方程，一维计算结果显示数值解基本等同于精确解，二维结果也比现有文献计算的结果有更高的分辨率.对准自相似Euler方程，新方法可以求解不具有自相似性但接近自相似的问题，并在计算时间足够长时可以取得自相似Euler方程的效果.数值求解自相似Euler方程对自相似问题的研究，高分辨率、高精度格式的设计乃至Euler方程的精确解都有重要启示.      

二维自相似变换理论和线怪波激发

我们提出了二维自相似变换理论,以聚焦的(2+1)维NLS方程(数学称为抛物型的非线性微分方程)为模型,构建了它被转变为聚焦的(1+1)维NLS方程的二维自相似变换,深入研究了它的空间怪波激发,发现除了(1+1)维NLS方程的Peregrine孤子、高阶怪波和多怪波诱导的线怪波所具有的短寿命特征外,由Akhmediev呼吸子(AB)和Kuznetsov-Ma孤子(KMS)诱导的线怪波也具有这种短寿命特征.这与由亮孤子(包括多孤子)诱导的空间相干结构保持形状和幅值不变的演化特征完全不同.通过图示展现了本文例举的各类线怪波的演化规律.本文揭示的线怪波激发新机制,有助于提升对高维非线性波动模型的相干结构的新认识.     

镜像对称缓变准周期结构一维光子晶体的缺陷模

利用传输矩阵方法,研究了镜像对称缓变准周期结构一维光子晶体的缺陷模。结果表明,当镜像对称缓变准周期结构一维光子晶体的周期数增加时,禁带宽度逐渐展宽;引入缺陷后,出现缺陷模,缺陷模的波长随缺陷层厚度增加和缺陷层介质折射率的增大而向长波方向移动。     

准周期铁电光学超晶格多波长二次谐波的产生

准周期材料的研究是凝聚态物理学的热门课题之一。我们利用外电场室温极化技术，成功地制备了准周期ＬｉＴａＯ３超晶格，首次获得了高效，多波长的二次谐波输出。对应的基波波长分别为０．９７６２，１．０８４６，１．８３４，１．３６５０和１．５６９９μｍ。     

一维准周期结构声子晶体透射性质的研究

提出了一维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了数值计算，并与周期结构的透射系数进行了比较.计算结果表明，弹性波通过一维准周期结构声子晶体时，同样会有带隙的出现，且带隙所在频率范围与周期结构的情形完全一样，不同的是在准周期结构声子晶体中，带隙内有很强的局域共振模.对此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： 准周期结构 声子晶体 局域化     

基于10 m光子晶体光纤的放大自相似锁模振荡器研究

基于单根10 m大模场面积保偏光子晶体光纤, 搭建了带有色散图的放大自相似振荡器; 通过仔细调节腔内色散量的大小以及位于色散补偿端的端镜前的狭缝位置和大小, 实现了稳定的锁模运转, 获得了抛物线形脉冲输出. 输出脉冲的重复频率为8.6 MHz, 脉冲宽度为6.2 ps, 光谱宽度为3.84 nm, 平均功率820 mW, 对应单脉冲能量95 nJ. 这是第一次在自相似振荡器中直接获得重复频率在10 MHz 以下的脉冲输出, 95 nJ也是目前自相似振荡器直接输出的最高脉冲能量. 通过数值模拟证实了在第一个光栅的零级反射处和狭缝滤波后可以分别实现抛物线型脉冲和高斯脉冲的两种锁模脉冲输出.     

混合准周期异质结构的带隙补偿与展宽

基于一维光子晶体异质结构的多帯隙交叠补偿思想,提出了一种新颖的混合准周期级联结构,用于扩大全方位光子带隙.该全方位反射器结构由Fibonacci准周期结构和Thue-Morse准周期结构级联构成,研究表明,相比单种准周期结构,其全方位光子带隙宽度有显著提高.系统研究了结构参数(如周期数、阶数、介质折射率和厚度)对该结构光子带隙的影响,通过与周期结构带隙特性的比较,分析了准周期结构易于实现多带隙交叠的原因,为更复杂带隙结构的补偿和展宽奠定了设计基础.     

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     

Studies on the cell structure of quasicrystals

The geometric and crystallographic ideas for cell models and tilings in non-periodic ordered structures are outlined. The basic concepts, among them the cell geometry and duality in a lattice are explained for the example of a one dimensional section through the root lattice A ₂. The corresponding constructions for 3D icosahedral sections through the 6D face-centered hypercubic lattice, equivalent to the root lattice D ₆, are described. Two different tilings, one with equivalent, one with three inequivalent vertex positions, are derived and discussed.     

Lie point symmetry algebras and finite transformation groups of the general Broer--Kaup system

Using a new symmetry group theory, the transformation groups and symmetries of the general Broer--Kaup system are obtained. The results are much simpler than those obtained via the standard approaches.     

Phase transformation of quasicrystals in aluminium-transition metal alloys

Quasicrystals in Al–Mn, Al–Cu–TM (TM = Fe, Cr, Mn and Ru) and Al–Cu–Fe–Cr alloys can undergo two different modes of phase transformation. Discontinuous transformations of quasicrystals are characterized by the existence of a definite reaction front separating the quasicrystalline phase from the resulting crystalline one; the kinetics are controlled by the migration of the reaction front. Continuous transitions, on the other hand, proceed by structural evolution such as modulation or chemical ordering inside the quasicrystalline phase without creating any high-energy interfaces. Both types of transformations are thermally activated and need atomic diffusion.     

Local scaling transformation function and atomic shell structure in density functional theory

The method of local scaling transformation in density functional theory calculates a transformation function (TRF) in order to generate an optimized atomic N-electron wave function from a trial density and a reference density/wave function. The TRFsf(r) for several atomic systems are studied and it is observed that the number of minima in df(r)/dr equals the number of atomic shells, except whenρ=ρ ₀ andf=r.     

Two-potential theory of electric and magnetic charges via duality transformation

Dirac, Schwinger and Zwanziger theories of electric and magnetic charges are obtained via duality transformation. Analogous construction for three Euclidean dimensions, with magnetic charges interacting with electric currents, is also done. The role of Dirac strings as dislocations in the configurations of gauge potential is emphasized.     

Self-similar behavior and chemistry tabulation of burnt-gas diluted premixed flamelets including heat-loss

In many combustion systems, the reactive gases feeding the reaction zones are diluted by burnt products, to favor flame stabilization, homogenize the temperature distribution and reduce pollutant emission. The objective of this paper is to discuss a premixed flamelet detailed chemistry tabulation strategy for vitiated and non-adiabatic combustion. Dilution by burnt products is parameterized here with two controlling quantities: the amplitude of the heat-loss in the burnt gases, for instance at walls, and the level of reactant vitiation. The chemical response of premixed flames to variations of these parameters is studied and it is shown that most chemical properties of burnt-gas diluted flames feature self-similar behavior, which can be used to dramatically downsize chemical tables based on canonical flamelets. The self-similar behavior of the flamelets is studied for both molecular diffusion and chemical source budgets in a progress variable composition space. It is found that two different scaling relations are needed to ensure self-similar behavior of both major and radical species.     

Lie symmetry and Mei symmetry of a rotational relativistic system in phase space

The Lie symmetry and the Mei symmetry of a rotational relativistic system in phase space are studied. The definition, criterion and conserved quantity of the Lie symmetry and the Mei symmetry of a rotational relativistic system in phase space are given. The relation between the Lie symmetry and the Mei symmetry is found. An example is given to illustrate the application of the result.     

Synthesis and characterization of GaP nanochains with a twin-modulated quasi-periodic structure

GaP nanochains have been synthesized by hydrogen-assisted thermal evaporation, and characterized using X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), photoluminescence (PL), and Raman spectroscopy. GaP nanochains possess a (111) twin crystal plane-modulated quasi-periodic structure, that gives a strong green photoluminescence at 618 nm. While the Raman spectrum of the nanochains is similar to that of the GaP crystal, the intensity of the longitudinal optical (LO) peak is stronger than that of the transverse optical (TO) peak, which is supposedly related to the nanochain microstructures.     

Characteristic functional structure of infinitesimal symmetry transformations of Birkhoffian systems

In this paper, it is shown that infinitesimal symmetry transformations of Birkhoffian systems have a characteristic functional structure, which is formulated by means of an auxiliary symmetry transformation function Z_μ(t,a) (introduced by the relation ξ_μ(t,a)=Z_μ(t,a)+\dot{a}^μξ_0 (t, a)) and is manifestly dependent upon the constants of motion of the system. At the end of the paper, an example is given to illustrate the application of the results.