GaAs/AlGaAs异质结动力学行为研究

建立在空间电荷转移框架下,考虑GaAs/AlGaAs异质结物理模型,推导相应动力学方程,比较详细地分析了系统随激励电场变化出现的复杂分支情况.分析表明,直流场下稳态解和周期振荡解并存,理论上对滞后现象进行解释.对GaAs/AlGaAs异质结在微波场中动力学行为进行数值模拟,得到在输入场强度变化的一定范围内,具有锁频、准周期和混沌特性 关键词： 负微分电导率 异质结 分支 混沌     

用逐次线性化法对储存环动力学孔径的解析研究

从逐次线性化法解粒子非线性Betatron振荡方程出发,对存在非线性六极场、八极场及六极场与八极场共存的粒子Betatron振荡方程进行研究.应用线性理论得出了粒子非线性Betatron振荡稳定性的判据,得到了动力学孔径的半解析表达式,分析了在小振幅下,导致粒子非线性不稳定性的另外一种机制———小振幅下,参量共振所引起的自激振荡.用此方法对实际lattice的动力学孔径进行了研究,所得结果与数值跟踪结果吻合得很好     

应变超晶格系统的共振行为及其动力学稳定性

在经典力学框架内和Seeger方程基础上,讨论了应变超晶格界面附近的位错动力学行为,指出了系统的非线性共振将导致位错的运动与堆积,并可能造成超晶格的分层或断裂.首先,引入阻尼项,在小振幅近似下,把描述一般位错运动的Seeger方程化为了超晶格系统的广义Duffing方程.利用多尺度法分析了系统的主共振、超共振和子共振,并找到了系统出现这三类共振的临界条件.结果表明,系统的临界条件与它的物理参数有关,只需适当调节这些参数就可以原则上避免共振的出现,保证了超晶格材料的完整性和性能的稳定性. 关键词： 位错动力学 应变超晶格 共振 分岔     

振荡场作用下聚合物/纳米棒混合体系的自组装

采用元胞动力学和布朗动力学联用方法研究了振荡场作用下两嵌段共聚物/均聚物/纳米棒混合体系的自组装相行为.通过计算模拟,探讨了振荡场的振幅和频率对混合体系相形貌形成和演化的影响.研究发现振荡场对体系有序结构的形成和转变有重要作用,随着外加振荡场频率的增大,混合体系形貌从平行于场方向的条纹结构过渡到斜层状结构再转变为垂直于场方向的条纹结构.进一步分析了振荡场作用下体系畴尺寸的演化及纳米棒取向角的变化情况.研究结果为制备和调控聚合物纳米复合材料有序结构提供了新的方法和参考.     

带注入信号的双光子激光器的双稳性质

以原子均匀展宽的单模环形双光子激光器为模型,用半经典方法讨论有注入信号的双光子激光器的双稳性质。论证在谐调情况下该系统会出现双稳态,并且对于“好腔”和“坏腔”极限,通过绝热消除描述了双稳性导致的输出光的瞬态行为和滞后循环。发现在低分支是单调地趋向稳态,而在高分支是振荡地趋向稳态;在输出场不连续变化之处出现临界慢化现象。     

横向补给系统高架索的稳定性与分岔研究

考虑集中质量对系统动力学行为的影响,建立了横向补给系统高架索振动的理论模型.利用Galerkin方法和多尺度方法对动力学方程进行渐近分析.通过对系统Jacobi矩阵特征值的讨论,分析了系统的稳定性.根据系统渐近解的消除永年项条件,得到了系统的振幅分岔方程.借助Mathematica软件,对系统的局部分岔行为进行研究,得到了系统的转迁集以及相应的局部分岔图,研究表明横向补给系统高架索的振动中存在的多种分岔现象.     

激光系统的Ginzburg-Landau方程及其相位扩散方程

讨论了激光系统Ginzburg-Landau方程的主要动力学行为,它描述激光系统的自发时空对称性破缺。当方程有非均匀静态解时,它存在合作频率锁定效应;而当方程有时空振荡解时,各横模仍有一个共同的光学载频。此模型还表明,混沌解可以发生在低抽运条件下。在较小失谐时,该方程的约化相位扩散方程能较精确地再现原方程的全程动力学行为。这说明在激光横向图形分布的自发形成中,电场的相位分布导引其动力学行为。 关键词：     

低频调制场中钾原子的激发

本文用含时多态展开方法计算了里德堡钾原子在静电场、微波场和低射频场[a radio-frequency(rf)field]共同作用下方波振荡的激发特性.研究计算了通过改变微波场的频率、振幅和静电场的振幅以及用低射频锯齿波代替低射频余弦波后方波振荡的变化,获得了一些非常有趣的结果,并给出了理论解释.     

调制振幅对粒子布居几率振荡的影响

为探讨调频场导致的量子效应的物理本质,运用密度矩阵方程和布洛赫矢量模型,对调频场作用下二能级原子系统中的粒子布居几率振荡现象进行了理论分析,讨论了光场调制振幅对振荡过程的影响。理论计算结果表明,光场调制振幅对粒子布居转移和几率振荡有较大的调制作用。当其他参量不变时,随着调制振幅的增大,粒子布居几率振荡减弱,布居转移效率增高,吸收增强。布洛赫矢量分析表明,该振荡过程是系统粒子数转移、吸收和极化三者之间的动态变化过程。     

分段Filippov系统的簇发振荡及擦边运动机理

本文旨在揭示非光滑Filippov系统中由频域上不同尺度耦合导致的簇发振荡行为及其产生机理.以经典的周期激励Duffing振子为例,通过引入对状态变量的分段控制及适当选取参数,使得激励频率与系统固有频率之间存在量级差距,建立了频域两尺度耦合的Filippov系统.当激励频率远小于系统的固有频率时,可以将整个激励项视为慢变参数或慢变子系统,从而得到广义自治快子系统.分析了由非光滑分界面划分的不同区域中各快子系统的平衡点及其分岔特性随慢变参数变化的演化过程.考察了两种典型参数条件下系统的振荡行为及其动力学特性,指出参数变化不仅会引起其相应子系统平衡曲线及其分岔特性的改变,也会导致不同模式的簇发振荡.同时,轨迹穿越非光滑分界面时会产生不同的动力学行为,特别是在一定参数条件下,由于运动轨迹受不同子系统的交替控制,存在着擦边运动现象,从而导致特殊形式的非光滑簇发振荡.基于转换相图及各区域中快子系统的平衡曲线及其分岔特性,揭示了非光滑分界面对系统簇发振荡的影响规律及不同簇发振荡的分岔机理.     

Stability of asymmetric spike solutions to the Gierer-Meinhardt system

In this paper, we study the spectra of asymmetric spike solutions to the Gierer-Meinhardt system. It has previously been shown that the spectra of such solutions may be determined by finding the generalized eigenvalues of matrices, which are determined by the positions of the spikes and various parameters from the system. We will examine the spectra of asymmetric solutions near the point at which they bifurcate off of a symmetric branch. We will confirm that all such solutions are unstable in a neighborhood of the bifurcation point and we derive an explicit expression for the leading order terms of the critical eigenvalues.     

一种可稳定计算Pekeris波导中声场的波数积分方法

提出一种可稳定计算Pekeris波导中声场的波数积分方法,并在此基础上开发出一个数值模型,可用于提供Pekeris波导中声场的精确、稳定的数值解。在这个方法中,由于与深度有关的波动方程齐次解中所有的上行波与下行波均采用了合理的归一化表示,从而得到的系统方程是无条件稳定的。在简正波方法中,割线积分一般只对近场有显著影响。因此,传统的简正波模型一般都忽略割线积分对声场的贡献。但是,如果某号简正波离割线非常近,则割线积分对非常远距离的声场仍可能有显著影响。在这种情况下,传统的简正波模型由于忽略割线积分的贡献,从而得到的声场结果是不准确的。本文通过数值算例比较本文提出的波数积分模型与传统的简正波模型。数值结果表明,本文提出的模型可以提供精确、稳定的Pekeris波导中声场的数值解,而在某些情况下传统的简正波模型得到的声场结果是不准确的。因此,本文提出的模型可以作为Pekeris波导中声传播问题的标准模型使用。      

Parametric scattering in a system of quasi-two-dimensional exciton polaritons under photoexcitation near the bottom of the upper polariton branch

Cascade processes of exciton-polariton scattering in a planar semiconductor microcavity taking place under resonance pumping near the bottom of the upper polariton branch are studied theoretically. When the conservation laws allow the decay of the resonantly excited state into two modes that belong to different (the upper and lower) polariton branches, the distribution of scattering directions has the general shape of two rings that correspond to the cross sections of the lower and upper polariton dispersion surfaces by constantenergy planes. Due to the interactions between the particles, instability develops in the system of scattered modes, which is accompanied by marked inhomogeneities in the distribution of the cavity photoluminescence signal. Self-organization in such a system leads to the appearance of solutions of an essentially collective nature. As the critical (threshold) pump power is attained, macroscopic occupancy of a predominant signal mode near the bottom of the lower polariton branch sets in. The characteristics of the signal for different powers and optical polarizations of the pump are analyzed.     

Wavefront depinning in semiconductor superlattices due to discrete-mapping failure

We investigate the wavefronts depinning in current biased, infinitely long semiconductor superlattice systems by the method of discrete mapping and show that the wavefront depinning corresponds to the discrete mapping failure. For parameter values near the lower critical current in both discrete drift model （DD model） and discrete drift-diffusion model （DDD model）, the mapping failure is determined by the important mapping step from the bottom of branch to branch α. For the upper critical parameters in DDD model, the key mapping step is from branch γ to the top of the corresponding branch α and we may need several active wells to describe the wavefronts.     

An elementary model of torus canards

We study the recently observed phenomena of torus canards. These are a higher-dimensional generalization of the classical canard orbits familiar from planar systems and arise in fast-slow systems of ordinary differential equations in which the fast subsystem contains a saddle-node bifurcation of limit cycles. Torus canards are trajectories that pass near the saddle-node and subsequently spend long times near a repelling branch of slowly varying limit cycles. In this article, we carry out a study of torus canards in an elementary third-order system that consists of a rotated planar system of van der Pol type in which the rotational symmetry is broken by including a phase-dependent term in the slow component of the vector field. In the regime of fast rotation, the torus canards behave much like their planar counterparts. In the regime of slow rotation, the phase dependence creates rich torus canard dynamics and dynamics of mixed mode type. The results of this elementary model provide insight into the torus canards observed in a higher-dimensional neuroscience model.     

Analysis of tunable diode-laser spectra of Q(J,0) lines in CH3F near 1475 cm using a multispectrum fitting technique

We have analyzed the methyl fluoride ^RQ(J,0)Q branch lines located near 1475 cm⁻¹ using a simultaneous multi-spectrum fitting technique. In this analysis we have used previously recorded diode-laser data in which we collected many data points covering only one or two Q branch lines in a particular run. The analysis consists of simultaneously fitting 57 spectra collected with numerous pressure and path length conditions for all absorption lines. The data are concatenated to create one continuous spectrum of the Q branch. We have determined the intensity and self-broadened widths at 296 K for 23 ^RQ(J,0) lines.     

Analytical solution based on the wavenumber integration method for the acoustic field in a Pekeris waveguide

An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide.     

含可饱和吸收体的单模驻波激光系统的定态行为

具体给出了含可饱和吸收体的单模驻波激光系统的哈密顿(Hamiltonian)量和序参量运动方程,并对序参量的定态解做了线性稳定性分析。结果表明,驻波系统在阈值附近的定态行为(非平衡相变行为、双稳行为、临界点附近的指数行为等)与行波系统定性类似,但具体细节有异。特别不同于行波的是,驻波情形下三个定态解中的I_分支有可能实现。     

Interrelating scattering characteristics to internal electric fields for Gaussian-random-sphere particles

We investigate the single-scattering interference mechanism related to the negative polarization branch (NPB) and intensity enhancement branch (IEB) near the backscattering direction for wavelength-scale Gaussian-random-sphere particles. Previously, we showed that for wavelength-scale spherical particles there is a two-part mechanism related to the longitudinal and the transverse components of the internal electric fields that are responsible for producing both the NPB and IEB near the backscattering direction. For comparison with the previous study, we have chosen the ensemble-averaged parameters of the Gaussian-random-sphere particles to be equivalent to those for spherical particles. We conclude that the same mechanism also can explain the NPB and IEB for non-spherical particles and that the mechanism seems to be stronger inside spherical particles, mainly because of stronger interference, and becomes weaker as the particle becomes more non-spherical.