Reissner-Nordstr?m de Sitte 黑洞的引力似正模

利用P?shl-Teller势近似方法,本文研究了径向和角向引力扰动引起的Reissner-Nordstr?m de Sitte 黑洞的似正模。研究表明,当宇宙常数增加时似正模虚部的强度变小,但它却随电荷、谐波数或轨道角动量增加而增加。当电荷固定而宇宙常数改变时,似正模的虚部与实部几乎成线性关系。研究还发现径向和角向引力扰动引起的似正模是一致的,这证实似正模只依赖于黑洞的参量而与初始扰动无关。     

Regge极点与π-N散射T=3/2,J=3/2的p波相移

在Khuri的最近的一篇文献中指出,散射振幅f(s,z)的Regge表示中的每一项在z平面上的割线起点,同f(s,z)的z割线起点不符合,这意味着在极点项和背景项之间还存在着某种抵消。这样,Regge表示的极点项并不完全反映Regge极点的全部贡献。因此他建议一个新的表示形式,其中每一项的z平面解析性都同f(s,z)的z解析性相符。Khuri的工作还表明,在某些特殊类型的势散射情况下,可以论证,新的表示(Regge-Khuri表示)的背景项很可能只由λ左半平面(λ=l+1/2)的奇异性所决定,而与右半     

软固态海底的复有效深度近似

引用Zhang和Tindle的更有效深度的概念;将Chapman提出的浅海Pekeris波导的海底(实)有效深度近似,推广到复有效深度近似,其实部和虚部分别反映平面波反射的相位变化和能量损失。通过对比计算表明:由复有效深度近似构成的均匀声场,能反映对应于小掠角的低号简正波的声学特性,有效地计算浅海远距离声场.有关结论可以推广到包含两层软固态海底的波导之中.     

复介电常量双缺陷层的镜像对称光子晶体特性

利用传输矩阵法研究了两个复介电常量缺陷层镜像对称一维光子晶体的带隙结构和光传输特性。重点讨论了缺陷层的复介电常量的虚部为负值且光学厚度为λ0/4的情形时对传输特性的影响。研究发现:当在光子晶体的两端加入具有负虚部的复介电常量缺陷层后,多处出现了较强的透射峰增益。随着缺陷层复介电常量的虚部与实部比值的增加,各处透射峰增益变化规律不同。但中心波长处的缺陷膜的位置和高度不变。这为光子晶体同时实现多通道超窄带滤波器和不同放大倍数的光放大微器件的设计提供了理论基础。而在光子晶体的两端加入具有正虚部的复介电常量缺陷层后,各透射峰都出现了吸收现象,且随着其正虚部值I的增加,吸收越明显,这给光子晶体实现放大功能提供了理论指导。     

基于噪声辅助非均匀采样复数据经验模态分解的混沌信号降噪

鉴于非均匀采样复数据经验模态分解(NSBEMD)相对传统分解方法的优势和噪声的NSBEMD特性,提出了一种基于噪声辅助NSBEMD的混沌信号自适应降噪方法.该方法首先以含噪混沌信号和高斯白噪声分别为实、虚部来构造复数据并进行NSBEMD,然后根据虚部各IMF的能量来估算实部各IMF中包含的噪声能量,最后根据噪声能量的估计值对实部IMF进行奇异值分解(SVD)降噪.噪声估计实验验证了噪声能量估计方法的可行性,而Lorenz信号和太阳黑子月平均数的降噪实验则表明,相对于现有EMD降噪方法,本文方法能够进一步消除噪声,更清晰地恢复出混沌吸引子的拓扑结构.     

二维随机增益介质中局域模的模面积和放大

随机激光形成于随机介质中局域模的放大,其放大特性依赖于局域模的空间分布。通过复折射率的虚部将光学增益引入系统,采用时域有限差分(FDTD)法,分析了增益介质中局域模的放大特性,并用模面积描述了局域模空间分布,着重对比分析了模面积对局域模放大特性的影响。模拟结果显示,局域模具有不同的空间分布,直接影响了局域模的放大特性,模面积较小的模式具有较低的损耗,能够获得更多能量,在介质中被优先放大,而模面积较大的模式,由于损耗较大,将获得较少的能量。     

基于非下采样双树复小波域的双变量模型去噪算法

提出一种基于非下采样双树复小波域的图像去噪算法.首先分析非下采样双树复小波变换同一方向实部与虚部小波系数之间的相关性,通过实例及统计规律得到其联合概率分布近似服从于椭圆边界的单峰各向异性二维非高斯分布.然后把双变量统计模型引入到非下采样双树复小波变换实部和虚部小波系数中,将实部与虚部小波系数的联合概率分布作为双变量先验模型,得到了非下采样双树复小波变换自适应各向异性双变量去噪模型.该模型可以很好地体现实部与虚部小波系数之间的相关性.运用最大后验概率来估计从含噪图像的小波系数恢复原图像的系数,达到去噪目的.最后根据该模型得到了一种具有闭式解的去噪算法.实验表明:该算法比经典算法提高了一定的峰值信噪比,且有良好的视觉效果,较好地保持了图像中的纹理特征.     

周期背景下怪波的激发和调制

为了研究怪波在周期背景中的激发和演化情况,以含有周期外势的自聚焦非线性薛定谔方程为模型,采用快速分步傅里叶算法,讨论了在两种周期势(实势和复势)的情况下,怪波的激发和演化情况.研究表明:在两种周期势背景下都能通过平面波加微扰来激发怪波;在实周期背景下,通过改变周期势的振幅和周期能够产生不同的光学现象;在复周期背景下,通过同样的初始波能够激发一种超大怪波,而且实部振幅对怪波具有能量耗散和减速作用,虚部振幅对怪波具有能量增益和加速作用,选择合适的实部振幅与虚部振幅可以产生强度不同的大怪波.研究结果有助于在光晶格中捕获和调节怪波,以及获得高功率波.     

掺杂光子晶体光纤自发辐射与掺杂激活杂质的光增益透射谱研究

借助光子晶体中二能级原子的自发辐射理论证明缺陷态的局域场存在的必然性以及局域场基本性质,为研究光子晶体光纤掺杂自发辐射的内在规律提供了理论依据。且将自发辐射理论与数值模拟相结合,在缺陷介质中掺激活杂质时,研究了光子晶体光纤的掺杂局域场特征以及受激辐射增强和透射率大于1现象与光子带隙群速度异常和掺杂层复有效折射率成负的虚部之间的内在关系。由此说明光子晶体光纤的缺陷介质中掺入激活杂质时,光子禁带中能出现品质因子非常高的杂质态,具有很大的态密度,较强的受激辐射放大。     

z~(-4)排斥位势的Regge极点

对z~(-4)排斥位势证明了:(1)当|λ|→∞,|argλ|<π/2-ε时,S矩阵元S(λ,k)→1。(2)当|λ|→∞时,有无穷多个极点存在于虚轴的小角邻域内,并且这些极点的实部和虚部同时趋于∞,因此通常的双色散关系不成立。     

On the Discrete Spectrum of the Nonstationary Schrödinger Equation and Multipole Lumps of the Kadomtsev–Petviashvili I Equation

The discrete spectrum of the nonstationary Schr?dinger equation and localized solutions of the Kadomtsev–Petviashvili-I (KPI) equation are studied via the inverse scattering transform. It is shown that there exist infinitely many real and rationally decaying potentials which correspond to a discrete spectrum whose related eigenfunctions have multiple poles in the spectral parameter. An index or winding number is asssociated with each of these solutions. The resulting localized solutions of KPI behave as collection of individual humps with nonuniform dynamics. Received: 30 September 1998 / Accepted: 30 March 1999     

The Rate of Convergence of Fourier Coefficients for Entire Functions of Infinite Order with Application to the Weideman-Cloot Sinh-Mapping for Pseudospectral Computations on an Infinite Interval

We analytically compute the asymptotic Fourier coefficients for several classes of functions to answer two questions. The numerical question is to explain the success of the Weideman-Cloot algorithm for solving differential equations on an infinite interval. Their method combines Fourier expansion with a change-of-coordinate using the hyperbolic sine function. The sinh-mapping transforms a simple function like exp(-z²) into an entire function of infinite order. This raises the second, analytical question: What is the Fourier rate of convergence for entire functions of an infinite order? The answer is: Sometimes even slower than a geometric series. In this case, the Fourier series converge only on the real axis even when the function u (z) being expanded is free of singularities except at infinity. Earlier analysis ignored stationary point contributions to the asymptotic Fourier coefficients when u(z) had singularities off the real z-axis, but we show that sometimes these stationary point terms are more important than residues at the poles of u(z).     

On the Connection between Particles and Poles of the S-Matrix

In axiomatic S-matrix theory it is usually assumed that stable particles give rise to simple poles of the S-matrix for real negative energies while unstable particles give rise to poles close to the real axis on an unphysical sheet of the energy Riemann surface. The stable particle — pole association has been known for a long time not to be always true. For example in potential scattering what is relevant in this case in fact is not the S-matrix but the Jost function. The zeroes of this function for real negative energies are in fact in one-to-one correspondence with the bound states, while the correspondence may break down for the poles of the S-matrix. On the other hand it has recently been pointed out that there also is in general no connection between unstable particles and poles of the S-matrix.     

The scattering of the Manning-Rosen potential with centrifugal term

In this Letter the approximately analytical scattering state solutions of the l-wave Schrödinger equation for the Manning-Rosen potential are carried out by a proper approximation to the centrifugal term. The normalized radial wave functions of l-wave scattering states are presented and the calculation formula of phase shifts is derived. It is well shown that the poles of the S-matrix in the complex energy plane correspond to bound states for real poles and scattering states for complex poles in the lower half of the energy plane. We consider and verify two special cases: the l=0 and the s-wave Hulthén potential.     

|m| Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

1 Introduction Though one-dimensional (1D) systems may clearly exhibit many features of quan-tum mechanics, systems with many degrees of freedom provide more opportunities tostudy many other important features, e.g. the degeneracy of energy eigenstates, whichneed a complete set of commuting observables to characterize an energy eigenstate. Inparticular, two-dimensional (2D) systems with two spatial degrees of freedom may ex-hibit symmetries not present in 1D systems, e.g. the rotational symme…     

Two-Body T-Matrices Without Angular-Momentum Decomposition: Energy and Momentum Dependences

The two-body T-matrix is calculated directly as function of two vector momenta for different Malfliet-Tjon-type potentials. At a few hundred MeV projectile energy the total amplitude is quite a smooth function showing only a strong peak in forward direction. In contrast, the corresponding partial-wave contributions, whose number increases with increasing energy, become more and more oscillatory with increasing energy. The angular and momentum dependence of the full amplitude is studied and displayed on as well as off the energy shell as function of positive and negative energies. The behaviour of the T-matrix in the vicinity of bound-state poles and resonance poles in the second energy sheet is studied. It is found that the angular dependence of T exhibits very characteristic properties in the vicinity of those poles, which are given by the Legendre function corresponding to the quantum number either of the bound state or the resonance (or virtual) state. This behaviour is illustrated along numerical examples. Received May 29, 1997; revised October 17, 1997; accepted for publication December 28, 1997     

Pole assignment of friction-induced vibration for stabilisation through state-feedback control

Friction-induced self-excited linear vibration is often governed by a second-order matrix differential equation of motion with an asymmetric stiffness matrix. The asymmetric terms are product of friction coefficient and the normal stiffness at the contact interface. When the friction coefficient becomes high enough, the resultant vibration becomes unstable as frequencies of two conjugate pairs of complex eigenvalues (poles) coalesce (when viscous damping is low).This short paper presents a receptance-based inverse method for assigning complex poles to second-order asymmetric systems through (active) state-feedback control of a combination of active stiffness, active damping and active mass, which is capable of assigning negative real parts to stabilise an unstable system.     

Charged scalar-tensor spheres: General solutions

The charged static and spherically symmetric vacuum field in the general Bergmann-Wagoner-Nordtvedt (BWN) theory of gravity is studied. By a conformal transformation, the field equations are brought into a standard form, which permits a decoupling of the differential equations for the relevant quantities. Using the electrostatic potential as an independent variable results in a particular Ricatti equation, the general solutions of which can be explicitly written down, for positive and for negative scalar energy densities. In distinction with the Reissner-Nordström solutions, all nontrivial positive energy BWN theories are shown to possess naked timelike singularities, whereas the negative energy theories admit a peculiar nonsingular solution, which may be interpreted as a field theoretical model of a charged particle. It is argued that the absence of an event horizon in the other solutions is not a consequence of the assumption of spherical symmetry: event horizons are absent in any static geometry which is a nontrivial solution of the (charged or uncharged) BWN equations with positive definite scalar density.     

Effective-interaction expansions in the Hartree-Fock basis and effects of “back-door” intruders

The use of the Hartrree-Fock (HF) Hamiltonian in effective-interaction expansions is found to “push” out the branch point singularities which are located on the positive side of the origin in the complex x-plane. The effect may however be the opposite for “back-door” intruders, which correspond to such singularities in the negative half-plane. The dependence of these behaviors on the HF stability conditions and the sign of the particle-hole interactions is discussed.     

Stability properties of classical solutions to non-linear σ models

We show that the classical solutions of two-dimensional euclidean O(2p + 1) non-linear σ models given in terms of spherical harmonics are unstable under small perturbations for p ? 2. The negative and zero energy fluctuation modes are displayed.