Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies

Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.

Hamiltonian long wave expansions for internal vaves over a periodically varying bottom

We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.

理想流体层中悬浮隧道管体动水荷载研究-P波

针对理想流体层中的悬浮隧道管体及锚索体系,借助波动方程理论对平面P-波作用下的悬浮隧道,通过引入其管体只在竖直方面上运动和产生刚体位移而不发生变形以及只考虑海水和管体质量产生的动力效应等假定,同时考虑管体上下部海水和锚索刚度及间距的影响,导出了在理想流体层中悬浮隧道管体受到的动水荷载的计算方程组和边界条件。结合一座典型的悬浮隧道,通过参数研究,分析了上部海水厚度h,P-波频率值ω,入射角度α,锚索刚度Kc和锚索间距L对动水荷载值的影响,结果表明:上部海水的存在有利于减小动水荷载值,P波频率值与海水频率一致时将产生共振,入射角度的增大会大幅减小动水荷载值,较小的锚索刚度和较大的锚索间距也会减小动水荷载值。

带有紧支集位势的波动方程解的L^p估计

考虑下列带有摄动位势波动方程解的Ｌｐ估计ｔｕ－Δｕ＋Ｖ（ｘ）ｕ＝０，ｕ（ｘ，０）＝０，ｔｕ（ｘ，０）＝ｆ（ｘ），｛（ｘ∈Ｒｎ，ｎ≥３）其中ｆ（ｘ）∈Ｌｐ（Ｒｎ），｜１ｐ－１２｜≤１ｎ－１．如果Ｖ（ｘ）是紧支集的小势，本文证明了以上问题的解和非摄动问题（Ｖ（ｘ）≡０）的解具有同样的Ｌｐ估计：ｕ（ｔ，）Ｐ≤Ｃｔｆｐ，ｔ＞０．

高阶摄动波动方程的L^p-L^(p′)估计

考虑下面高阶摄动方程解ｕ（ｘ，ｔ）的ＬｐＬｐ′估计：ｔｕ＋（－Δ）ｍｕ＋Ｖ（ｘ）ｕ＝０，ｕ（ｘ，０）＝０，ｕｔ（ｘ，０）＝ｆ（ｘ），｛ｘ∈Ｒｎ，ｎ＞３ｍ．假设势函数Ｖ（ｘ）和初值ｆ（ｘ）具紧支集，Ｖ（ｘ）是小势，则上面问题的解满足‖ｕ（·，ｔ）‖ｐ′≤ｃｔ－ｄ‖ｆ‖ｐ，ｔ＞０，这里ｍ≥１，ｄ＝ｎｍ（１ｐ－１ｐ′）＝１，１ｐ＋１ｐ′＝１，ｍ２ｎ≤１ｐ－１２＜ｍｎ．

高阶摄动波动方程解的L^p-L^p′估计(英文)

研究了高阶摄动波动方程 ttu+ (-Δ) mu+V(x)u =0 ,u(x ,0 ) =0 , tu(x ,0 ) =f(x) ,x ∈Rn,n >3m ,解的Lp -Lp′ 估计 在摄动和始值 f(x)为紧支且V(x)充分小的假定下 ,得到了该问题解的Lp-Lp′ 估计 :‖u(· ,t)‖p′ ≤Ct-d‖f‖p,t >0 ,其中m >1,d =n/m (1/p- 1/p′) - 1,1/p+ 1/p′=1,m /(2n) <1/p- 1/2

Kadomtsev–Petviashvili(KP) Burgers Equation in Dusty Negative Ion Plasmas:Evolution of Dust-Ion Acoustic Shocks

We study the nonlinear propagation of dust-ion acoustic(DIA) shock waves in an un-magnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev–Petviashivili–Burgers(K-P-Burgers) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the K-P-Burgers equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves.

基于岩石物理模型的纵、横波速度反演方法

纵、横波速度是储层特征评价、流体识别的重要参数。针对勘探生产中缺乏速度测井资料的情况,研究并提出了基于岩石物理模型的速度反演预测方法。首先介绍了前人给出的速度-孔隙度关系式和基于岩石物理模型的速度估算过程;然后以岩石孔隙参数为基础,建立测井数据与岩石弹性参数之间的岩石物理关系;最后重构反演目标函数,通过模拟退火反演获得可靠的纵、横波速度。实验室数据和实际测井资料的计算结果表明,该方法能够在不使用速度测井信息作为先验约束的情况下得到可信度较高的速度预测结果。

利用地震资料估算孔隙度和饱和度的一种新方法

应用Gassmann方程,计算分析了孔隙度和饱和度与纵波速度、横波速度、介质密度和纵、横波速度比值的关系。结果表明,波速度、介质密度对孔隙度的变化较为敏感,速度比值对饱和度的变化较为敏感。对联合利用纵波速度(或纵波波阻抗)与纵、横波速度比值计算孔隙度和饱和度方法的稳定性分析结果表明,此方法是较稳定的,其精度受油气物性的影响。论述了利用地震资料估算孔隙度和饱和度的方法和步骤。

扰动KdV方程解的先验估计

对于带微扰的KdV方程ut+6uux+uxx=εR(u),(ε>0),在初值u0(x)∈C∞(-∞,+∞),当|x|→∞时指数衰减的条件下,分别构造出带两种不同扰动项的KdV方程的扰动孤立波解满足的能量关系式,并运用能量分析方法对扰动的孤立波解进行先验估计,得到如下结论:(1)R(u)=δ(tε)u,δ(s)∈C[0,+∞),δ(0)=0,时,解在-∞<x<+∞,0≤εt≤T内一致有界;(2)R(u)=-Δ(tε)uxxx,Δ(0)=0,Δ(s)∈C1[0,+∞),解在-∞<x<+∞,0≤tε≤T,0≤ε≤ε1内一致有界。

一类四阶非线性波动方程解的爆破与衰减

本文研究了非线性阻尼项与源项的竞争对具有强阻尼项的四阶波动方程解的影响.利用不动点原理和势井方法给出了方程局部弱解存在唯一性满足的条件,证明了当m<p且初始能量E(0)<0时,解将在有限时间内爆破.同时对m,p的大小关系不加任何限制但存在t_0使0<E(t_0)<d的情况下,利用稳定集,研究了整体解的存在性,并得到了解的能量衰减估计.最后借助修正的能量泛函,指出当m≥p时弱解也是整体存在的,推广并改进了文献[1-6]中的结果.

周期底地形上内波的Hamilton长波展开

给出了周期底部边界条件下两层密度成层流体中2-维非线性长波问题的Hamilton公式.从该公式出发,应用Hamilton摄动理论,导出了底地形短尺度变化下描述双向长波运动的有效Boussinesq方程和描述单向长波运动的近似KdV方程.结果的推导都是在多重尺度算子渐近分析理论框架下完成的.

强阻尼波动方程组解的性质

运用了Potential Well方法研究了一类强阻尼波动方程组初边值问题在Rn解的存在性,定义了该方程组的位势深度d,运用Poincaré-Soblev嵌入定理证明了位势深度d>0,再通过构建适当的能量函数E(t),稳定集和不稳定集,当初始值属于不稳定集时,解在有限时间爆破和解的衰减估计.

表面等离子体无掩膜干涉光刻系统的数值分析(英文)

表面等离子体激元具有近场增强效应,可以代替光子作为曝光源形成纳米级特征尺寸的图像.本文数值分析了棱镜辅助表面等离子体干涉系统的参量空间,并给出了计算原理和方法.结果表明,适当地选择高折射率棱镜、低银层厚度、入射波长和光刻胶折射率,可以获得高曝光度、高对比度的干涉图像.入射波长为431nm时,选择40nm厚的银层,曝光深度可达200nm,条纹周期为110nm.数值分析结果为实验的安排提供了理论支持.

3-D NONLINEAR SUPERCAVITATING FLOW IN A GRAVITY FIELD

Perturbation method and Fourier-cosine-expansion method were used to solve a 3-D nonlinear super-cavitating flow in an inclined field under gravity effect at large Froude numbers. By expanding the velocity potential into a power series of a small parameter, the original 3-D nonlinear problem was reduced to a number of 2-D one. The solutions of the first three orders were derived and expressed in terms of the complete elliptic integrals of the first and second kinds. The boundary integral equations method was applied to getting the numerical solutions. Computational results were obtained for super-cavitating flow past cone under various flow conditions.

具有阻尼的半线性波动方程解的衰减估计

研究具有阻尼的半线性波动方程的初边值问题u_(tt)-△u+βu_t=|u|^(p-1)u,x∈Ω,t>0u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈Ωu|_((?)Ω)=0,t≥0其中γ为正常数,Ω■R^n为有界域,当n≥3时,1<p≤(n+2)/(n-2);当n=1,2时,1<p<∞.首先利用紧致性方法和位势井方法证明了此问题整体弱解的存在性.而后,利用位势井族方法证明了,当时间t→+∞时,此解依t的指数形式衰减于零.结果从根本上改进了已有结果.