瞬态热传导问题的复变量重构核粒子法

在重构核粒子法的基础上,引入复变量,讨论了复变量重构核粒子法.复变量重构核粒子法的优点是在构造形函数时采用一维基函数建立二维问题的修正函数.然后,将复变量重构核粒子法应用于瞬态热传导问题的求解,结合瞬态热传导问题的Galerkin积分弱形式,采用罚函数法引入本质边界条件,建立了瞬态热传导问题的复变量重构核粒子法,推导了相应的计算公式.与传统的重构核粒子法相比,复变量重构核粒子法具有计算量小、精度高的优点.最后通过数值算例证明了该方法的有效性. 关键词： 重构核粒子法 复变量重构核粒子法 修正函数 瞬态热传导问题     

Makarov势的Dirac方程的束缚态解

给出了Makarov型标量势与矢量势相等条件下的Dirac方程的束缚态解. Dirac方程的角向方程用因子分解方法求解，在得出角向波函数的过程中，自然地得到了属于同一本征值的不同角向波函数间的递推操作. 径向束缚态波函数用合流超几何函数表示，束缚态的能量方程可由径向波函数满足的边界条件得到. 关键词： Makarov势 Dirac方程 束缚态 因子分解方法     

叶栅全三维粘性反问题的数值解

本文发展了一种解叶栅全三维粘性反问题的新的数值方法.基于非正交曲线坐标与相应的非正交速度分量下完全守恒型的Navier－Stokes方程,全三维反问题规定叶片表面的无量纲压力分布反求叶型。计算中叶片表面的边界条件采用一种特殊的方式来处理，即一方面强加给定的压力分布条件,另方面叶面的几何位置在迭代过程中又是可移动的，其移动速度将与Navier—Stokes方程在当地的解联系起来，从而形成一种解定常问题的新的不定常过程.试算证明了本文方法的可行性。     

基于极大似然目标状态估计的传感器管理

依据贝叶斯概率知识,采用一种极大似然的最优化方法来估计目标运动的状态估计值。基于极大似然目标状态估计方法不仅可通过最优化策略求解目标状态估计值的显示解,还可处理各种关于观测变量和状态变量的约束条件。依据目标状态估计的误差协方差矩阵与其Fisher信息矩阵间的紧密联系,详细推导似然函数关于目标状态各个分量的偏导。采用随机离散时间系统的知识,推导出对角式Fisher信息矩阵的所有对角线上的各个元素。以Fisher信息矩阵的迹范数作为传感器管理中的最优代价函数,采用0-1整数规划算法来求解传感器的分配矩阵。最后利用某仿真算例来验证方法的有效性.     

磁化尘埃等离子体中的冲击波及其横向扰动稳定性

利用双曲函数法得到ZKB方程的一组冲击波解,并对波在横向扰动下的动力学稳定性进行研究.对冲击波解进行线性稳定性分析,并构造高精度的有限差分格式求解所得本征值问题.结果表明：对于正耗散的情形,该冲击波在线性意义下稳定;对于负耗散情形,该冲击波在线性意义下不稳定.构造有限差分格式对受扰动的冲击波进行非线性动力学演化,结果表明：对于正耗散的情况,该冲击波是稳定的.     

二维涡流的反馈与操控

本文研究方向为二维涡流的反馈效应和操控技术.首先研究了无损探测中最重要的涡流探测,借鉴电磁辐射问题的结论,证明了该逆问题解的唯一性.其次,探究了涡流探测在工业中的原理以及影响涡流探测的因素.最后,利用麦克斯韦方程组在任意曲面坐标系和直角坐标系下形式是等价的这一结论,通过改变磁导率、介电常数来改变电磁场的坐标,达到对涡流操控的目的.     

用松弛法解薛定谔方程

求解定态薛定谔方程常常会涉及到常微分方程的本征值问题.目前解常微分方程本征值用的比较多的方法是以龙格-库塔方法为基础的打靶方法.打靶方法常用,但是计算时间长.当边界条件比较复杂或比较敏感的时候,用松弛法会有更好的效果.本文用松弛法解薛定谔方程,并和理论解进行比较.发现松弛法得到的数值解和理论解符合度很高,而且使用松弛法能够很快得到符合要求的解.     

不确定动态混沌系统的最优控制

对于混沌系统的控制问题,考虑到控制系统能量限制的要求,首先确立一个二次目标函数,然后给出了求解最优控制律的一个简单方法,该方法通过求解线性二次最优控制问题,获得了混沌系统的最优控制律,避免了求解非线性Hamilton-Jacobi-Bellman偏微分方程(HJB方程)的困难.利用Lyapunov方法证明了闭环系统的稳定性.对统一混沌系统和Liu混沌系统的仿真结果表明了控制策略的有效性.     

不确定动态混沌系统的最优控制

对于混沌系统的控制问题,考虑到控制系统能量限制的要求,首先确立一个二次目标函数,然后给出了求解最优控制律的一个简单方法,该方法通过求解线性二次最优控制问题,获得了混沌系统的最优控制律,避免了求解非线性Hamilton-Jacobi-Bellman 偏微分方程(HJB方程)的困难.利用Lyapunov方法证明了闭环系统的稳定性.对统一混沌系统和Liu混沌系统的仿真结果表明了控制策略的有效性.     

瞬态温度场的解及其振荡

本文在子空间内求解瞬态温度场，有效地避免了产生违背传热规律的解及其振荡。产生解的振荡的根本原因是传统的全空间解法，而不是时间差分格式。当热源为非减函数（升温过程）或非增函数（降温过程）时，在新算法中所用的时间步长可不受限制。     

脉冲涡流检测瞬态涡流场的时域解析模型

应用Laplace反变换技术建立脉冲涡流检测瞬态涡流场的时域解析模型.首先,基于电磁波的反射与透射理论,应用截断区域特征函数展开式法建立瞬态涡流场的复频域模型,然后通过求解模型极点及其留数应用部分分式展开法求解复频域模型的Laplace反变换,从而建立阶跃型和指数型电流激励下瞬态涡流场的时域解析模型.所建模型具有实现简单、效率高、模型精度不受吉布斯效应影响等优点.最后应用基于Fourier反变换的探头瞬态感应电压模型对本文所建模型,实验结果验证了本文所建模型的正确性.     

Transient electromagnetic simulation and thermal analysis of the DC-biased AC quadrupole magnet for CSNS/RCS

Due to the large eddy currents at the ends of the quadrupole magnets for CSNS/RCS, the magnetic field properties and the heat generation are of great concern. In this paper, we take transient electromagnetic simulation and make use of the eddy current loss from the transient electromagnetic results to perform thermal analysis. Through analysis of the simulated results, the magnetic field dynamic properties of these magnets and a temperature rise are achieved. Finally, the accuracy of the thermal analysis is confirmed by a test of the prototype quadrupole magnet of the RCS.     

A representation of Kerr-like nonlinearity for the analytical TM surface polariton solution

The TM-polarized waves propagating along the interface between a nonlinear Kerr-like material and linear cladding are investigated. We analyse the nonlinear dielectric permittivity as a function of the electromagnetic field. It is shown that an exact analytical solution of Maxwell's equations corresponding to the TM surface polariton in the form described by sech function do exist in a Kerr-like nonlinear medium with the permittivity profile given by a hypergeometric function. We compare our analytical solution and analogous exact numerical solution in a Kerr medium. The power flow down the interface between two media is also discussed.     

Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution

Surface plasmons (SPs) are surface-bound electromagnetic waves supported by metals, offering the possibility of strong spatial confinement of electromagnetic fields on the micro- and nanoscales. They suffer, however, from strong damping caused by internal absorption and radiation losses. Here we demonstrate amplification of SPs by stimulated emission, which marks a possible solution to this problem. We use an attenuated-total-reflection setup to detect stimulated emission of SPs at the interface between a silver film and an optically pumped dye solution acting as the amplifying medium. Clear evidence of stimulated emission is provided by an excellent agreement of the experimental observations with a theoretical analysis. Amplification of SPs can be considered analogous to photon amplification in a laser, thereby suggesting novel approaches in the field of nano-optics.     

On the structure of the velocity field under the free spheroidal surface of a viscous liquid drop oscillating in an electrostatic field

An asymptotic analytical solution to an initial boundary-value problem considering (i) the time evolution of the capillary oscillation amplitude as applied to a viscous spheroidal liquid drop placed in a uniform electrostatic field and (ii) the liquid flow velocity field inside the drop is found. The problem is solved in an approximation that is linear in two small parameters: the dimensionless oscillation amplitude and the dimensionless field-induced constant deformation of the equilibrium (spherical) shape of the drop. Terms proportional to the product of the small parameters are retained. In this approximation, interaction between oscillation modes is revealed. It is shown that the intensity of the eddy component of the oscillation-related velocity field depends on the liquid viscosity and the external uniform electrostatic field strength. The intensity of the eddy component decays rapidly with distance from the free surface. The depth to which the eddy flow (which is caused by periodical flows on the free surface) penetrates into the drop is a nonmonotonic function of the polar angle and increases with dimensionless viscosity and field strength.     

A generalized Milne solution for the correlation effects of multiple light scattering with polarization

The Wiener-Hopf method is used to obtain a generalized Milne solution for scalar and electromagnetic fields with single-scattering anisotropy. For the scalar field, the solution found for the time correlation function and the interference component of backscattering is in good agreement with available experimental data. A solution of the Milne problem is constructed for the electromagnetic field. Given anisotropy, the generalized Milne equation is solved in the P₁ approximation for the quantity that describes the degree of depolarization of the scattered light. It is shown that the depolarization of the scattered light can change sign at large anisotropies.     

Analytical solutions of transient pulsed eddy current problem due to elliptical electromagnetic concentrative coils

The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing.In this paper,we propose a figure-8-shaped coil being composed of two arbitrary oblique elliptical coils,which can change the electromagnetic concentrative region and the magnitude of eddy current density by changing the elliptical shape and/or spread angle between two elliptical coils.Pulsed current is usually the excitation source in the functional magnetic stimulation,so in this paper we derive the analytical solutions of transient pulsed eddy current field in the time domain due to the elliptical concentrative coil placed in an arbitrary position over a half-infinite plane conductor by making use of the scale-transformation,the Laplace transform and the Fourier transform are used in our derivation.Calculation results of field distributions produced by the figure-8-shaped elliptical coil show some behaviours as follows:1) the eddy currents are focused on the conductor under the geometric symmetric centre of figure-8-shaped coil;2) the greater the scale factor of ellipse is,the higher the eddy current density is and the wider the concentrative area of eddy current along y axis is;3) the maximum magnitude of eddy current density increases with the increase of spread angle.When spread angle is 180,there are two additional reverse concentrative areas on both sides of x axis.     

New Method for 3D Transient Eddy Current Field Calculation and Its Application in Magneto-Acoustic Tomography

A new method of 3 D transient eddy current field calculation is proposed. The Maxwell equations with time component elimination(METCE) are derived under the assumption of magnetic quasi static approximation, especially for the sample of low conductivity. Based on METCE, we deduce a more efficient reconstruction algorithm of a3 D transient eddy current field. The computational burden is greatly reduced through the new algorithm, and the computational efficiency is improved. This new algorithm decompounds the space-time variables into two individual variables. The idea is to solve the spatial vector component firstly, and then multiply it by the corresponded time component. The iterative methods based on METCE are introduced to recover the distribution of conductivity in magneto-acoustic tomography. The reconstructed images of conductivity are consistent with the original distribution, which validate the new method.     

Interpolation method for transient electromagnetic fields

Summary The method for the transient electromagnetic fields interpolation from the irregular to the uniform array is suggested. It is based on the approximation of the observed data by the field of the current plane disposed at some depth in the homogeneous conductive Earth. The interpolation problem is reduced to solving the Fredholm integral equation of the first kind for unknown distribution of the current in the plane. The discretization of the integral equation results in the systems of the linear equations which are solved by the method of the singular value decomposition. The distribution of the current in the plane is used not only for the interpolation of the observed field but also for the calculation of the linear transformations of the field components. The results of testing of the method on theoretical models are presented. To speed up publication, the proofs were not sent to the authors and were supervised by the Scientific Committee.     

A theoretical and numerical resolution of an acoustic multiple scattering problem in three-dimensional case

This paper develops an analytical solution for sound, electromagnetic or any other wave propagation described by the Helmholtz equation in three-dimensional case. First, a theoretical investigation based on multipole expansion method and spherical wave functions was established, through which we show that the resolution of the problem is reduced to solving an infinite, complex and large linear system. Second, we explain how to suitably truncate the last infinite dimensional system to get an accurate stable and fast numerical solution of the problem. Then, we evaluate numerically the theoretical solution of scattering problem by multiple ideal rigid spheres. Finally, we made a numerical study to present the “Head related transfer function” with respect to different physical and geometrical parameters of the problem.