Application of the transfer matrix for tuning the CSNS-DTL

In the construction of a drift tube LINAC (DTL), many factors caused during the fabrication and assembly of the structure cells cause the electric field distribution not as the same as the design curve. To solve this problem, the traditional way is to solve the equation of Slater's perturbation theorem to obtain the electrical field variation due to local frequency shift. However, that is very difficult under complicated conditions. Since the field perturbation equation is similar to the particle's transverse motion equation, which can be simply solved by using the transfer matrix method, we thus propose to apply a transfer matrix method in tuning the DTL. We demonstrate the availability and advantages of this method with 3D microwave code simulation and the LabVIEW calculation program. After two iterations, the initial error of the electric field of 19.5% has been improved greatly down to 1.3%- -4.5%. This indicates that the transfer matrix method is very useful and convenient for the simplification of tuning procedures.     

微粗糙面上方球形粒子的光散射及其散射截面的计算

基于互易定理研究了光波入射时微粗糙面与其上方球形粒子复合模型的光散射。根据粗糙表面电流积分方程并利用表面微扰展开，得到了微粗糙面表面极化电流的迭代解，给出了耦合电场的计算方法。结合散射耦合场散射矩阵和已有的微粗糙面及球形粒子的散射矩阵，给出了复合模型散射截面的计算公式，数值计算了复合模型的后向散射截面并进行了详细讨论。     

基于Geant4的回旋加速器束流动力学计算

针对回旋加速器的束流动力学设计,基于Geant4模拟研究,提供一种可行的数值模拟方法。通过电磁场仿真软件Opera建立相应的电磁场数据导入到Geant4中进行插值计算,利用Geant4自带的电磁场微分方程与微分方程求解器计算粒子的平衡轨道,振荡频率以及加速轨道。其结果表明:对于横向运动而言,Geant4的计算结果与传统数值方法计算结果趋于一致;对于轴向运动而言,由于磁场插值方法的差异性,二者有一定的区别,对于在加速过程中的非平衡粒子,其能量变化围绕平衡粒子振荡。对于束损,通过限制粒子的运动时间,轴向位移加快计算效率,加入电极碰撞的判定使模拟更趋近实际情况。     

NON-LINEAR FORCED VIBRATIONS OF PLATES BY AN ASYMPTOTIC-NUMERICAL METHOD

Non-linear forced vibrations of thin elastic plates have been investigated by an asymptotic-numerical method (ANM). Various types of harmonic excitation forces such as distributed and concentrated are considered. Using the harmonic balance method and Hamilton's principle, the equation of motion is converted into an operational formulation. Based on the finite element method a starting point corresponding to a non-linear solution associated to a given frequency and amplitude of excitation is computed. Applying perturbation techniques in the vicinity of this solution, the non-linear governing equation obtained is transformed into a sequence of linear problems having the same stiffness matrix. Employing one matrix inversion, a large number of terms of the perturbation series of the displacement and frequency can be easily computed with a small computation time. Iterations of this method lead to a powerful path-following technique. Comprehensive numerical tests for forced vibrations of plates subjected to time-harmonic lateral excitations are reported.     

Nuclear spin echo model based on Floquet–Lyapunov theory

The method of nuclear spin-echo amplitude calculation based on the density matrix technique is improved. The Floquet–Lyapunov theorem for a system of the ordinary differential equations with coefficients periodically dependent on time is used to find the solution of the Schrödinger equation for the time-evolution operator which describes behavior of a nuclear spin in the presence of a radiofrequency pulsed magnetic field. NQR spin echo for the case of nuclear spin I?=?1 and NMR spin echo for I?=?1/2 are considered as the simplest illustrations of the approach. The appearance of multiple spin echoes is predicted in the case of strong radiofrequency field.     

Low Frequency Circular Polarized Soliton in a Ferromagnetic System Under a Strong Bias Magnetic Field

The derivative nonlinear Schrodinger equation for the low frequency circular polarized wave, propagating parallel to the bias magnetic field in a ferromagnetic system, is derived by the reductive perturbation expansion method.     

含负折射率材料并具有零平均折射率的半无限一维光子晶体的表面态

用传输矩阵方法和Bloch定理,从理论上分析以色散介质为背景,由正负折射率材料组成的半无限一维光子晶体的表面态,发现以色散介质为背景,在满足平均折射率等于零的情况下,第一层厚度变化时,表面态将会在较大频率范围内显著变化。讨论了同一入射角度下不同频率的表面态的电场分布情况,结果表明：远离带边的表面态局域长度较小。     

Symplectic Symmetries of Hamiltonian Systems

Abstract

We prove a generalization to the case of s × s matrix linear differential operators of the classical theorem of E. Cotton giving necessary and sufficient conditions for equivalence of eigenvalue problems for scalar linear differential operators. The conditions for equivalence to a matrix Schrödinger operator are derived and formulated geometrically in terms of vanishing conditions on the curvature of a gl(s, R)-valued connection. These conditions are illustrated on a class of matrix differential operators of physical interest, arising by symmetry reduction from Dirac’s equation for a spinor field minimally coupled with a cylindrically symmetric magnetic field.     

KAM Theory in Configuration Space and Cancellations in the Lindstedt Series

The KAM theorem for analytic quasi-integrable anisochronous Hamiltonian systems yields that the perturbation expansion (Lindstedt series) for any quasi-periodic solution with Diophantine frequency vector converges. If one studies the Lindstedt series by following a perturbation theory approach, one finds that convergence is ultimately related to the presence of cancellations between contributions of the same perturbation order. In turn, this is due to symmetries in the problem. Such symmetries are easily visualised in action-angle coordinates, where the KAM theorem is usually formulated by exploiting the analogy between Lindstedt series and perturbation expansions in quantum field theory and, in particular, the possibility of expressing the solutions in terms of tree graphs, which are the analogue of Feynman diagrams. If the unperturbed system is isochronous, Moser’s modifying terms theorem ensures that an analytic quasi-periodic solution with the same Diophantine frequency vector as the unperturbed Hamiltonian exists for the system obtained by adding a suitable constant (counterterm) to the vector field. Also in this case, one can follow the alternative approach of studying the perturbation expansion for both the solution and the counterterm, and again convergence of the two series is obtained as a consequence of deep cancellations between contributions of the same order. In this paper, we revisit Moser’s theorem, by studying the perturbation expansion one obtains by working in Cartesian coordinates. We investigate the symmetries giving rise to the cancellations which makes possible the convergence of the series. We find that the cancellation mechanism works in a completely different way in Cartesian coordinates, and the interpretation of the underlying symmetries in terms of tree graphs is much more subtle than in the case of action-angle coordinates.     

Regular and singular perturbation expansions in the analysis of extensional vibrations of plates

The Kane-Mindlin differential equations appropriate for the study of low and high frequency extensional vibrations in elastic plate strips are solved by means of perturbation techniques. These procedures permit the development of simple expressions that can be used for the rapid calculation of the natural frequencies of vibration as a function of material and geometric parameters. A regular perturbation expansion yields an approximate form of the frequency relationship that is useful in the high frequency range, whereas in the low frequency range a singular perturbation procedure is used since the expansion parameter appears in the coefficient of the highest order derivative in the fundamental differential equation. Approximate formulas and some numerical results are presented for three types of boundary conditions.     

在均匀强磁场中氢原子塞曼效应久期方程的简化公式

在均匀强磁场中,当氢原子的哈密顿量中B2项不能忽略时,氢原子的库仑场对称性遭到破坏,能级简并被全部解除.在应用变分法和数值法计算氢原子的能级过程中,计算十分复杂,而应用微扰法求解氢原子的能级,存在解久期方程的n2高阶行列式的困难.本文应用简并态微扰理论和球谐函数的性质,得到久期方程中非零微扰矩阵元普遍表达式.根据非零微扰矩阵元普遍表达式的性质,可以将氢原子塞曼效应久期方程的n2高阶行列式分解成1阶到n阶共n个低阶行列式的乘积,得到氢原子塞曼效应久期方程的简化公式,使得求解均匀强磁场中氢原子塞曼效应能级过程简化.而且由该公式可以得到氢原子在低能态时塞曼效应能级的解析解.根据该久期方程的简化公式计算了n=3氢原子塞曼效应一级近似能级.     

Closed-form solutions for the frequency shift of V-shaped probes scanning an inclined surface

The analytical method to determine the frequency shift of an AFM V-shaped probe scanning the relative inclined surface in non-contact mode is proposed. If the tip is not perpendicular to the surface plane, the lateral force to the tip will occurs. Consequently, there exists a moment to the end of probe. The closed-form solution of the partial differential equation with a nonlinear boundary condition is derived. The error of transforming the distributed-masses system into lumped-masses one in the force gradient method or the perturbation method is eliminated. The dimensionless parameters are introduced for reducing the numerical transaction error. The limiting case such as a uniform or tapered beam can be obtained easily from the general system. The assessments of the force gradient method, the perturbation method and the propose method determining the frequency shift of a V-shaped probe are made. It is discovered that increasing the absolute inclined angle θ decreases the frequency shift especially for a small tip-surface distance.     

Photo- and electroreflectance spectra from spatially inhomogeneous heterostructures calculated by means of a new method

The problem of calculating photo and electro-reflectance spectra from weakly inhomogeneous layers of semiconductor heterostructures is solved by combining two former approaches; the transfer matrix method and the perturbation theoretical treatment of the weak inhomogeneity. The electric field profile and its perturbation by pump light is calculated from an integral equation. The method is applied to several heterostructures based on (Ga,Al)As. Due to its speed and accuracy the method is capable of online simulation of PR and ER spectra.     

广义Birkhoff方程的积分方法

场方法和最终乘子法是求解运动微分方程的基本方法.本文将这两种方法应用于广义Birkhoff系统,求出了场方法的基本偏微分方程和该方程的完全积分;根据Jacobi最终乘子定理求出了广义Birkhoff方程的解.并举例说明结果的应用.     

Ket-Bra纠缠态方法研究含时外场中与热库耦合Qubit的演化

采用Ket-Bra纠缠态方法求解主方程, 研究了具有含时外场情况下单qubit和无相互作用的两qubit与热库耦合时的量子退相干、退纠缠现象. 对两qubit情形, 我们以共生纠缠度(concurrence)作为纠缠度量, 研究了其纠缠动力学演化过程. 研究表明即使系统内部不存在直接、间接的相互作用, 施加含时外场也能引起纠缠的震荡和复活, 这为通过施加控制外场抑制开放系统的退相干、退纠缠过程提供了理论支持.     

Small perturbations in the γ-field behind a barrier

The variations in the functionals of the radiation field behind a barrier caused by a local inhomogeneity of the cavity type in the barrier are treated in the small perturbation approximation. An equation is derived for the variation which is convenient in using the statistical-test method in numerical calculations.     

An integral equation approach to acoustic cloaking

The paper presents an original boundary integral equation (BIE) formulation for the analysis of the acoustic cloaking of a scatterer. The advantage of such an approach is the lower computational burden, especially when the analysis of a large portion of the hosting domain is required. The partial differential equation governing the propagation inside the cloak is recast in the form of non-homogeneous wave equation, with field sources depending on the mechanical properties of the cloak. The boundary integral formulation is derived using the standard procedure. The boundary element method (BEM) is used to derive the matrix transfer function of the cloak. The latter is applied to the incident field at the cloak's outer boundary to obtain the total field at arbitrary locations in the host. The formulation is applied to the simple case of a radially symmetric cloak embedding a circular obstacle. Numerical results are presented for sound-hard and sound-soft obstacles, including a study of the cloaking efficiency as a function of the frequency.     

Variation of wave action: Modulations of the phase shift for strongly nonlinear dispersive waves with weak dissipation

Strongly nonlinear dispersive waves described by a general Klein—Gordon equation with slowly varying coefficients and a dissipative perturbation are analyzed using the method of multiple scales. We use the exact equation of wave action. The spatial and temporal slow modulations of the phase shift are shown to be governed by a new equation, which results from linearization of the wave action, its flux, and its dissipation due to perturbations of the slow parameters: frequency and wave number (vector). This result extends to nonlinear partial differential equations, the quite recent work by the authors on nonlinear oscillations governed by ordinary differential equations.     

Circular Polarized Soliton Propagating at a Small Angle to Strong Bias Magnetic Field in a Ferromagnetic System

A variant of the derivative nonlinear Schrödinger equation for the low frequency circular polarized wave, propagating at a small angle to the bias magnetic field in a ferromagnetic system, is derived by the reductive perturbation expansion method. Bright and dark solitons are obtained.     

圆管结构中周向导波非线性效应的模式展开分析

在二阶微扰近似条件下, 采用导波模式展开分析方法研究了圆管结构中周向导波的非线性效应. 伴随基频周向导波传播所发生的二次谐波, 可视为由一系列二倍频周向导波模式叠加而成. 从动量定理出发, 结合柱坐标系下非线性应力张量及其散度的数学表达式, 针对圆管中某一基频周向导波模式, 推导出相应的二倍频应力张量及二倍频彻体驱动力的数学表达式, 建立了确定二倍频周向导波模式展开系数的控制方程, 得到了伴随基频周向导波传播所发生的二次谐波声场的形式解. 理论分析和数值计算表明, 当构成二次谐波声场的某一二倍频周向导波模式与基频周向导波的相速度匹配时, 该二倍频周向导波模式的位移振幅表现出随传播周向角积累增长的性质; 当两者的相速度失配时, 二倍频周向导波的振幅随传播周向角表现出“拍”效应.