Impact of a Bumpy Nonuniform Electric Field on Oscillations of a Massive Point-Like Charged Particle

As a general feature, the electric field of a localized electric charge distribution diminishes as the distance from the distribution increases;there are exceptions to this feature. For instance, the electric field of a charged ring (being a localized charge distribution) along its symmetry axis perpendicular to the ring through its center rather than as expected being a diminishing field encounters a local maximum bump. It is the objective of this research-oriented study to analyze the impact of this bump on the characteristics of a massive point-like charged particle oscillating along the symmetry axis. Two scenarios with and without gravity along the symmetry axis are considered. In addition to standard kinematic diagrams, various phase diagrams conducive to a better understanding are constructed. Applying Computer Algebra System (CAS), [1] [2] most calculations are carried out symbolically. Finally, by assigning a set of reasonable numeric parameters to the symbolic quantities various 3D animations are crafted. All the CAS codes are included.

A Solvable Model in Two—Dimensional Gravity Coupled to a Nonlinear Matter Field

The two-dimensional gravity model with a coupling constant k = 4 and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.

Effects of Interaction Between Gravitation and Nonlinear Electrodynamics On Scalar Field Evolution

在这份报纸，我们由使用第三顺序的 WKB 近似在 dyadosphere spacetime 调查分级的地进化。我们发现在引力和非线性的 electrodynamics 之间的联合术语让分级的地更快速腐烂，它也让分级的地更慢慢地震荡。在另外的词上，这个联合术语作为一个抑制因素在分级的地进化上生效。同时，这些效果与更高的角度量数字为分级的地变得更明显。

STUDY OF EXPLICIT ANALYTIC SOLUTIONS FOR THE NONLINEAR COUPLED SCALAR FIELD EQUATIONS

By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.

Phased Array Beam Fields of Nonlinear Rayleigh Surface Waves

This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation. Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays, a more general model equation and integral forms of quasilinear solutions are introduced. Some features of steered and focused beam fields radiated from a linear phased array of the second harmonic Rayleigh wave are presented.

Effective Response of Nonlinear Spherical Coated Composites Under External AC and DC Electric Field

在外部交流和 DC 电场下面，非线性的球形的涂的 composites 的有效反应，服从电的排水量和电场的组成的关系，被使用不安方法在 dilute 限制调查。在包括和主人区域的本地潜力根本被导出泛音。而且，有效线性、非线性的回答的公式在 dilute 限制被给。

Enhanced Kerr nonlinearity in a left-handed three-level atomic system driven by a bichromatic field

China） Enhanced Kerr nonlinearity in a left-handed atomic system consisting of three levels driven by a bichromatic field is presented in this paper. Based on bichromatic field coherence, the real parts of the permittivity and permeability can obtain negative values simultaneously in the same detuning frequency region. By adjusting the frequency difference and the Rabi frequencies of the bichromatic field, the multi-band left-handed behavior of the presented atomic metamaterial is exhibited. Meanwhile, the enhanced Kerr nonlinearity can be realized in this multi-band left-handed three-level atomic system. It is shown that the third-order susceptibility possesses focusing or defocusing properties in the same frequency band.

A Model for Periodic Nonlinear Electric Field Structures in Space Plasmas

In this study,we present a physical model to explain the generation mechanism of nonlinear periodic waveswith a large amplitude electric field structures propagating obliquely and exactly parallel to the magnetic field.The'Sagdeev potential' from the MHD equations is derived and the nonlinear electric field waveforms are obtained when theMach number,direction of propagation,and the initial electric field satisfy certain plasma conditions.For the parallelpropagation,the amplitude of the electric field waves with ion-acoustic mode increases with the increase of initial electricfield and Mach number but its frequency decreases with the increase of Mach number.The amplitude and frequency ofthe electric field waves with ion-cyclotron mode decrease with the increase of Mach number and become less spiky,andits amplitude increases with the increase of initial electric field.For the oblique propagation,only periodic electric fieldwave with an ion-cyclotron mode obtained,its amplitude and frequency increase with the increase of Mach number andbecome spiky.From our model the electric field structures show periodic,spiky,and saw-tooth behaviours correspondingto different plasma conditions.

Structures, Fields and Methods of Identification of Nonlinear Static Systems in the Conditions of Uncertainty

The field of structures on set of secants is offered and methods of its construction for various classes of one-valued nonlinearities of static systems are considered. The analysis of structural properties of system is fulfilled on specially generated set of data. Representation on which modification it is possible to judge to nonlinear structure of static systems is introduced. It is shown, that structures of nonlinear static systems have a special V-point. The adaptive algorithm of an estimation of structure of nonlinearity on a class poly-nomial function is offered.

Preparation of AgCl Nano-Crystal Embedded Tellurite Nonlinear Optical Glasses under Electric Field Accompanied Heat Treatment

The quantum effect of nano-crystals is an important factor to improve nonlinear optical performance of nanocrystal embedded glasses, while controlling the size distribution and content of nano-crystals in the glass accurately is a key to obtain good quality. The auxiliary direct current electric field, accompanied with heat treatment, was applied on AgCI containing niobic tellurite glass sheet. The nucleation and crystallization of the glass were well controlled under auxiliary electric field. It was found that the average size of AgCI nano-crystal particles in the glass is smaller than that under single heat treatment, and the content of nano- crystals is higher. Therefore the third-order nonlinear optical performance of the glass was increased a lot. The local-area distributed AgCl nano-crystal particles can also be embedded into a glass sheet by using locally applied electric field.

Effects of Nonlinear Couplings on Entanglement in a Two-Qutrit Heisenberg XXX Chain under an Inhomogeneous Magnetic Field

这份报纸在一个不同类的磁场下面与非线性的 couplings 调查 two-qutrit 海森堡 XXX 链的纠纷。由否定性的概念，我们发现批评温度随不同类的磁场 b 的增加增加。我们的学习为任何 | K 显示那|>|J| ，或 | K |<| J |纠纷总是为某些区域存在。我们也发现在批评的点，纠纷成为 B 的 nonanalytic 功能，量阶段转变发生。

Novel Localized Excitations of Nonlinear Coupled Scalar Fields

印射非线性的联合分级的领域和著名 4 模型的关系的某扩大答案被介绍。同时，由最近 Jia，黄和 Lou 建议的著名 4 模型的新解决方案启发了，非线性的联合数量的五种新局部性的刺激回答(NCSF ) 系统被获得。

Analysis of a Gyroscope′s Rotor Nonlinear Supported Magnetic Field Based on the B-Spline Wavelet-FEM

A supported framework of a gyroscope＇s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling function of the B-spline wavelet is considered as the shape function of a tetrahedton. The magnetic field is spited by an artificial absorbing body which used the condition of field radiating, so the solution is unique. The resolution is improved via the varying gradient of the B-spline function under the condition of unchanging gridding. So there are some advantages in dealing with the focus flux and a high varying gradient result from a nonlinear magnetic field. The result is more practical. Plots of flux and in the space is studied via simulating the supported system model. The results of the study are useful in the research of the supported magnetic system for the gyroscope rotor.

General Formulations of Finite-field Method Classifiedby Symmetry for Molecular Linear and Nonlinear Polarizabilities

The formulations of the finite-field approach to calculate the linear and non-linear optical coefficients (i, (ij, (ijk and (ijkl of a molecular system with different symmetries have been deduced and summarized. The possible choices of the energy sets of the 48 frequent point groups have been optimized and categorized into 11 classes. With the restriction of symmetry operators, a minimum of 9, no more than 21 energy points have to be calculated in order to determine the coefficients, except in the case of the first class to which C1 point group belongs and in which the 34 non-relative energy points selected in our uniform and general scheme are all needed. The symmetric operators that cause some of the tensor components to vanish have been demonstrated as well.

The internal circulations on internal mass transfer rate of a single drop in nonlinear uniaxial extensional flow

The internal flow of a droplet in the nonlinear extensional flow field will exhibit more than two internal circulations with the variation of nonlinear intensity(E).In this paper,the effect of positions and sizes of internal circulations on internal mass transfer rate of a single spherical droplet in a nonlinear extensional flow field is studied and compared with that in a linear extensional flow field.The simulation results show that when E≥0,there are two symmetrical internal circulations in the droplet,which is the same with that in a linear extensional flow.The limit value of mass transfer rate Sh is 15,which is equal to that in a linear extensional flow,no matter how large E is.When E≤-3/7,the number of internal flow circulation of a droplet increase to four and the transfer rate Sh increases.When E=-1,the maximum internal transfer rate Sh equals 30 which is twice of that in a linear extensional flow.The generation of new flow circulations in droplets and the circulation positions will enhance mass transfer when E≤-3/7,which provides a new idea for enhancing the internal mass transfer rate of droplets.

Effective Response of Nonlinear Composite under External AC and DC Electric Field

A perturbation method is used to study effective response of nonlinear Kerr composites, which are subject to the constitutive relation of electric displacement and electric field, Dα = εαE + xα|E|2E. Under the external AC and DC electric field Eapp = Eα(1 + sinwt), the effective nonlinear responses and local potentials are induced by the cubic nonlinearity of Kerr materials at all harmonics. As an example in three dimensions, we have investigated this kind of nonlinear composites with spherical inclusions embedded in a host. At all harmonic frequencies, the potentials in inclusion and host regions are derived. Furthermore, the formulae of the effective linear and nonlinear responses are given in the dilute limit.

Electric field distribution and effective nonlinear AC and DC responses of graded cylindrical composites

The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current（AC） and direct-current（DC） electric field E app = E 0（1 ＋ sin ωt）.The dielectric profile of the cylindrical inclusions is modeled by function ε i（r） = C k r k（r ≤ a）,where r is the radius of the cylindrical inclusion,and C k,k,a are parameters.In the dilute limit,the local potentials and the effective nonlinear responses at all harmonics are derived.Meanwhile,the general effective nonlinear responses are also derived and compared with the effective nonlinear responses at harmonics under the AC and DC external field.It is found that the effective nonlinear AC and DC responses at harmonics can be calculated by those of the general effective nonlinear of the graded composites under the external DC electric field.Moreover,the obtained local electrical fields show that the electrical field distribution in the cylindrical inclusions is controllable,and the maximum of the electric field inside the cylinder is at its center.

Effective response of nonlinear cylindrical coated composites under external AC and DC electric field

This paper uses the perturbation method to study effective response of nonlinear cylindrical coated composites. Under the external AC and DC electric field Ea （1 ＋sin ωt）, the local potentials of composites at all harmonic frequencies are induced. An effective nonlinear response to composite is given for the cylindrical coated inclusions in the dilute limit.

Effective response in nonlinear spherical coated composites under external AC and DC electric fields

By using the perturbation method, effective nonlinear direct current （DC） and alternating current （AC） responses of nonlinear composites with spherical coated inclusions randomly embedded in a host medium are studied under the action of an external electric field Ea = E0 ＋ E1 sinωt ＋ E3 sin 3ωt with different amplitudes and frequencies. The local potentials of composites at all harmonics are given in the inclusion particles and the host regions. All effective nonlinear responses to composites and the relationship between the effective nonlinear responses at all harmonics are also deduced for the spherical coated inclusions in a dilute limit.

透明硬脆材料激光剥离关键问题研究(特邀)

透明硬脆材料由于其优异的力学性能、热稳定性、耐腐蚀性以及光电性能,广泛应用于半导体与电子领域。传统透明硬脆材料切片方法效率低、材料损耗大,制约了硬脆材料的推广应用。激光剥离技术是近年来新兴的一种透明硬脆材料切片新方法,较传统金刚线切割方法大幅提升硬脆材料的切片效率和材料利用率,目前已发展成为硬脆材料激光加工领域学术研究与产业应用的焦点。文中深入分析透明硬脆材料激光剥离物理过程,归纳激光剥离过程关键科学问题:透明硬脆材料对激光的非线性吸收、激光作用下材料内部微观结构演化与缺陷扩展规律,以及激光光场调控对材料改质影响机制等。基于这些科学问题,综述了近年来激光剥离不同类型透明硬脆材料的研究进展,目前用于激光剥离的材料已涵盖了SiC、Si、GaN、金刚石等半导体材料,蓝宝石、多晶Al_(2)O_(3)、氧化锆等陶瓷材料,激光剥离技术已发展出超快激光双脉冲诱导剥离、超快激光-化学辅助剥离、多激光复合剥离等。激光剥离物理过程是一个典型的激光-材料-热学-力学多学科交叉问题,尽管在实验结果方面获得了显著突破和迅猛发展,但目前对于工艺机理仍缺乏深入的理论与数值建模研究。未来透明硬脆材料激光剥离技术将会朝着百微米以下超薄厚度剥离、改质层低损伤、工艺自适应等方向发展,将为半导体与电子等领域快速发展提供更大的技术支撑。