A new nonlinear optical silicate carbonate K2Ca[Si2O5](CO3) with a hybrid structure of kalsilite and soda-like layered fragments

Single crystals of a new silicate carbonate, K₂Ca[Si₂O₅](CO₃), have been synthesized in a multi-components hydrothermal solution with a pH value close to neutral and a high concentration of a carbonate mineralizer. The new compound has an axial structure (s.g. P6₃22) with unit cell parameters a = 5.04789 (15), c = 17.8668 (6) Å. Pseudosymmetry of the structure corresponds to s.g. P6₃/mmc which is broken only by one oxygen position. The structure consists of two layered fragments: one of the type of the mineral kalsilite (KAlSiO₄) and the other of the high-temperature soda-like α-Na₂CO₃, Ca substituting for Na. The electro-neutral layer K₂[Si₂O₅] (denoted K) as well as the layer Ca(CO₃) (denoted S) may separately correspond to individual structures. In K₂Ca[Si₂O₅](CO₃) the S-K layers are connected together via Ca-O interactions between Ca atoms from the carbonate layer and apical O atoms from the silicate one, and also via K-O interlayer interactions. A hypothetical acentric structure, sp.gr. P-62c, is predicted on the basis of the order-disorder theory. It presents another symmetrical option for the arrangement of K-layers relative to S-layers. The K,Ca-silicate-carbonate powder produces a moderate SHG signal that is two times larger that of the α-quartz powder standard and close to other silicates with acentric structures and low electronic polarizability.     

Stationary Oberbeck–Boussinesq model of generalized Newtonian fluid governed by multivalued partial differential equations

A generalization of the Oberbeck–Boussinesq model consisting of a system of steady state multivalued partial differential equations for incompressible, generalized Newtonian of the p-power type, viscous flow coupled with the nonlinear heat equation is studied in a bounded domain. The existence of a weak solution is proved by combining the surjectivity method for operator inclusions and a fixed point technique.     

Higher-order Dirac solitons in binary waveguide arrays

We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range.     

Switching adaptive controllers to control fractional‐order complex systems with unknown structure and input nonlinearities

This article investigates the chaos control problem for the fractional‐order chaotic systems containing unknown structure and input nonlinearities. Two types of nonlinearity in the control input are considered. In the first case, a general continuous nonlinearity input is supposed in the controller, and in the second case, the unknown dead‐zone input is included. In each case, a proper switching adaptive controller is introduced to stabilize the fractional‐order chaotic system in the presence of unknown parameters and uncertainties. The control methods are designed based on the boundedness property of the chaotic system's states, where, in the proposed methods the nonlinear/linear dynamic terms of the fractional‐order chaotic systems are assumed to be fully unknown. The analytical results of the mentioned techniques are proved by the stability analysis theorem of fractional‐order systems and the adaptive control method. In addition, as an application of the proposed methods, single input adaptive controllers are adopted for control of a class of three‐dimensional nonlinear fractional‐order chaotic systems. And finally, some numerical examples illustrate the correctness of the analytical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 211–223, 2015     

Small Data Scattering for the One-Dimensional Nonlinear Dirac Equation with Power Nonlinearity

We study scattering problems for the one-dimensional nonlinear Dirac equation (?_t + α?_x + iβ)Φ = λ|Φ|^p?1Φ. We prove that if p > 3 (resp. p > 3 + 1/6), then the wave operator (resp. the scattering operator) is well-defined on some 0-neighborhood of a weighted Sobolev space. In order to prove these results, we use linear operators D(t)xD(?t) and t?_x + x?_t ? α/2, where {D(t)}_t∈? is the free Dirac evolution group. For the reader's convenience, in an appendix we list and prove fundamental properties of D(t)xD(?t) and t?_x + x?_t ? α/2.     

Variational Solution of Stochastic Schrödinger Equations With Power-Type Nonlinearity

We investigate a Schrödinger problem with multiplicative Gaussian noise term and power-type nonlinearity on a bounded one-dimensional domain. In order to prove the existence and uniqueness of the variational solution, a further process will be introduced which allows to transform the stochastic nonlinear Schrödinger problem into a pathwise one. Galerkin approximations and compact embedding results are used.     

灌浆理论浅析

详细分析了两种灌浆液体的类型牛顿体和宾汉姆体的力学特征以及二者之间异同和联系,介绍了岩土体结构的基本理论、灌浆的基本理论、渗透灌浆理论机制及内容、劈裂灌浆理论机制及内容、压密灌浆理论机制及内容。     

Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.

     

用于双光子激发荧光寿命显微成像的高重复频率皮秒扫描相机

建立了一台基于新研制的高重复频率皮秒扫描相机的双光子激发荧光寿命显微成像系统,重点介绍所研制的高重复频率皮秒扫描相机。为了在高时间分辨力的同时扩大时间测量范围,实现大面积两维空间高时间分辨取样测量,从而提高采样速率和更有效地发挥扫描相机的作用,设计和研制了一种大面积、高时间分辨力扫描变像管和一种重复频率高达1MHz的斜坡电压扫描电路。基于上述关键部件所研制的扫描相机具有重复频率高、扫描速度可调、时间分辨力高、工作面积大、非线性低、触发晃动小等优点。用钛宝石飞秒激光器作为激光脉冲源,通过脉冲提取器将76MHz的高重复频率降低为1MHz,采用可调延时器和标准具对扫描相机的时间分辨力、扫描速度和非线性进行标定。该系统的时间分辨力达到6.5ps,非线性为2.60%,可测量的时间范围从十几皮秒到几十纳秒。测量了若丹明6G和香豆素314两种标准荧光染料的荧光寿命,取得了与参考文献一致的实验结果。     

单极型马赫-曾德尔调制器的互调失真分析

针对单极型马赫曾德尔电光调制器在Radio over Fiber(RoF)和副载波复用系统中的应用,讨论了输入两路射频信号的情形,给出了电光调制器互调失真的严格通用解析解。该解析解可用于表示任意阶的互调失真项和谐波项。数值结果表明了该解析解的正确性。分析结果表明,调制器的三阶互调失真与调制器偏置相移无关,只与输入射频信号的调制系数有关,并且当外加偏置电压等于调制器的半波电压时,只存在偶数阶的失真项。根据该解析解,可方便地设计模拟光通信系统,精确地预计外调制器的非线性特征,优化系统性能。