Solitary Wave and Doubly Periodic Wave Solutions to Three-Dimensional Nizhnik-Novikov-Veselov Equation

The generalized transformation method is utilized to solve three-dimensional Nizhnik-Novikov-Veselov equation and construct a series of new exact solutions including kink-shaped and bell-shaped soliton solutions, trigonometric function solutions, and Jacobi elliptic doubly periodic solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh methods and Jacobi function method, the method we used here gives more general exact solutions without much extra effort.     

Dispersive Solitary Wave Solutions of Strain Wave Dynamical Model and Its Stability

In the materials of micro-structured, the propagation of wave modeling should take into account the scale of various microstructures. The different kinds solitary wave solutions of strain wave dynamical model are derived via utilizing exp\((-\phi(\xi))\)-expansion and extended simple equation methods. This dynamical equation plays a key role in engineering and mathematical physics. Solutions obtained in this work include periodic solitary waves, Kink and anti-Kink solitary waves, bell-shaped solutions, solitons, and rational solutions. These exact solutions help researchers for knowing the physical phenomena of this wave equation. The stability of this dynamical model is examined via standard linear stability analysis, which authenticate that the model is stable and their solutions are exact. Graphs are depicted for knowing the movements of some solutions. The results show that the current methods, by the assist of symbolic calculation, give an effectual and direct mathematical tools for resolving the nonlinear problems in applied sciences.     

修正cKdV方程组的孤立波结构及其稳定性

利用函数展开法求解修正耦合KdV(Coupled KdV,cKdV)方程组,得到几类孤立波解,包括扭结型-钟型、双扭结型、双钟型以及双扭结-双钟型结构的单孤子解.在不同的极限情况下,这些解分别退化为修正cKdV方程的扭结状或钟状孤波解.对孤立波的稳定性进行了数值研究,结果表明:修正cKdV方程既存在稳定的孤立波解,也存在不稳定的孤立波解.     

Solitary Wave Solutions for the Coupled Ito System and a Generalized Hirota-Satsuma Coupled KdV System

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An Improved F-Expansion Method and Its Application to Coupled Drinfel'd-Sokolov-Wilson Equation

With the aid of computerized symbolic computation, an improved F-expansion method is presented to uniformly construct more new exact doubly periodic solutions in terms of rational formal Jacobi elliptic function of nonlinear partial differential equations (NPDEs). The coupled Drinfel'd-Sokolov-Wilson equation is chosen to illustrate the method. As a result, we can successfully obtain abundant new doubly periodic solutions without calculating various Jacobi elliptic functions. In the limit cases, the rational solitary wave solutions and trigonometric function solutions are obtained as well.     

New Explicit Solitary Wave Solutions and Periodic Wave Solutions for the Generalized Coupled Hirota-Satsuma KdV System

In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained.     

动态柱形空穴膨胀模型及其在侵彻问题中的应用

 在侵彻问题中的应用进行了研究。通过采用相似变换求解塑性区控制方程,获得了动态柱形空穴膨胀中的弹塑性界面速度、径向应力分布、空穴表面应力的解。基于柱形空穴模型,推导了侵彻方程,并将其得到的预测结果与侵彻实验数据进行了比较。结果表明,模型的理论解与现有数据吻合得很好。 结果还显示了材料的可压缩性和塑性强化模量对柱形空穴膨胀以及侵彻阻力的影响。     

初始点火条件引起的三维旋转爆震波单/双波传播模式

在不同工况下,旋转爆震波能够以单波、双波、多波模式进行传播.但在同一工况下,是否存在不同模式的稳定传播爆震波还有待进一步研究.基于Euler方程,耦合氢气/空气的有限化学反应速率模型,并采用高分辨率的5阶有限差分格式WENO-PPM5离散对流项,对三维旋转爆震波进行了数值模拟.计算结果表明,在同一特定工况下,旋转爆震波能够以两种不同的传播模式稳定传播,即单波模式和双波模式.详细地对比了两种传播模式下的流场特征、爆震波传播特性、推力性能等.在同一工况下,两种传播模式的爆震波周向传播速度相差不多,但双波模式的频率约为单波模式的2倍;双波模式下质量流量、比冲、推力的平均值均略高于单波模式;且双波模式的可燃混气层高度约为单波模式的1/2,这有助于缩小旋转爆震发动机的长度,使之更加紧凑.      

Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations

By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.     

Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations

By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.     

An Efficient Improved Greedy Harris Hawks Optimizer and Its Application to Feature Selection

To overcome the lack of flexibility of Harris Hawks Optimization (HHO) in switching between exploration and exploitation, and the low efficiency of its exploitation phase, an efficient improved greedy Harris Hawks Optimizer (IGHHO) is proposed and applied to the feature selection (FS) problem. IGHHO uses a new transformation strategy that enables flexible switching between search and development, enabling it to jump out of local optima. We replace the original HHO exploitation process with improved differential perturbation and a greedy strategy to improve its global search capability. We tested it in experiments against seven algorithms using single-peaked, multi-peaked, hybrid, and composite CEC2017 benchmark functions, and IGHHO outperformed them on optimization problems with different feature functions. We propose new objective functions for the problem of data imbalance in FS and apply IGHHO to it. IGHHO outperformed comparison algorithms in terms of classification accuracy and feature subset length. The results show that IGHHO applies not only to global optimization of different feature functions but also to practical optimization problems.     

Model Equations and Their Solitary Wave Solutions in Cylindrical Coordinate System

The method of multiple-scales is used to investigate the evolution of a weak nonlinear internal waves between two-layer fluids in cylindrical coordinate system. Two reduced model wave equations, which we call a modified cylindrical KdV equation for axially symmetric case and a modified cylindrical KP equation for non-axially symmetric case, are derived and their solitary wave solutions are also obtained by relating them i to the modified KdV equation by means of an appropriate variable transformation.     

New Cnoidal and Solitary Wave Solutions of Coupled Higher-Order Nonlinear SchrSdinger System in Nonlinear Optics

The coupled higher-order nonlinear Schroedinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By using coupled amplitude-phase formulation, a series of new exact cnoidal and solitary wave solutions with different parameters are obtained, which may have potential application in optical communication.     

三维电子散斑干涉技术及其应用研究

通过大错位剪切镜和一作为参考物的压电陶瓷相移器将三个电子散斑干涉系统组成一新的三维电子散斑干涉系统。利用该系统，结合相移技术和图像处理技术，可得到独立的位移场(u,v和w场)。该技术的特点是用三个激光器作为光源，一个压电陶瓷相移器产生参考光并实现相移，CCD摄像机前放置大错位剪切镜以使物光和参考光产生干涉。将该技术应用到柴油发动机零部件测量上，得到了主轴承孔周的三维位移场。     

Boundary Conditions for Coupled Quasilinear Wave Equations with Application to Isolated Systems

We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form [0, T] × Σ, where Σ is a compact manifold with smooth boundaries ∂Σ. By using an appropriate reduction to a first order symmetric hyperbolic system with maximal dissipative boundary conditions, well posedness of such problems is established for a large class of boundary conditions on ∂Σ. We show that our class of boundary conditions is sufficiently general to allow for a well posed formulation for different wave problems in the presence of constraints and artificial, nonreflecting boundaries, including Maxwell’s equations in the Lorentz gauge and Einstein’s gravitational equations in harmonic coordinates. Our results should also be useful for obtaining stable finite-difference discretizations for such problems.     

光纤倏逝波生物传感器及其应用

以光纤倏逝波原理，研制成功一台光纤倏逝波生物传感器。该传感器对纯净的Cy5荧光染料溶液的检测灵敏度达0．01μmo1／1；对浓度为0．01μmo1／1的嗜肺军团菌核酸样品的测量信噪比为4．61。所有检测结果与商品化生物芯片扫描仪同时检测得到的结果具有很好的一致性。     

极限思维法及其在解题中的应用

1极限思维法 极限思维法是一种科学的思维方法,在物理学的研究中,常常用它来解决某些不能直接验证的实验和规律.例如在研究落体定律时,伽利略由于无法用实验直接验证自己的论断,只好求助于极限思维法间接证明.他先证明了从斜面上滚落的小球总做匀变速直线运动,后把结论外推到斜面倾角增大到90°的极限情况,此时,小球将自由下落,从而说明自由落体运动也是匀变速直线运动.     

A Data-Driven Space-Time-Parameter Reduced-Order Model with Manifold Learning for Coupled Problems: Application to Deformable Capsules Flowing in Microchannels

An innovative data-driven model-order reduction technique is proposed to model dilute micrometric or nanometric suspensions of microcapsules, i.e., microdrops protected in a thin hyperelastic membrane, which are used in Healthcare as innovative drug vehicles. We consider a microcapsule flowing in a similar-size microfluidic channel and vary systematically the governing parameter, namely the capillary number, ratio of the viscous to elastic forces, and the confinement ratio, ratio of the capsule to tube size. The resulting space-time-parameter problem is solved using two global POD reduced bases, determined in the offline stage for the space and parameter variables, respectively. A suitable low-order spatial reduced basis is then computed in the online stage for any new parameter instance. The time evolution of the capsule dynamics is achieved by identifying the nonlinear low-order manifold of the reduced variables; for that, a point cloud of reduced data is computed and a diffuse approximation method is used. Numerical comparisons between the full-order fluid-structure interaction model and the reduced-order one confirm both accuracy and stability of the reduction technique over the whole admissible parameter domain. We believe that such an approach can be applied to a broad range of coupled problems especially involving quasistatic models of structural mechanics.     

An Easy and Efficient Fluorescent Method for Detecting Aldehydes and Its Application in Biotransformation

Water-soluble aldehydes (acetaldehyde, propionaldehyde) and non-water-soluble aldehydes (butyraldehyde and phenylacetaldehyde) were easily detected by an efficient fluorescent method with 5-aminofluorescein as probe. Under optimal detection conditions, 5-aminofluorescein could selectively respond to aldehydes with high sensitivity in comparison with other carbonyl compounds like ketones and acids. Thus, the proposed method was used to monitor microbial oxidation and succeeded in trapping transiently-produced aldehydes during biotransformation of primary alcohols by Gluconobacter oxydans.