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Acta Mathematica Scientia 1991年第1期11卷 48-55页

作者：郭柏灵潘兴德 Inst. of Appl. Phys. & Comp. Math. Beijing China Dept. of Math. Zhejiang University Hangzhou China

The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.

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Eigen Spectra of the Dirac Equation for Deformed Woods-Saxon Potential via the similarity transformation

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Chinese Physics Letters 2014年第12期31卷 1-5页

作者： ALSADIKhalidS DepartmentofPhysics FacultyofScienceTaibahUniversityMadina41481SaudiArabia

Over the last few years, an exact solution of the Dirac equation has become an important research topic in quantum mechanics. This solution acquires its importance due to the fact that it is a useful tool to improve theoretical models and numerical solution methods. It is well known that the description of a spin-l/2 particle motion can be attained by the Dirac equation. This equation plays a fundamental role in relativistic quantum mechanics since it can be used to solve problems in high-energy *** techniques have been used for solving the Dirac equation, for example, the super- symmetry （SUSY） technique,shape invariance, the asymptotic iteration method （AIM）,factor- ization method, and the Nikiforov Uvarov （NU） technique.

关键词： Eigen Spectra Dirac Equation similarity transformation

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Theoretical & Applied Mechanics Letters 2022年第3期12卷 184-188页

作者： Bo-Hua Sun School of Civil Engineering&Institute of Mechanics and Technology Xi’an University of Architecture and TechnologyXi’an 710055China

The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been *** the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential *** ordinary differential equation is numerically solved and some useful quantities are *** numerical calculations,a complete Maple code is provided.

关键词： Turbulent boundary layers Laminar boundary layers similarity transformation similarity solution Prandtl mixing length Reynolds number

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The Deformation Analysis of the 3D Alignment Control Network Based on the Multiple Congruence Models

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Journal of Geodesy and Geoinformation Science 2023年第2期6卷 21-31页

作者： Xudong ZHANG Wenjun CHEN Xiaodong ZHANG Yajun ZHENG Bin ZHANG Shaoming WANG Jiandong YUAN Guozhen SUN Institute of Modern Physics Chinese Academy of SciencesLanzhou 730000China

In the construction and maintenance of particle accelerators,all the accelerator elements should be installed in the same coordinate system,only in this way could the devices in the actual world be consistent with the design ***,with the occurrence of the movements of the reinforced concrete cover plates at short notice or building deformations in the long term,the control points upon the engineering structure will be displaced,and the fitness between the subnetwork and the global control network may be ***,it is necessary to evaluate the deformations of the 3D alignment control *** from the extant investigations,in this paper,to characterize the deformations of the control network,all of the congruent models between the points measured in different epochs have been identified,and the congruence model with the most control points is considered as the primary or fundamental model,the remaining models are recognized as the additional ***,the discrepancies between the primary S-transformation parameters and the additional S-transformation parameters can reflect the relative movements of the additional congruence *** the iterative GCT method and the iterative combinatorial theory are proposed to detect multiple congruence models in the control *** the actual work of the alignment,it is essential to identify the competitive models in the monitoring network,which can provide us a hint that,even the fitness between the subnetwork and the global control network is good,there are still deformations which may be *** numerical experiments show that the suggested approaches can describe the deformation of the 3D alignment control network roundly.

关键词： similarity transformation 3D alignment control network deformation analysis hypothesis testing iterative global congruence test iterative combinatorial theory

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An experimental method for squealer tip flow field considering relative casing motion

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Chinese Journal of Aeronautics 2020年第7期33卷 1942-1952页

作者： Fei ZENG Jinlin DU Lin HUANG Liming XUAN Qiang ZHAO Zhengping ZOU National Key Laboratory of Science and Technology on Aero-Engine Aero-thermodynamics School of Energy&Power EngineeringBeihang UniversityBeijing 100083China Collaborative Innovation Center for Advanced Aero-Engine School of Energy&Power EngineeringBeihang UniversityBeijing 100083China

Squealer tip is widely used in turbines to reduce tip leakage *** typical turbine environment,the squealer tip leakage flow is affected by multiple factors such as the relative casing motion and the wide range of variable incidence *** development of experimental methods which can accurately model the real turbine environment and influencing factors is of great significance to study the squealer tip leakage flow *** the present paper,a low-speed turbine cascade test facility which can model the relative casing motion and wide range of variable incidence angles(-25°to 55°)is *** on the similarity criteria,a high-low speed similarity transformation method of the turbine cascade is established by considering the thickness of the turbine blade.A combined testing method of Particle Image Velocimetry(PIV)and local pressure measurement is proposed to obtain the complex flow structures within the tip *** results show that the experimental method can successfully model the relative casing motion and the wide range of variable incidence *** low-speed cascade obtained by the similarity transformation can model the high-speed flow *** measurement technique developed can obtain the complex flow field and successfully capture the scraping vortex within the squealer tip.

关键词： Blade tip/casing gap measurement Particle Image Velocimetry(PIV) Relative casing motion similarity transformation Turbine Wide range of variable incidence angles

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Analytical solutions and rogue waves in （3+1）-dimensional nonlinear Schrdinger equation

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Chinese Physics B 2012年第3期21卷 138-144页

作者：马正义马松华 College of Mathematics and Physics Zhejiang Lishui University

Analytical solutions in terms of rational-like functions are presented for a（3+1）-dimensional nonlinear Schrdinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct *** free functions of time t are involved to generate abundant wave *** types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.

关键词： nonlinear Schrdinger equation similarity transformation rational-like solution rogue

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Exact Solutions of Klein-Gordon Equation with Scalar and Vector Rosen-Morse-Type Potentials

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Chinese Physics Letters 2008年第8期25卷 2754-2757页

作者： A. Soylu O. Bayrak I. Boztosun Department of Physics Nigde University 51350 Nigde Turkey Department of Physics Bozok University 66200 Yozgat Turkey Department of Physics Erciyes University 38039 Kayseri Turkey

We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.

关键词： ASYMPTOTIC ITERATION METHOD NON-HERMITIAN HAMILTONIANS PT-SYMMETRIC POTENTIALS BOUND-STATES EIGENVALUE PROBLEMS DIRAC-EQUATION SCHRODINGER-EQUATION similarity transformation REAL PARTICLES

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Spatiotemporal self-similar solutions for the nonautonomous (3+1)-dimensional cubic-quintic Gross-Pitaevskii equation

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Chinese Physics B 2012年第3期21卷 145-150页

作者：戴朝卿陈瑞品王悦悦 School of Sciences Zhejiang Agricultural and Forestry University

With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.

关键词： Gross-Pitaevskii equation similarity transformation self-similar solutions

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Fractional Analysis of Viscous Fluid Flow with Heat and Mass Transfer Over a Flexible Rotating Disk

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Computer Modeling in Engineering & Sciences 2020年第4期123卷 377-400页

作者： Muhammad Shuaib Muhammad Bilal Muhammad Altaf Khan Sharaf J.Malebary Department of Mathematics City University of Science and Information TechnologyPeshawarPakistan Institute for Groundwater Studies Faculty of Natural and Agricultural SciencesUniversity of the Free StateBloemfonteinSouth Africa Department of Information Technology Faculty of Computing and Information TechnologyKing Abdulaziz UniversityRabighSaudia Arabia

An unsteady viscous fluid flow with Dufour and Soret effect,which results in heat and mass transfer due to upward and downward motion of flexible rotating disk,has been *** upward or downward motion of non rotating disk results in two dimensional flow,while the vertical action and rotation of the disk results in three dimensional *** using an appropriate transformation the governing equations are transformed into the system of ordinary differential *** system of ordinary differential equations is further converted into first order differential equation by selecting suitable ***,we generalize the model by using the Caputo *** numerical result for the fractional model is presented and validated with Runge Kutta order 4 method for classical *** compared results are presented in Table and *** is concluded that the fractional model is more realistic than that of classical one,because it simulates the fluid behavior at each fractional value rather than the integral values.

关键词： Caputo derivatives similarity transformation RK4 soret effect Dufour effect

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A Computational Investigation of the Lid-Driven Cavity Flow

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American Journal of Computational Mathematics 2022年第2期12卷 283-296页

作者： Nawal Odah Al-Atawi Daoud Suleiman Mashat Department of Mathematics Numerical Analysis King Abdulaziz University Jeddah Saudi Arabia

The lid-driven cavity is an important fluid mechanical system that serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. These flows are driven by the tangential motion of a bounding wall. The lid-driven cavity serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. This article presents a complete study of lid-driven cavity flows, with the primary focus being placed on the development of the flow when the Reynolds number was increased. In order to fully comprehend the physics of flow, it is necessary to take into consideration not only pure two-dimensional flows but also flows that are periodic in one space direction and the whole three-dimensional flow.

关键词： Steady Two Dimensional Navier Stokes similarity transformation Finite Difference Scheme

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