Back-and-forth shooting method for solving two-point boundary-value problems

The paper proposes a special iterative method for a nonlinear TPBVP of the form (t)=f(t, x(t),p(t)), (t)=g(t, x(t),p(t)), subject toh(x(0),p(0))=0,e(x(T),p(T))=0. Certain stability properties of the above differential equations are taken into consideration in the method, so that the integration directions associated with these equations respectively are opposite to each other, in contrast with the conventional shooting methods. Via an embedding and a Riccati-type transformation, the TPBVP is reduced to consecutive initial-value problems of ordinary differential equations. A preliminary numerical test is given by a simple example originating in an optimal control problem.     

惯性约束核聚变多路打靶激光光束引导方法的研究

提出了一种用于惯性约束核聚变(ICF)的多路激光光束引导的新型传感器。通过内置面阵CCD来监测激光光点位置,并利用共轭光路法引导光束到预定位置。在引导过程中光束不直接打到靶上,避免了靶的不同形状对光束引导的影响。提出了激光光束的引导方法和流程。设计了零位角测量光路,并用于测量激光光束的入射角。     

A quantum dissipative system in an anisotropic non-linear absorbing environment

A canonical quantization scheme is represented for a quantum system interacting with a non-linear absorbing environment. The environment is taken anisotropic and the main system is coupled to its environment through some coupling tensors of various ranks. The non-linear response equation of the environment against the motion of the main system is obtained. The non-linear Langevin-Schrödinger equation is concluded as the macroscopic equation of motion of the dissipative system. The effect of non-linearity of the environment is investigated on the spontaneous emission of an initially excited two-level atom imbedded in such an environment.     

具有分布偏差变元的二阶中立型方程的振动准则(英文)

利用Riccati变换及积分平均技巧,建立一类具有非线性中立项及分布偏差变元的二阶中立型方程的振动准则,我们的结果推广并改进了一些已有的结果.     

Three-dimensional mixed convection flow with variable thermal conductivity and frictional heating

In this article,three-dimensional mixed convection flow over an exponentially stretching sheet is investigated.Energy equation is modelled in the presence of viscous dissipation and variable thermal conductivity.Temperature of the sheet is varying exponentially and is chosen in a form that facilitates the similarity transformations to obtain self-similar equations.Resulting nonlinear ordinary differential equations are solved numerically employing the Runge-Kutta shooting method.In order to check the accuracy of the method,these equations are also solved using bvp4c built-in routine in Matlab.Both solutions are in excellent agreement.The effects of physical parameters on the dimensionless velocity field and temperature are demonstrated through various graphs.The novelty of this analysis is the self-similar solution of the threedimensional boundary layer flow in the presence of mixed convection,viscous dissipation and variable thermal conductivity.     

Thermal Buckling Analysis of FGM Sandwich Circular Plates Under Transverse Nonuniform Temperature Field Actions北大核心CSCD

Based on the von Kármán geometric nonlinear plate theory, the displacement⁃type geometric nonlinear governing equations for FGM sandwich circular plates under transverse nonlinear temperature field actions were derived. With the immovable clamped boundary condition, the analytical formula for dimensional critical buckling temperature differences of the system was obtained from the solution of the linear eigenvalue problem. Moreover, the 2⁃point boundary value problem of ordinary differential equations was solved with the shooting method. The effects of geometric parameters, constituent material properties, gradient indexes, temperature field parameters and layer⁃thickness ratios on the critical buckling temperature differences, the thermal postbuckling equilibrium paths, and the buckling equilibrium configurations of FGM sandwich circular plates, were investigated. The results show that, with the increases of the thickness⁃radius ratio, the relative thickness of the FGM layer and the gradient index, the FGM sandwich circular plate's critical buckling temperature difference will increase monotonically. Given a fixed radius and a fixed total thickness, the postbuckling deformation of the FGM sandwich circular plate will decrease significantly with the relative thickness of the FGM layer. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Growth,optical, mechanical and electrical studies of nonlinear optical crystal: l-Valinium oxalate

l-Valinium oxalate (LVO) single crystal has been grown by solution growth technique at room temperature. The crystal structure and lattice parameters were determined for the grown crystal by single crystal X-ray diffraction studies. Optical constants like band gap, refractive index, reflectance, extinction coefficient and electric susceptibility were determined from UV–vis–NIR spectrum. The microhardness studies reveal the mechanical strength of the grown crystal. The dielectric constant, dielectric loss and AC conductivity of the compound were calculated at different temperatures and frequencies to analyze the electrical properties. Nonlinear optical property was discussed to confirm the SHG efficiency of the grown crystal.     

Novel shooting method with simple control strategy for fiber lasers

A novel shooting method with excellent simple control strategy is developed for solving the failure to convergence of the traditional shooting methods themselves in fiber lasers model. Compared with the published literature, the novel shooting method provides a clear physical understanding method for getting the threshold pump power and the exact results with given random functions in Yb³⁺-doped fiber lasers and Er³⁺-doped fiber lasers. Then, the results in Er³⁺-doped fiber lasers and Yb³⁺-doped fiber lasers demonstrate that the solutions using the novel shooting method has high accuracy of 10⁻⁸ W with several iteration steps, which have extended the applicable range of the end-pumped power even lower than 1 mW pump power. Furthermore, compared with 1480 nm pump for the threshold and slope efficiencies of the Er³⁺-doped fiber lasers, 978 nm fiber lasers can extend wider scope of application and be pump source in the coming future. Finally, the lower threshold and higher slope efficiency at 975 nm than those of 910 nm pump in Yb³⁺-doped fiber lasers, 975 nm pump laser provides for broad band excellent cladding pump source.     

年龄相关的非线性时变种群扩散系统最优分布控制的存在性

讨论了一类非线性时变种群扩散系统的最优分布控制问题,利用LionsJL的偏微控制理论和先验估计,证明了系统最优分布控制的存在性.所得结果可为非线性种群扩散系统中的最优控制问题的实际研究提供必要的理论基础.