On the integrability aspects of nonparaxial nonlinear Schrödinger equation and the dynamics of solitary waves

The integrability nature of a nonparaxial nonlinear Schrödinger (NNLS) equation, describing the propagation of ultra-broad nonparaxial beams in a planar optical waveguide, is studied by employing the Painlevé singularity structure analysis. Our study shows that the NNLS equation fails to satisfy the Painlevé test. Nevertheless, we construct one bright solitary wave solution for the NNLS equation by using the Hirota's direct method. Also, we numerically demonstrate the stable propagation of the obtained bright solitary waves even in the presence of an external perturbation in a form of white noise. We then numerically investigate the coherent interaction dynamics of two and three bright solitary waves. Our study reveals interesting energy switching among the colliding solitary waves due to the nonparaxiality.     

Theory of particle transport phenomena during fatigue and time-dependent fracture of materials based on mesoscale dynamics and their practical applications

In this work, the mesoscale mechanics of metals, which links their microscopic physics and macroscopic mechanics, was established. For practical applications, the laws for quantitatively predicting life of cycle and time-dependent fracture behavior such as fatigue, hydrogen embrittlement, and high-temperature creep were derived using particle transport phenomena theories such as dislocation group dynamics, hydrogen diffusion, and vacancy diffusion. Furthermore, these concepts were also applied for estimating the degree of viscoelastic deterioration of blood vessel walls, which is dominated by a time-dependent mechanism, and for the diagnosis of aneurysm accompanied by the viscoelastic deterioration of the blood vessel wall. In these theories, new mechanical indexes were derived as dominant factors for predicting the life of fatigue crack growth and the time-dependent fracture of notched specimens of materials such as hydrogen embrittlement and high-temperature creep. Furthermore, as an example of a practical application, these theories were applied to estimate the degree of viscoelastic deterioration and chaotic motions of blood vessel walls, which are closely related to blood vessel diseases such as atherosclerosis and aneurysm. Moreover, new indexes to diagnose them were also proposed for clinical applications.     

适用于等熵流动的交错拉氏Godunov方法

为消除传统单元中心型Godunov方法在求解稀疏波问题时的非物理过热现象，发展一种适用于等熵流动的交错拉氏Godunov方法.主要的特征是采用速度与热力学变量交错分布的形式，避免在单元内进行速度平均，从而消除由于动量平均过程导致的动能耗散.与传统的von Neumann型交错网格方法相比，网格的边界通量由节点处的多维黎曼求解器提供，克服了多维人工粘性选取带来的困难.为减少多维黎曼求解器在求解稀疏波问题时的非物理熵增，给出稀疏波出现的合理判据，从而保证了热力学关系式的满足.数值实验表明：该方法能很好地消除稀疏波的过热现象，同时在求解激波问题时又能保持与传统单元中心型拉氏方法相同的激波捕捉能力.     

Nd∶YVO4/Nd∶GdVO4双波长激光器的功率均衡实验研究

实验研究了Nd∶YVO4/Nd∶GdVO4双波长激光器在不同抽运功率条件下,通过调节热沉温度达到功率均衡时的输出特性.实验结果表明:对于Nd∶YVO4/Nd∶GdVO4双波长激光器,当提高抽运功率,需要重新降低热沉温度达到功率均衡输出,降温幅度与抽运功率增加之比为11.23℃/W.与此同时,随着抽运功率和热沉温度的变化,双波长激光器的中心波长会出现小幅度的漂移,左峰波长随抽运功率增加的蓝移速率为0.056 nm/W,右峰波长随抽运功率增加的蓝移速率为0.054 nm/W.实验还发现功率均衡条件下激光器的输出总功率随抽运功率的增加而增加,拟合斜效率为8.7%,当抽运功率为5.58 W时,输出最大总功率达到115.7 mW.     

非PLL相位平均型参考线原型验证

射频相位参考线是粒子加速器的重要组成部分之一,为射频低电平控制系统(LLRF)、束流诊断系统、定时系统等提供稳定的相位锁定参考信号。为减少远距离传输过程中由环境温度变化导致的射频传输线中的射频相位漂移,多个加速器装置中已经采用射频相位参考线提供射频相位参考,这些相位参考的实现方案主要是基于恒温控制和基于光纤锁相。与这些方案相比,采用相位平均方法不仅可以保持长距离节点之间的相位稳定,而且更易于现场安装与维护。现有的带有锁相环(PLL)的终端短路方式实现相位平均参考线的方案仍有一些节点数量限制等方面的不足,本文对相位平均参考线结构进行了去除PLL的简化设计并进行了验证,以期增加更多的相位分配节点以及降低对射频器件参数的要求。对非PLL的单端输入终端短路相位平均方案与两端输入各节点间互为参考的相位平均方案分别进行了实验测试,结果表明两者的相位RMS精度可以达到0.1°~0.3°。并对不同的相位平均实现方案中相位不稳定的产生原因进行了分析,结果表明,除环境温度外,同轴线缆材质、合成相位与幅度的不平衡合成等也是重要影响因素。     

Soliton and other solutions to the (1+2)-dimensional chiral nonlinear Schrödinger equation

The (1+2)-dimensional chiral nonlinear Schrödinger equation (2D-CNLSE) as a nonlinear evolution equation is considered and studied in a detailed manner. To this end, a complex transform is firstly adopted to arrive at the real and imaginary parts of the model, and then, the modified Jacobi elliptic expansion method is formally utilized to derive soliton and other solutions of the 2D-CNLSE. The exact solutions presented in this paper can be classified as topological and nontopological solitons as well as Jacobi elliptic function solutions.     

Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics

The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point,the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He's semi-inverse variational principle(SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc.     

Entropy of higher-dimensional charged Gauss–Bonnet black hole in de Sitter space

The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.     

大规模合成具有氧空位的多孔Bi2O3用于有效降解亚甲基蓝

光催化降解有机污染物由于其具有低能耗和绿色环保的特点，已经成为研究的热点. 氧化铋纳米晶体的带隙在2.0∽2.8 eV之间，利用它催化可见光降解有机污染物具有较高的活性，从而引起了越来越多的关注. 尽管近年来已经开发了几种制备Bi₂O₃基半导体材料的方法，但是仍然难以用简单的方法大规模地制备高活性的Bi₂O₃催化剂. 因此，开发简单可行的大规模制备Bi₂O₃纳米晶体的方法对于工业废水处理的潜在应用具有重要意义. 本文通过蚀刻商用BiSn粉末，然后进行热处理，成功地大规模制备了多孔Bi₂O₃. 获得的多孔Bi₂O₃在亚甲基蓝(MB)的光催化降解中表现出优异的活性和稳定性. 对该机理的进一步研究表明，多孔Bi₂O₃合适的能带结构允许生成活性氧物种，例如O₂^-·和·OH，可有效降解MB.