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.     

Exact solutions of the nonlinear differential-difference equations associated with the nonlinear electrical transmission line through a variable-coefficient discrete（G＇/G）-expansion method

We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete（G /G）-expansion method, we solve the nonlinear differential–difference equations associated with the network. We obtain some exact traveling wave solutions which include hyperbolic function solution, trigonometric function solution, rational solutions with arbitrary function, bright as well as dark solutions.     

行波前置短磁聚焦飞秒条纹管设计

设计了一款长度为265 mm的飞秒条纹管。采用短磁聚焦透镜和行波偏转板,并将行波偏转板置于磁透镜之前以提高偏转灵敏度。采用蒙特卡罗方法对阴极表面理想点和阴极狭缝发射的光电子初始参量进行了模拟抽样,用CST软件的Particle Tracking模块模拟跟踪了光电子的运行轨迹,统计分析了光电子在最佳像面上的位置分布和渡越时间,给出了光电子在最佳像面上的点扩展函数和调制传递函数。计算结果显示,所设计的条纹管阴极有效尺寸达到6 mm,放大率为2.4~2.5,动态空间分辨力大于55 lp/mm。经保守估算,条纹管的时间分辨力有望达到245 fs。     

Improvement of 1D off-axis computer-generated holograms

Creation of Fresnel off-axis computer-generated holograms and improvement of images reconstructed from the holograms are described. To improve the reconstructed images, we have created the holograms with high construct diffraction patterns by using a histogram method. From reconstruction experiments of the holograms, clear images have been obtained and 3D images have been seen directly with eyes.     

利用GM(1,1)模型预测曲线波形

针对给出的函数y=f(x),x∈[a,b],将其值域进行n等分,设yi为其中任一分点,对应x=xi(i=1,2,…,m),用GM(1,1)模型对序列{x1,x2,…,xm}进行预测,得到曲线y=f(x)在下一段时间与直线y=yi的交点位置.当GM(1,1)模型的误差较大时,可利用带有残差修正的GM(1,1)模型进行残差修正,以提高GM(1,1)模型预测值的精确度.     

New Exact Travelling Wave Solutions to Kundu Equation

Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.     

An analysis of seismic attenuation in random porous media

The attenuation of seismic wave in rocks has been one of the interesting research topics, but till now no poroelasticity models can thoroughly explain the strong attenuation of wave in rocks. In this paper, a random porous medium model is designed to study the law of wave propagation in complex rocks based on the theory of Biot poroelasticity and the general theory of stochastic process. This model sets the density of grain, porosity, permeability and modulus of frame as random parameters in space, and only one fluid infiltrates in rocks for the sake of better simulation effect in line with real rocks in earth strata. Numerical simulations are implemented. Two different inverse quality factors of fast P-wave are obtained by different methods to assess attenuation through records of virtual detectors in wave field (One is amplitude decay method in time domain and the other is spectral ratio method in frequency domain). Comparing the attenuation results of random porous medium with those of homogeneous porous medium, we conclude that the attenuation of seismic wave of homogeneous porous medium is far weaker than that of random porous medium. In random porous media, the higher heterogeneous level is, the stronger the attenuation becomes, and when heterogeneity σ = 0.15 in simulation, the attenuation result is consistent with that by actual observation. Since the central frequency (50 Hz) of source in numerical simulation is in earthquake band, the numerical results prove that heterogeneous porous structure is one of the important factors causing strong attenuation in real stratum at intermediate and low frequency.     

Next-to-leading-order calculation in kT factorization

We explain the framework for calculating next-to-leading-order (NLO) corrections to exclusive processes in the kT factorization theorem, taking πγ→γ T as an example. Partons off-shell by k2T are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the kT-dependent hard kernel as their difference. The light-cone singularities in the kT-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. Both the large double logarithms In2 kT and ln2x, x being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function, and the latter into a jet function.     

Explicit models for elastic and piezoelastic surface waves

^** Email: julius.kaplunov{at}brunel.ac.uk Explicit models for the Rayleigh and Bleustein–Gulyaevsurface waves are extracted from the original 2D formulationswithin the general framework of linear elasticity and electroelasticity.The derivations are based on perturbing in slow time the self-similarsolutions for homogeneous surface wave. Both the proposed modelsinvolve hyperbolic equations on the surface along with ellipticequations over the interior, emphasizing the dual nature ofa surface wave. Comparisons with exact solutions are presented,including that for the plane Lamb problem.