A New Trial Equation Method and Its Applications

As an improved version of trial equation method, a new trial equation method is proposed. Using this method, abundant new exact traveling wave solutions to a high-order KdV-type equation are obtained.     

Multiple Jacobi Elliptic Function Solutions to Integrable Higher Order Broer-Kaup Equation in (2+1)-Dimensional Spaces

In this paper, we improve the method for deriving Jacobi elliptic function solutions of nonlinear evolution equations given in Ref. [12] and apply it to the integrable higher-order Broer-Kaup system in (2 1)-dimensional spaces.Some new elliptic function solutions are obtained.     

The Kinetics of Formation of Microporous Polytriazine in Diphenyl Sulfone

This study highlights the value of nonisothermal kinetic methods in selecting temperature conditions for the isothermal preparation of microporous polymeric materials. A dicyanate ester is synthesized and the kinetics of its polymerization in diphenyl sulfone are studied by calorimetry under nonisothermal conditions. The kinetics are analyzed by a model-based approach, using the Kamal model, as well as by a model-free approach, using an advanced isoconversional method. Both approaches correctly predict the time to completion of polymerization at a given temperature. The material prepared independently at the predicted temperature is characterized by electron microscopy and CO₂ adsorption measurements and is confirmed to possess a microporous structure with a multimodal distribution of micropores with two major maxima at ~0.5 and 0.8 nm.     

Lossless Medical Image Compression by Using Difference Transform

This paper introduces a new method of compressing digital images by using the Difference Transform applied in medical imaging. The Difference Transform algorithm performs the decorrelation process of image data, and in this way improves the encoding process, achieving a file with a smaller size than the original. The proposed method proves to be competitive and in many cases better than the standards used for medical images such as TIFF or PNG. In addition, the Difference Transform can replace other transforms like Cosine or Wavelet.     

Numerical Study on an RBF-FD Tangent Plane Based Method for Convection–Diffusion Equations on Anisotropic Evolving Surfaces

In this paper, we present a fully Lagrangian method based on the radial basis function (RBF) finite difference (FD) method for solving convection–diffusion partial differential equations (PDEs) on evolving surfaces. Surface differential operators are discretized by the tangent plane approach using Gaussian RBFs augmented with two-dimensional (2D) polynomials. The main advantage of our method is the simplicity of calculating differentiation weights. Additionally, we couple the method with anisotropic RBFs (ARBFs) to obtain more accurate numerical solutions for the anisotropic growth of surfaces. In the ARBF interpolation, the Euclidean distance is replaced with a suitable metric that matches the anisotropic surface geometry. Therefore, it will lead to a good result on the aspects of stability and accuracy of the RBF-FD method for this type of problem. The performance of this method is shown for various convection–diffusion equations on evolving surfaces, which include the anisotropic growth of surfaces and growth coupled with the solutions of PDEs.     

Quantum Chaos,Random Matrices,and Irreversibility in Interacting Many-Body Quantum Systems

The Pauli master equation describes the statistical equilibration of a closed quantum system. Simplifying and generalizing an approach developed in two previous papers, we present a derivation of that equation using concepts developed in quantum chaos and random-matrix theory. We assume that the system consists of subsystems with strong internal mixing. We can then model the system as an ensemble of random matrices. Equilibration results from averaging over the ensemble. The direction of the arrow of time is determined by an (ever-so-small) coupling to the outside world. The master equation holds for sufficiently large times if the average level densities in all subsystems are sufficiently smooth. These conditions are quantified in the text, and leading-order correction terms are given.     

在任意温度的热库中量子位的消相干

本文在Markov 近似下推导了在任意温度的热库中,一个量子位(qubit)的主方程,并由此讨论了由于振幅阻尼而引起的量子位消相干(decoherence). 结论表明量子位的跃迁频率与热库的特征频率及截止频率的关系对消相干有明显的影响。     

利用“神光-Ⅱ”激光装置多路光束叠加直接驱动下的冲击波平面性及稳定性

利用“神光-Ⅱ”的3路基频光输出及小透镜列阵束匀滑技术,通过优化设计和合理地选择光路组合,实现了多路叠加斜入射的驱动激光, 在靶材料中产生一个650~750μm范围内平面性良好的冲击波,有效地提高了“神光-Ⅱ”输出光束的利用率。同时,利用斜面靶进行的冲击稳定性实验表明,在靶面功率密度分别为3.26×1014及2.56×1014W/cm2时,冲击波至少在28.38~55.82和22.13~35.07μm的Al样品厚度内是稳定传播的。     

电子束泵浦氩中高能电子分布的理论计算

改进了文献中报导的Boltzmann基本方程。与Boltzmann基本方程相比,改进后的Boltzmann方程更全面地描述了电子与基态氩原子碰撞的物理过程,并能计算出整个能量区间的电子分布。利用Boltzmann基本方程和改进的Boltzmann方程,对电子束泵浦氩中能量大于氩原子第一激发态能量(11.56eV)的高能电子分布函数进行了理论计算。计算中,选取了电子碰撞氩的微分电离截面和激发截面的解析表达式。对计算所得的稳态电子分布函数以及达到稳态分布所需的特征时间进行了分析和讨论。     

通过有光阑近轴ABCD光学系统激光束的近似解析传输公式

用傅立叶级数展开法研究光束通过有光阑限制的近轴ABCD光学系统的传输特性,导出了光阑透射率函数不同时的传输公式。硬边光阑的情况可作为其它光阑的特例得到,其它光阑也可视作硬边光阑来处理。数值计算表明了该方法快速的优点,并得到与用Collins公式直接积分一致结果。