原子核单粒子共振态的研究进展

共振是自然界普遍存在的有趣现象。在核物理领域,存在许多奇特现象,共振在其中扮演着重要角色。介绍了近期发展的RMF-CSM、RMF-CGF和RMF-CMR方法及其对原子核单粒子共振态的研究。给出了120Sn,31Ne等核的单粒子共振态的能量和宽度及其随质量数、形变的变化规律,分析了19C,31Ne和39Mg等核的晕形成的物理机制和在N=20附近能级反转的原因。特别是新发展的RMF-CMR方法,在描述稳定核和奇特核方面都取得了成功,支持Zr同位素存在巨晕的预言。Resonance is an interesting phenomenon in nature. In nuclear physics, resonance plays an important role in the formation of many exotic phenomena. This paper introduces the recently developed RMF-CSM, RMFCGF, and RMF-CMR methods and their researches on nuclear single-particle resonances. The energies and widths of the single-particle resonant states in 120Sn and 31Ne and their evolution to mass number and deformation are given. In addition, the physical mechanism of the halo formation in 19C, 31Ne and 39Mg and the cause of energy level inversion near N=20 are analyzed. In particular, the newly developed RMF-CMR approach has been successful in describing stable and exotic nuclei and supports the prediction that Zr isotopes exist in a giant halo.     

On the developments of Darcy's law to include inertial and slip effects

The empirical Darcy law describing flow in porous media, whose convincing theoretical justification was proposed almost 130 years after its original publication in 1856, has however been extended to account for particular flow conditions. This article reviews historical developments aimed at including inertial and slip effects (respectively, when the Reynolds and Knudsen numbers are not exceedingly small compared to unity). Despite the early empirical extensions to include inertia and slip effects, it is striking to observe that clear formal derivations of physical models to account for these effects were reported only recently.     

Local structure-preserving methods for the generalized Rosenau-RLW-KdV equation with power law nonlinearity

Local structure-preserving algorithms including multi-symplectic, local energy-and momentum-preserving schemes are proposed for the generalized Rosenau–RLW–Kd V equation based on the multi-symplectic Hamiltonian formula of the equation. Each of the present algorithms holds a discrete conservation law in any time–space region. For the original problem subjected to appropriate boundary conditions, these algorithms will be globally conservative. Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes. Numerical results show that the proposed algorithms have satisfactory performance in providing an accurate solution and preserving the discrete invariants.     

Studies on convergence and scaling law of Thomson backscattering spectra in strong fields

With the saddle point analysis method for the Bessel function structure and property, the convergence problem and the scaling laws of Thomson backscattering spectra are solved and studied in both cases that are for the plane wave laser field without and with applied external constant magnetic field. Some unclear points appeared in previous work are clarified. The extension of the method to a general situation for the laser field with an arbitrary polarization is discussed. We also make a simple analysis and discussion about the optimal spectra dependence of field parameters and its implication to practical applications.     

Nonlocal-in-time kinetic energy in nonconservative fractional systems,disordered dynamics,jerk and snap and oscillatory motions in the rotating fluid tube

In this article we generalize the basic theoretical properties of nonlocal-in-time kinetic energy approach introduced in the framework of nonlocal classical Newtonian mechanics for the case of fractional dynamical systems explored in the context of the fractional actionlike variational approach. Two independent fractionally Lagrangians weights are considered independently: the Riemann-Liouville fractional weight and the extended exponentially fractional weight. For each weight, the corresponding nonlocal fractional Newton's law of motion is derived. Three main physical applications were discussed in details: free particles, oscillators and dynamics of particles in a rotating tube with earth frame. A number of differential equations depending on fractional and nonlocal-in-time parameters were obtained and their solutions are discussed accordingly. For specific parameters and particular initial conditions, it was observed that the dynamics exhibit a kind of strange phase plot trajectories that indicate the presence of disordered motions. However one of the main results concerns the physics of particles in the rotating tube which display, for specific values of fractional and nonlocal-in-time parameters, oscillatory motions controlled by the nonlocal-in-time parameter.     

Ac conductivity and dielectric behavior of hydrated homoionic alkali-cations-exchanged montmorillonite

The dielectric properties of a series of homoionic alkali-exchanged montmorillonites were studied at different treatment temperatures and various water loadings by means of complex impedance spectroscopy. To date, however, this method has been underutilized in clay minerals studies. The main objective of the present work is to understand the relaxation mechanisms of water molecules interacting with different hydration centers in clay minerals, with a view to eventually control their interactions with the alkali extra-framework cations. The other part of our study is to study the dielectric properties such as real and imaginary parts of dielectric permittivity, loss tangent, and ac conductivity in the frequency range 10^?2–10⁶?Hz and temperature range 173–333?K of these clay minerals. The obtained results have been discussed in terms of the Jonscher model.     

利用指数律了解溶液中复杂高分子单链及聚集态结构的形状特征

高分子在溶液中的单链构象和聚集态结构是高分子科学的重要内容,在研究中往往应用到许多指数经验规律. 总结了几种通常用来研究高分子溶液的指数律方法,并介绍了指数律如何应用于复杂高分子单链及聚集态结构的形状特点研究. 通过前体溶液的调控实现对薄膜凝聚态结构以及形貌的操纵是一种新思路、新方法. 因此,深刻认识高分子在前体溶液中的本征性质尤为重要. 通过指数律研究,结合电镜、光谱等方法,可深入研究高分子溶液单链、聚集尺寸及形态结构演变与各层次结构单元的运动过程及规律,为高分子材料的分子设计、功能开发及应用奠定理论基础.     

Large deflection and post-buckling analysis of non-linearly elastic rods by wavelet method

We propose a wavelet method in the present study to analyze the large deflection bending and post-buckling problems of rods composed of non-linearly elastic materials, which are governed by a class of strong non-linear differential equations. This wavelet method is established based on a modified wavelet approximation of an interval bounded L²-function, which provides a new method for the large deflection bending and post-buckling problems of engineering structures. As an example, in this study, we considered the rod structures of non-linear materials that obey the Ludwick and the modified Ludwick constitutive laws. The numerical results for both large deflection bending and post-buckling problems are presented, illustrating the convergence and accuracy of the wavelet method. For the former, the wavelet solutions are more accurate than the finite element method and the shooting method embedded with the Euler method. For the latter, both bifurcation and limit loads can be easily and directly obtained by solving the extended systems. On the other hand, for the shooting method embedded with Runge–Kutta method, to obtain these values usually needs to choose a good starting value and repeat trial solutions many times, which can be a tough task.     

基于能量法的矿柱稳定性分析

能量法因可以避免研究采场结构失稳破坏的中间复杂受力过程,所以受到研究者的青睐. 人工矿柱是地下矿山一种重要的采场结构,由于其失稳破坏过程的应力、应变较复杂,因此从能量守恒的角度对其承载上覆岩体的稳定性进行综合评判和研究. 通过对人工矿柱的受力特性和破坏模式进行分析,建立其力学模型,根据能量守恒原理得出考虑外载荷做功、自重势能和应变能条件下的人工矿柱总能量方程,推导出了人工矿柱势能函数表达式. 基于突变理论知识,构建了在考虑弹性模量、高宽比等参数条件下的人工矿柱能量极限状态方程,根据势函数的稳定判据得出外载荷的临界应力函数关系式,系统讨论和分析了外载荷变化过程对人工矿柱稳定性的影响,定量评判了人工矿柱受外界载荷的影响程度. 最后将所建立的临界应力函数关系式对焦冲金矿人工矿柱尺寸进行优化设计,经现场实测人工矿柱承受载荷约为其理论设计临界载荷的十分之一,达到安全支护规范要求;经过多年的金属矿山现场生产实践,人工矿柱及覆岩都较稳定,能够满足矿山安全生产的需要. 研究结果表明所建立的人工矿柱能量极限状态方程,可为地下金属矿山人工矿柱的合理设计提供理论依据.