具有非线性传染率和时滞的随机SIQR计算机病毒模型的渐近行为

研究了一类具有非线性发生率和时滞的随机SIQR计算机病毒模型.首先证明了该系统具有唯一的全局正解,然后通过构造适当的Lyapunov函数并利用伊藤公式,分析了该模型的解在无病平衡点附近及地方病平衡点附近的渐近行为,最后通过数值模拟对随机系统解的渐近行为做了进一步的分析并给出了结论.     

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.     

Stokes equations under nonlinear slip boundary conditions coupled with the heat equation: A priori error analysis

In this work, we consider the heat equation coupled with Stokes equations under threshold type boundary condition. The conditions for existence and uniqueness of the weak solution are made clear. Next we formulate the finite element problem, recall the conditions of its solvability, and study its convergence by making use of Babuska–Brezzi's conditions for mixed problems. Third we formulate an Uzawa's type iterative algorithm that separates the fluid from heat conduction, study its feasibility, and convergence. Finally the theoretical findings are validated by numerical simulations.     

基于摄动法的压敏储层非线性渗流问题研究

研究地层压力变化对渗流特征的影响,对低渗透储层、碳酸盐岩储层,或其他致密性储层的油气开采和储层改造都具有重要意义.在考虑渗流压力梯度平方项存在的前提下,运用摄动法求解的相关理论,将渗透率随压力的变化融入到渗流问题的求解过程中,有效地求解了该类压敏型储层的非线性渗流问题.结果表明,在实际应用中,尤其是在储层压敏性较弱的情况下,可考虑直接用0阶摄动解即可满足较好的计算精度;储层的压敏性越强,越适宜通过用摄动解的修正,来达到精确求解的目的.     

Well-posedness for the massive nonlinear wave equation on asymptotically AdS spacetimes

In this paper, we prove some well-posedness theorems for the nonlinear massive wave equation (with the mass satisfying the Breitenlohner-Freedman bound) on asymptotically anti-de Sitter spaces. The solution is constructed by contraction mapping method and also as a limit of solutions to an initial boundary value problem with boundary at a finite location in spacetime by finally pushing the boundary out to infinity. The solution obtained is unique within the energy class.     

A new formulation for fictitious mass of viscous dynamic relaxation method

Abstract

In this article, a new relationship is proposed for the fictitious mass of viscous dynamic relaxation (DR) method. First, incremental equations are derived for DR steps. Using transformed Gershgörin theory, a new relationship is achieved for fictitious mass of viscous DR by formulating modified time step ratio. This procedure presents a new algorithm for the viscous DR method. To evaluate the numerical efficiency of the proposed method, some 2D and 3D truss and frame structures are analyzed with elastic linear and geometrically nonlinear behaviors. Results show that by using the proposed algorithm for fictitious mass, the convergence rate of the viscous DR method is improved so that the proposed algorithm presents the structural response with lower iterations in comparison with other common DR techniques.

Communicated by Joerg Fehr.     

Li[LiCs2Cl][Ga3S6]: A Nanoporous Framework of GaS4 Tetrahedra with Excellent Nonlinear Optical Performance

A large nonlinear optical (NLO) coefficient and a wide band gap are two crucial but contradictory parameters that are difficult to achieve simultaneously in a single infrared (IR) NLO compound. A salt‐inclusion chalcogenide (SIC), Li[LiCs₂Cl][Ga₃S₆] ( 1 ), was prepared that presents a nanosized tunnel framework constructed from monotype chalcogenide tetrahedra. Highly oriented covalent GaS₄ tetrahedra in the host lead to a moderate second harmonic generation response (0.7 AgGaS₂), and ionic guests effectively broaden the band gap to the widest value (4.18 eV) among all IR NLO chalcogenides, thereby achieving a remarkable balance between NLO efficiency and band gap.     

ZnS Nanospheres for Optical Modulator in an Erbium-Doped Fiber Laser

Zinc sulfide (ZnS), which belongs to transition metal monochalcogenides, is a semiconductor material with wide direct band gap. It can potentially show some special applications (such as luminescence, phosphor, sensors, infrared window materials, photocatalysis) by changing the morphology, size, and crystal structure of semiconductor materials. However, ZnS nanospheres have not been studied as optical modulators until now. Herein, ZnS nanospheres are synthesized by the hydrothermal method and are used to realize optical modulators in an Er-doped fiber laser. The evanescent field effect is utilized to incorporate the ZnS nanospheres on a tapered fiber. Furthermore, with the increase in pump power, the modulation interval gradually decreases to a minimum of 34.36 ns corresponding to the modulation frequency of 29.1 MHz, which is the highest modulation frequency to our knowledge in a ring cavity all-fiber laser. These results demonstrate ZnS nanospheres together with the interaction of dispersion and nonlinearity in optical fibers can modulate the proposed lasers. This not only provides a new method for controlling the power and frequency of all optical modulators, but also marks an important step for ZnS materials in optics research and device applications.     

Heteroborospherene nanoclusters as high-performance nonlinear optical materials

Today, the design of new compounds with giant nonlinear optical responses is attracted to many researchers. Inspired by an interesting finding of a new class of heteroborospherenes which were formed by doping four carbon atoms in the B364- nanocluster (C4B32), we suggest the alkali metal-doped C4B32 (M@C4B32, M=Li, Na, and K) nanoclusters as high-performance nonlinear optical materials. Our results show that the alkali metal atoms have a considerable effect on the structural and electronic properties of the C4B32 nanocluster. We found that the doping alkali metal can remarkably decrease the HOMO-LUMO gap and significantly increases the first hyperpolarizability of the C4B32 nanocluster. Also, our results reveal that the first hyperpolarizability of the M@C4B32 nanoclusters can be progressively enhanced by increasing the atomic number of alkali metals. The effect of external electric fields on the nonlinear optical responses of the M@C4B32 has been systematically explored. We found that the first hyperpolarizability of the M@C4B32 compounds can be gradually increased by increasing the imposed external electric field from zero to the critical external electric field along the charge transfer direction (M→C4B32). Accordingly, this work presents an efficient strategy to improve the nonlinear optical responses of the heteroborospherenes.     

一种新的岩石非线性黏弹塑性蠕变模型研究

为了克服传统元件组合模型不能描述岩石蠕变过程中非线性特征的缺陷，首先根据加速蠕变阶段的应变和应变率随蠕变时间急剧增大的特点，建立黏塑性应变与蠕变时间的指数函数关系并提出非线性黏塑性体．将该非线性黏塑性体与广义Burgers蠕变模型串联，建立可以描述岩石全蠕变过程的非线性黏弹塑性蠕变模型，根据叠加原理得到一维应力状态下的轴向蠕变方程．然后基于塑性力学理论指出岩石三维蠕变本构方程建立过程中的不足之处，并给出非线性黏弹塑性蠕变模型合理的三维蠕变方程．最后采用不同应力水平下砂岩轴向蠕变试验对模型合理性进行验证，结果表明：拟合曲线与试验曲线吻合度较高，所建蠕变模型能够很好地描述砂岩在不同应力水平下的蠕变变形规律，尤其对加速蠕变阶段的非线性特征描述效果很好，验证了模型的合理性．