GURTIN-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF A NON-LOCAL THERMAL EQUILIBRIUM SATURATED POROUS MEDIUM

Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.

Variational solutions for Hermite-Gaussian solitons in nonlocal nonlinear media

The physical features exhibited by Hermite-Gaussian （HC） beams propagating in nonlocal nonlinear media with Gaussian-shaped response are discussed with an approximate variational method.Using direct numerical simulations,we find that the beam properties in the normalized system are different with the change of the degree of nonlocality.It is shown that initial HG profiles break up into several individual beams with propagation when the degree of nonlocality α is small.HG beams can propagate stably when a is large enough.

An overview on nonlinear porous flow in low permeability porous media

This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy＇s linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir~ is established. This model can describe various patterns of porous flow, as Darcy＇s linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.

Elegant Ince-Gaussian breathers in strongly nonlocal nonlinear media

A novel class of optical breathers, called elegant Ince-Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell＇s mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear SchrSdinger equation.

Nonlinear optical properties in double-sided nonlinear media with Z-scan technique based on the Huygens-Fresnel principle

We present a theoretical model to analyse the propagation of a Gaussian laser beam through double-sided nonlinear media. This model is based on the Huygens-Fresnel diffraction integral method. This theoretical model is not only consistent with the cascade structure model for a small nonlinear phase-shift but also can be used for a large nonlinear phase-shift. It has been verified that it is suitable to characterize the double-sided nonlinear media compared with the cascade structure model. A good agreement between the experimental data and the results from the theoretical model is obtained. It will be useful for the design of multi-sided nonlinear materials.

MATHEMATICAL MODEL OF TWO-PHASE FLUID NONLINEAR FLOW IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS

A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oilfields with scientific basis.

Propagation of optical vortex solitons due to the Gouy phase in strongly nonlocal nonlinear media

In this paper, we present a study on the propagation of the symmetrical optical vortices formed by two collinear Laguerre-Gauss solitons in strongly nonlocal nonlinear media. The optical vortices, which move along the beam axis as the light propagates, result in a rotation of the beam＇s transverse profile. This physical reason of the rotation is the Gouy phase acquired by the component beams.

Dark incoherent spatial solitons in logarithmically saturable nonlinear media

This paper studies numerically the dark incoherent spatial solitons propagating in logarithmically saturable nonlinear media by using a coherent density approach and a split-step Fourier approach for the first time. Under odd and even initial conditions, a soliton triplet and a doublet are obtained respectively for given parameters. Simultaneously, coherence properties associated with the soliton triplet and doublet are discussed. In addition, if the values of the parameters are properly chosen, five and four splittings from the input dark incoherent spatial solitons can also form. Lastly, the grayness of the soliton triplet and that of the doublet are studied, in detail.

Grey Self-similar Solitary Waves in Inhomogeneous Nonlinear Media

这篇论文在等级索引分析空间灰自我类似的独居的波浪繁殖和碰撞有自我集中、自我散焦的克尔非线性的非线性的波导放大器。新准确自我类似的答案用新奇转变被发现，他们的主要特征被使用直接计算机模拟调查。

Coupled-generalized nonlinear Schr¨odinger equations solved by adaptive step-size methods in interaction picture

We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schr ¨odinger equation(GNLSE): one is the conservation quantity error adaptive step-control method(RK4IP-CQE), and the other is the local error adaptive step-control method(RK4IP-LEM). The methods are developed in the vector form of fourthorder Runge–Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step-size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP-LEM spends more time than RK4IP-CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step-size algorithms.

受媒体信息影响的一类随机传染病模型的研究

考虑到媒体信息对疾病预防和控制具有重要作用,建立了一类受媒体信息影响和具有非线性传染率的随机SEIS传染病模型,并运用随机微分方程的相关理论研究了该模型的绝灭性、持久性和平稳分布.数值模拟验证表明,当环境随机干扰越强或媒体信息报道得越及时时,传染病的绝灭速度越快.该研究结果改进和丰富了文献[12]的相关研究结果,并可为利用媒体信息进行预防和控制疾病提供良好参考。

各向同性介质的三阶非线性极化统一理论

探讨了入射至各向同性介质的不同频率的多光束;推导了三阶非线性极化矢量形式的表达式,并利用它解释了多个已知且独立的非线性光学现象,验证了该表达式的普适性和正确性.结果表明,三阶非线性极化矢量形式的表达式可为各向同性介质中的三阶非线性光学效应提供统一描述;将其拓展至六角晶系材料,能对各种复杂问题提供简单的处理方式.这对于系统地理解各向同性介质和六角晶系材料中的三阶非线性光学效应具有重要意义,有望促进非线性光学在频率转换、偏振态检测和量子信息等领域中的应用.

Numerical calculation of Z-scan measurements for nonlinear media with large phase shift

We have reported the characteristics of a Z-scan for the poly(azaneylylidene-acylene)(DAZA) polymer, as nonlinear medium with a large nonlinear phase shift using continuous-wave(CW) laser beam. It has been verified that the Fresnel diffraction model is applicable for analyses of Z-scan measurements with DAZA polymer at high laser power. It was found that Z-scan curves with peak-to-valley features appear as the applied light intensity increases in the case of a large nonlinear phase shift. The Z-scan experiments were carried out using a CW laser to verify the theoretical calculations in the case of a large nonlinear phase shift model. Our results show good agreements between the experimental data and the proposed theoretical models.

纳米多孔介质中的流体流动

Fluid flow at nanoscale is closely related to many areas in nature and technology(e.g.,unconventional hydrocarbon recovery,carbon dioxide geo-storage,underground hydrocarbon storage,fuel cells,ocean desalination,and biomedicine).At nanoscale,interfacial forces dominate over bulk forces,and nonlinear effects are important,which significantly deviate from conventional theory.During the past decades,a series of experiments,theories,and simulations have been performed to investigate fluid flow at nanoscale,which has advanced our fundamental knowledge of this topic.However,a critical review is still lacking,which has seriously limited the basic understanding of this area.Therefore herein,we systematically review experimental,theoretical,and simulation works on single-and multi-phases fluid flow at nanoscale.We also clearly point out the current research gaps and future outlook.These insights will promote the significant development of nonlinear flow physics at nanoscale and will provide crucial guidance on the relevant areas.

Strength criterion of porous media: Application of homogenization techniques

The present paper aims at giving some general ideas concerning the micromechanical approach of the strength of a porous material. It is shown that its determination theoretically amounts to solving a nonlinear boundary value problem defined on a representative elementary volume(REV). The principle of nonlinear homogenization is illustrated based on the case of a solid phase having a Green’s strength criterion. An original refinement of the so-called secant method(based on two reference strains) is also provided. The paper also describes the main feature of the Gurson’s model which implements the principle of limit analysis on a conceptual model of hollow sphere. The last part of the paper gives some ideas concerning poromechanical couplings.

非线性非一致介质二维Maxwell方程leap-frogCrank-Nicolson多区域Legendre-tau配置谱方法

该文研究了具有非线性电导率的非一致介质二维Maxwell方程的数值求解方法,提出了多区域Legendre-tau配置谱方法.该数值方法空间上达到谱精度,时间上是二阶精度.时间方向采用leap-frog Crank-Nicolson三层格式进行离散.非线性项放在中间已知层采用谱配置法显式处理,线性项采用Legendre谱方法隐式处理.利用显隐数值格式,既有较好的稳定性又方便算法实施.基于合理的弱形式,不需要使用额外附加的连接条件,以自然边界条件的方式处理交界面条件.定义不同次数多项式逼近空间,构建一致的数值格式.详细证明了半离散和全离散数值格式的稳定性和收敛性,并得到L^(2)-范数的最优误差估计.算例中,利用快速Legendre变换在Chebyshev点上计算非线性项,提高算法效率.数值结果证实了该数值方法求解此类非线性问题的有效性,并且没有因为解的间断而损失谱精度.

超重力下CuAg合金熔体在石墨多孔介质中的非线性渗流

合金熔体的超重力浸渗是制备金属基复合材料最重要的工艺之一。高温熔体在超重力浸渗过程中极易发生坩埚渗漏,严重影响合金凝固过程的传热和形核,进而影响材料的凝固组织。本文借助超重力凝固工艺,研究超重力下Cu-8%Ag合金熔体在石墨坩埚多孔介质中的渗流过程,分析超重力下Cu-8%Ag合金熔体在石墨坩埚多孔介质中渗流的影响因素,揭示超重力下CuAg合金熔体在石墨多孔介质中的非线性渗流机理,提出抑制超重力下高温熔体在多孔介质中渗流的预防措施。

二维颗粒结构中非线性波的传播和脉冲衰减

有序颗粒介质在冲击振动缓解、能量捕获和吸收等领域具有重要的研究价值。本文运用赫兹接触理论建立二维颗粒链数学模型,在冲击激励作用下,研究二维颗粒系统中脉冲波的传播特性、能量传递规律和传递力的降低机理。二维均匀颗粒系统嵌入了耦合颗粒以传递动能,初始脉冲激励在2列颗粒链间发生能量交换和脉冲等分现象,脉冲波在激励施加点附近发生强能量散射,激发出混合型的非线性波,即纵向传播的近零频率孤立波与横向高频剪切波。与一维均匀颗粒链相比,二维颗粒系统的末端传递力峰值得到了大幅度降低。通过改变颗粒间的质量比,在二维均匀颗粒链中引入轻珠链构成非均匀结构,沿纵向传播的孤立波在轻-重颗粒交界面发生反射,能量被局部约束在轻珠链中,使得一系列低幅值脉冲波按照不同的波速,延时释放到颗粒链末端,导致末端传递力峰值的进一步降低。

Threshold Dynamics of an SIR Epidemic Model with Nonlinear Incidence Rate and Non-Local Delay Effect

In this paper, we are concerned with a reaction-diffusion SIR epidemic model with nonlinear incidence rate and non-local delay effect in a continuous bounded spatial domain. We introduce the basic reproduction number R_0 of the model by the idea of next generation operator. By means of the theory of dynamical systems and uniform persistence, we investigate the global dynamics of the model in terms of R_0. Finally, we implement numerical simulations to show the feasibility of our results and explore some epidemiological insights.

强非局域介质中余弦高斯光束的动力学行为

基于强非局域非线性薛定谔方程的简化形式,采用分步傅里叶方法数值研究了余弦高斯光束在强非局域非线性介质中的演化行为,讨论了抛物势阱深度和余弦调制参数对光束传输动力学的影响。研究结果表明,光束传输周期只与抛物势阱深度有关,抛物势阱深度越大传输周期越小,光束振荡振幅越小。余弦调制参数对光束演化行为的影响也被考虑,结果显示:余弦调制参数会影响光束的分裂程度,调制参数越大光分裂行为就会越显著。这些研究结果有可能在余弦高斯光束的操控方面有着潜在的应用价值。