First-order approximate analytical expressions of oblique incident elastic wave at an interface of porous media saturated with a nonviscous fluid

The analysis technology of Amplitude Variation with Offset(AVO)is one of the important methods for oil and gas reservoir prediction.Zoeppritz equation and its approximations are the theoretical basis of AVO analysis,which assumes that the upper and lower media of a horizontal interface are single-phase media.Limited by this assumption,AVO analysis has limited prediction and identification accuracy for complex porous reservoirs.In view of this,the first-order approximate analytical expressions of oblique elastic wave at an interface of porous media are derived.Firstly,the incident and scattering characteristics of various waves at the interface of porous media are analyzed,and the displacement vectors generated by these elastic waves are described by exponential function.Secondly,the kinematic and dynamic boundary conditions at the interface of porous media are discussed.Thirdly,by substituting the displacement vectors of incident and scattered waves into boundary conditions,the exact analytical equation is derived.Then,considering the symmetry of scattering matrix in the equation,the exact analytical expressions of each scattered wave are obtained.Furthermore,under the assumptions of small incident angle,weak elasticity at an interface of porous media,and ignoring the second-and higherorder terms,the first-order approximate analytical expressions are derived.Establishing a model of sandstone porous media with different porosity in upper and lower media,the correctness of the approximate analytical expressions is verified,and the elastic wave response characteristics of lithology and pore fluids are analyzed.

New approximate solution for time-fractional coupled KdV equations by generalised differential transform method

In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.

Fuzzy stochastic generalized reliability studies on embankment systems based on first-order approximation theorem

In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.

Approximate analytic solutions for a generalized Hirota—Satsuma coupled KdV equation and a coupled mKdV equation

This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries （KdV） equation and a coupled modified Korteweg-de Vries （mKdV） equation. This method provides a sequence Of functions which converges to the exact solution of the problem and is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.

Seismic safety assessment with non-Gaussian random processes for train-bridge coupled systems

Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.

Approximate Controllability of the System Governed by Double Coupled Semilinear Degenerate Parabolic Equations

This paper concerns the approximate controllability of the initialboundary problem of double coupled semilinear degenerate parabolic equations.The equations are degenerate at the boundary,and the control function acts in the interior of the spacial domain and acts only on one equation.We overcome the difficulty of the degeneracy of the equations to show that the problem is approximately controllable in L2 by means of a fixed point theorem and some compact estimates.That is to say,for any initial and desired data in L2,one can find a control function in L2 such that the weak solution to the problem approximately reaches the desired data in L2 at the terminal time.

Approximate Analytical Solutions of Fractional Coupled mKdV Equation by Homotopy Analysis Method

In this paper, the approximate analytical solutions of the fractional coupled mKdV equation are obtained by homotopy analysis method (HAM). The method includes an auxiliary parameter which provides a convenient way of adjusting and controlling the convergence region of the series solution. The suitable value of auxiliary parameter is determined and the obtained results are presented graphically.

Evolution of entanglement between qubits ultra-strongly coupling to a quantum oscillator

We investigate the dynamics of two qubits coupled with a quantum oscillator by using the adiabatic approximation method. We take account of the interaction between the qubits and show how the entanglement is affected by the interaction parameter. The most interesting result is that we can prolong the entanglement time or improve the entanglement degree by using an appropriate interaction parameter. As the generation and preservation of entanglement of qubits are crucial for quantum information processing, our research will be useful.

Cumulant Expansion in Intermediate Coupling Region in U(l)Lattice Gauge Theory

Determining the parameters in the i-th order approximation in the cumulant expansion from the requirement that the correction to the zeroth order approximation is zero or the smallest,we show in the example of calculating the Polyakov line<L>of U(1)gauge model at finite temperature with N_(T)=1-to 5-th order that the expansion works well not only in the strong and weak coupling regions,but also in the intermediate coupling region except the very vicinity of the phase transition point.The calculated<L>is in agreement with Monte Carlo simulations.

The First-Order Comprehensive Sensitivity Analysis Methodology (1^st-CASAM) for Scalar-Valued Responses: II. Illustrative Application to a Heat Transport Benchmark Model

This work illustrates the application of the 1st-CASAM to a paradigm heat transport model which admits exact closed-form solutions. The closed-form expressions obtained in this work for the sensitivities of the temperature distributions within the model to the model’s parameters, internal interfaces and external boundaries can be used to benchmark commercial and production software packages for simulating heat transport. The 1st-CASAM highlights the novel finding that response sensitivities to the imprecisely known domain boundaries and interfaces can arise both from the definition of the system’s response as well as from the equations, interfaces and boundary conditions that characterize the model and its imprecisely known domain. By enabling, in premiere, the exact computations of sensitivities to interface and boundary parameters and conditions, the 1st-CASAM enables the quantification of the effects of manufacturing tolerances on the responses of physical and engineering systems.

基于协同优化的耐压柱壳多学科多目标优化

为提高耐压柱壳的设计效率和结构性能,本文基于多学科设计优化思想,进行了耐压柱壳多学科设计优化的学科分解,确定了耐压柱壳多学科优化设计的设计参数,明确了设计变量间的耦合关系,设计了耐压柱壳参数化分析流程,进行了设计变量灵敏度分析。在利用响应面模型建立了具有较高拟合精度耐压柱壳近似模型的基础上,以质量排水量比和极限载荷为目标函数,建立了基于协同优化方法的耐压柱壳多学科多目标优化模型,在确定了系统层和学科层的优化求解方法基础上,设计了基于协同优化的耐压柱壳多学科多目标优化框架,进行了优化的求解工作,得到了优化方案。与初始方案的对比表明:所得到的Pareto解集中,部分方案在2个目标函数上均得到了优化,验证了优化框架的有效性。

基于机电耦合方程近似解的低频电磁激振器谐波控制

针对大行程低频电磁激振器非线性参数导致输出振动信号严重波形失真问题,在建立激振器机电耦合模型及等效传递函数分析基础上,对输出振动信号进行基于传递函数的初步谐波补偿控制。通过计算表征激振器非线性特性机电耦合方程对应的输出振动位移一次及二次近似解,得到在输入信号叠加的准确谐波补偿控制量,进而实现对输出信号波形失真的高精度补偿控制。仿真分析及实验测试结果表明:基于传递函数及近似解的控制方法可在整个频率范围对输出信号谐波进行有效补偿,0.1 Hz对应的加速度失真度由传递函数控制前的22.81%降低为4.5%,一次及二次近似解控制进一步降低为4.42%及1.78%,基于二次近似解的谐波控制方法具有更高的控制精度。

数值求解耦合Gross-Pitaevskii方程组基态解的离散归一化梯度流方法

本文提出了一种求解磁场项为常数的耦合Gross-Pitaevskii方程组基态解的数值方法.基于单组分近似理论,本文将方程组的能量函数等价为单组分的能量泛函,然后基于降阶后的能量表达式提出了离散归一化梯度流数值方法.数值算例表明,该方法高效且可靠.

环保型混合气体绝缘介质散射截面微观机理研究

为推进电力设备绝缘介质新型环保绝缘气体开发工作,本文采用量子力学微观计算方法,以电子/气体分子碰撞散射截面作为计算目标,采用密耦近似方法,计算了He-H2混合气体多粒子体系相对碰撞能量E=0.2 eV时00-00弹性碰撞和00-02,00-04非弹性激发碰撞的微分反射截面,进一步分析相对碰撞能量值对弹性及非弹性碰撞计算结果的影响,总结了该碰撞体系微分散射截面的变化规律,为探索混合气体绝缘特性的机理提供理论基础和指导。研究表明,He-H2的00-00弹性碰撞微分截面主要发生在小角度部分,00-02非弹性碰撞的散射主要发生在大角部分,00-04跃迁能实现,但非弹性碰撞微分截面很小,而He-H2碰撞的00-06激发不可能实现。

面向多任务动态场景的雷达与干扰空时协同波束联合优化方法

现代雷达对抗形势复杂多变,体系与体系的作战已成为基本特点,而体系整体性能关乎着战场的主动权乃至最终的胜负。通过优化体系中雷达与干扰波束资源可以提升整体性能,获得在空间、时间域优效的低截获探测性能,然而空时域协同波束联合优化是一个复杂多参数耦合的非凸问题。该文针对空时域多任务动态场景,建立了以雷达探测性能为优化目标,以干扰性能以及能量限制为约束条件的优化模型。为求解该模型,该文提出了基于迭代优化的空时协同波束联合设计方法,即以雷达发射、接收、多干扰机发射波束交替迭代优化。其中,针对多干扰机协同优化的不定矩阵二次约束二次规划(QCQP)问题,该文基于可行点追踪-连续凸逼近(FPP-SCA)算法,在SCA算法的基础上,通过引入松弛变量与惩罚项,保证算法在合理松弛度下的可行性,解决了矩阵不定情况下难以获得可行解的问题。仿真表明,在一定的干扰机能量约束下,该文所提方法在保证雷达高性能探测目标且不受干扰情况下,同时实现了多干扰机在空时域干扰对方每个平台以掩护我方雷达探测的效果;相比传统算法,在动态场景中基于FPP-SCA算法的协同干扰具有更优效果。

Dynamics of two arbitrary qubits strongly coupled to a quantum oscillator

Using adiabatic approximation, a two arbitrary qubits Rabi model has been studied in ultra-strong coupling. The analytical expressions of the eigenvalues and the eigenvalues are obtained. They are in accordance with the numerical determined results. The dynamical behavior of the system and the evolution of entanglement have also been discussed. The collapse and revival phenomena has garnered particular attention. The influence of inconsistent coupling strength on them is studied. These results will be applied in quantum information processing.

The Harmonic Approximation in Heavy-Ion Reaction Study

The derivation of the harmonic approximation of the Hamiltonian of a model of coupled three-dimensional harmonic oscillator is presented. It is shown how the splitting of the total Hamiltonian into the intrinsic and collective Hamiltonians leads to the description of the mechanism for energy dissipation in physical systems.

Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation

In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.

双不确定参数作用下双稳态能量采集系统的随机响应分析

非线性多稳态能量采集系统模型复杂、结构参数较多,由于测量、加工、装配过程中不可避免的存在误差,这些结构参数都存在一定的不确定性.而关键参数的微小变化都可能对系统输出电压产生显著影响,特别当多不确定参数同时存在时,可能会对系统能量采集性能产生更加复杂的影响.因此,研究多不确定参数作用下非线性能量采集系统的随机行为十分必要.本文针对具有双不确定参数的双稳态能量采集系统,首先,利用Routh-Hurwitz定理分析了确定性双稳态系统平衡点的稳定性及其静态分岔特性;继而,借助正交多项式逼近法,将具有两个相互独立的不确定机电耦合系数的随机双稳态系统转化为等价确定性扩阶系统,使系统的随机响应问题转换为等价系统的响应问题;之后,从全局和局部两个角度出发,通过等价系统与确定性系统吸引子、吸引域、相轨、均方电压以及能量转化率的对比,揭示了不确定参数对系统动力学行为和发电性能的影响.结果表明,在一些敏感的参数区间内,两机电耦合系数的不确定性均会导致系统运动状态发生变化,且不确定参数强度越大,系统会越早通过倍周期分岔级联进入混沌状态;此外,在两机电耦合系数的不确定性作用下,系统均方电压均会出现一定程度的降低;且与电方程中机电耦合系数相比,机械方程中机电耦合系数对系统的影响更显著,当两不确定参数共同作用时,系统的能量采集性能变化更显著.

STOKES COUPLING METHOD FOR THE EXTERIOR FLOW PART Ⅰ:APPROXIMATE ACCURACY

1.IntroductionLetΩ0beasimply-connectedboundedopensetofR2withthesmoothboundaryΓandletΩdenotethecomplementofΩ0Γ,wheretheoriginofcoordinatesislocatedintheinteriorofΩ0.InQ+=Ω×R+,weconsiderthefollowinginitial-boundaryvalueproblemoftheNavier-Stokes...