A CONDITION OF THE EXISTENCE OF STABLE POSITIVE STEADY-STATE SOLUTIONS FOR A ONE PREDATOR TWO PREY SYSTEM

One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.

Positive Solutions Bifurcating from Zero Solution in a Lotka-Volterra Competitive System with Cross-Diffusion Effects

A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.

POSITIVE STEADY STATES AND DYNAMICS FOR A DIFFUSIVE PREDATOR-PREY SYSTEM WITH A DEGENERACY

In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by the degeneracy of the intra-specific pressures for the prey. By the bifurcation method, the degree theory, and a priori estimates, we discuss the existence and multiplicity of positive steady states. Moreover, by the comparison argument, we also discuss the dynamical behavior for the diffusive predator-prey system.

Fractional variant of Stokes–Einstein relation in aqueous ionic solutions under external static electric fields

Both ionic solutions under an external applied static electric field E and glassy-forming liquids under undercooled state are in non-equilibrium state.In this work,molecular dynamics(MD)simulations with three aqueous alkali ion chloride(NaCl,KCl,and RbCl)ionic solutions are performed to exploit whether the glass-forming liquid analogous fractional variant of the Stokes–Einstein relation also exists in ionic solutions under E.Our results indicate that the diffusion constant decouples from the structural relaxation time under E,and a fractional variant of the Stokes–Einstein relation is observed as well as a crossover analogous to the glass-forming liquids under cooling.The fractional variant of the Stokes–Einstein relation is attributed to the E introduced deviations from Gaussian and the nonlinear effect.

Modified Lindstedt-Poincaré Method for Obtaining Resonance Periodic Solutions of Nonlinear Non-autonomous Oscillators

A modified Lindstedt-Poincaré(LP) method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equations are converted into a group of linear ordinary differential equations by introducing a set of simple transformations.An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modified method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation,and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.

DC steady-states analysis of lossy uniform transmission lines

A method for computing DC steady-state solutions in complex frequency-domain is put forward. It starts with complex frequency-domain transmission line equations, obtains the complex expressions of voltage and current at zero initial states, and find the DC steady-state solutions of voltage and current by using the fina value theorem of Laplace transform thory. The solutions are discussed with special internal resistances of DC voltage source and loads. A case study demonstrated that the proposed method is applicable to acquiring the DC steady-state voltage waveform and current waveform without first obtaining the analytic solutions.

A Newton multigrid method for steady-state shallow water equations with topography and dry areas

A Newton multigrid method is developed for one-dimensional （1D） and two- dimensional （2D） steady-state shallow water equations （SWEs） with topography and dry areas. The nonlinear system arising from the well-balanced finite volume discretization of the steady-state SWEs is solved by the Newton method as the outer iteration and a geometric multigrid method with the block symmetric Gauss-Seidel smoother as the inner iteration. The proposed Newton multigrid method makes use of the local residual to regularize the Jacobian matrix of the Newton iteration, and can handle the steady- state problem with wet/dry transition. Several numerical experiments are conducted to demonstrate the efficiency, robustness, and well-balanced property of the proposed method. The relation between the convergence behavior of the Newton multigrid method and the distribution of the eigenvalues of the iteration matrix is detailedly discussed.

喷雾热解法加热壁温对铈锆固溶体生产过程的影响

【目的】为了探究喷雾热解过程中加热壁温对铈锆固溶体生产过程的影响,分析热解炉内的流量场和浓度场的变化情况,实现对热解炉的设计优化。【方法】采用数值模拟的方法,建立喷雾热解炉的物理模型,分别探讨加热壁温对铈锆固溶体在热解炉的不同阶段及热解炉中水蒸气分布和HCl分布的影响。【结果】当热解温度为850℃时,液滴的反应主要分2个阶段,在炉膛高度为0~0.05 m处,为加热蒸发阶段,在炉膛高度为0.05~0.6 m处,为稳态热解阶段。当炉壁温度为550~650℃时,在炉膛高度为0.9 m处温度变化放缓,喷雾处于稳定热解阶段;而壁温在750~850℃时,在炉膛高度为0.6 m处温度变化放缓;当壁温为850℃时,在炉膛高度为0.1~0.6 m处的温度曲线斜率最大,液滴达到稳定蒸发阶段的时间缩短,水分蒸发变快,热解时间变短。【结论】炉壁加热区的温度越高,HCl生成的速度越快,速度的最大值越小,在炉膛高度为0.4 m处速度变化最大,达到1.6 m/s左右;并且整体HCl生成的量随温度的升高而增大,平均速度变化随着热空气温度的升高而减小。

华龙一号反应堆上腔室及热段流-热耦合场数值模拟

压水型反应堆(pressurized water reactor,PWR)系统主管道热段内冷却剂的温度和流量,直接反映了核功率和堆芯换热状态,是反应堆功率控制和安全保护的核心参数。为全面掌握华龙一号反应堆上腔室及热段内冷却剂流-热耦合场分布及演变规律,为核心参数测控提供参考,基于有限元分析(finite element method,FEA)方法,对上腔室及热段冷却剂流域进行了计算流体力学(computational fluid dynamics,CFD)数值模拟。首先建立了合理简化后的华龙一号(Hualong One)反应堆上腔室及相连热段的3D几何结构模型。随后对模型计算域进行了离散化网格划分和网格敏感性分析。最后通过计算,获得了冷却剂非等温流动的稳态特性解,流量、温度与相关设计估算值、实际测量值的相对误差均小于2%。对稳态特性研究表明,高、低温冷却剂在上腔室垂直内壁附近的不充分换热导致热段入口冷却剂温度分布不均,存在14.0~16.3℃的温差。随冷却剂沿轴向流动,冷却剂温度场分布和流场分布均逐渐趋于均匀和稳定,且是热段内低温冷却剂的流动主导了冷却剂温度分布的变化。

在禽类与人之间传播的禽流感反应扩散模型

为了研究禽类和人的流动性对禽流感传播的影响,考虑禽和人的流动性,建立了一个禽流感在禽与人之间传播的反应扩散模型。首先证明了模型解的全局存在性,其次利用下一代算子的谱半径方法计算了模型的基本再生数,并分析了模型的阈值动力学,证明了无病稳态的稳定性、疾病的持久性以及正稳态的存在性。最后通过数值模拟,验证了模型的理论结果。结果表明,对染病禽类进行隔离,从而降低禽与人的接触率可有效控制禽流感的传播。

Boussinesq方程稳态解的存在性与正则性

研究二维Boussinesq方程稳态解的存在性与正则性.首先,利用弱连续算子锐角原理得到方程弱解存在性的条件.其次,利用ADN理论、线性椭圆理论和迭代方法证明方程强解的存在性.最后,利用Sard-Smale定理得到解的有限性,并通过ADN理论和线性椭圆方程理论研究方程古典解的存在性.

一种改进后的闭环解码算法

针对传统的闭环解码算法量测方程、传递函数在加速时易造成稳态误差等问题,文中提出了一种改进后的闭环解码算法。在闭环解算之前,使用最小二乘法对旋转变压器输出的信号参数进行数据拟合,获得更加准确的旋转变压器信号,设计校正装置,避免抑制参数波动及非线性因素对系统性能的影响,增强系统的稳定性。利用仿真实验对解码算法进行了稳态误差、角位置和角速度误差分析,结果表明改进后的闭环解码算法更稳定、稳态误差更小,角位置误差波动从(-10,0)变为(-4.0,3.5),角速度误差波动从(-0.50,-0.25)变为(-0.15,0.10)。

激光超声时频参数对裂纹试件的温度检测

为了实现对高温工作环境下含表面裂纹试件的温度测量,提出了利用激光超声瑞利波的时、频参数实现表面裂纹试件温度测量的新思路。采用稳态解作为瞬态初始值的温度加载方法,建立了293.15~743.15 K温度范围内结构钢的表面裂纹试件模型,分析了激光超声瑞利波与表面裂纹的相互作用。在时域上,利用瑞利反射、透射波的归一化峰值来定义反射率、透射率这两个时域参数,得出反射率和透射率都与温度成线性增长关系,反射率和透射率随温度的变化率分别为1.45×10^(-3)dB·K^(-1)和2.3×10^(-3)dB·K^(-1);在频域上,提出了瑞利波的小波时频分析(TFA)分布下超声能量强度的特征极值点关系法,得出在特征频率为2.4 MHz时,能量强度的特征极值随温度的线性增长率为2.56×10^(-4)dB·K^(-1);实验分析证明了仿真结果的可行性。时、频域的研究结果结合实验分析表明,利用时、频参数与温度的线性关系和变化率,可实现表面含裂纹的试件的温度测量表征。

Improvement of Convergence to Steady State Solutions of Euler Equations with Weighted Compact Nonlinear Schemes

The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes （WCNS） [Deng X. and Zhang H. （2000）, J. Comput. Phys. 165, 22–44 and Zhang S., Jiang S. and Shu C.-W. （2008）, J. Comput. Phys. 227, 7294-7321] is studied through numerical tests. Like most other shock capturing schemes, WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level. In this paper, the techniques studied in [Zhang S. and Shu. C.-W. （2007）, J. Sci. Comput. 31, 273–305 and Zhang S., Jiang S and Shu. C.-W. （2011）, J. Sci. Comput. 47, 216–238], to improve the convergence to steady state solutions for WENO schemes, are generalized to the WCNS. Detailed numerical studies in one and two dimensional cases are performed. Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS. The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed.

A brief review on the convergence to steady state solutions of Euler equations with high-order WENO schemes

Weighted essentially non-oscillatory(WENO)schemes are a class of high-order shock capturing schemes which have been designed and applied to solve many fluid dynamics problems to study the detailed flow structures and their evolutions.However,like many other high-order shock capturing schemes,WENO schemes also suffer from the problem that it can not easily converge to a steady state solution if there is a strong shock wave.This is a long-standing difficulty for high-order shock capturing schemes.In recent years,this non-convergence problem has been studied extensively for WENO schemes.Numerical tests show that the key reason of the non-convergence to steady state is the slight post shock oscillations,which are at the small local truncation error level but prevent the residue to settle down to machine zero.Several strategies have been proposed to reduce these slight post shock oscillations,including the design of new smoothness indicators for the fifth-order WENO scheme,the development of a high-order weighted interpolation in the procedure of the local characteristic projection for WENO schemes of higher order of accuracy,and the design of a new type of WENO schemes.With these strategies,the convergence to steady states is improved significantly.Moreover,the strategies are applicable to other types of weighted schemes.In this paper,we give a brief review on the topic of convergence to steady state solutions for WENO schemes applied to Euler equations.

NON-CONSTANT POSITIVE STEADY-STATES OF A PREDATOR-PREY-MUTUALIST MODEL

In this paper, the authors deal with the non-constant positive steady-states of a predator-prey-mutualist model with homogeneous Neumann boundary condition. They first give a priori estimates (positive upper and lower bounds) of positive steady-states,and then study the non-existence, the global existence and bifurcation of non-constant positive steady-states as some parameters are varied. Finally the asymptotic behavior of such solutions as d3 →∞ is discussed.

STABILITY OF STEADY－STATE SOLUTIONS OF THE COMPETITION MODEL IN THE CHEMOSTAT

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POSITIVE PERIODIC SOLUTION FOR A CLASS OF DIFFERENTIAL EQUATION WITH STATE-DEPENDENT DELAYS

By utilizing the Krasnoselskii＇s fixed point theorem in cones we obtain some sufficient conditions which guarantee the existence of positive periodic solution for a class of differential equations with state-dependent delays. The results in the papers [1,2] have been improved.

Positive Steady States of a Competitor-Competitor-Mutualist Model

In this paper we deal with the positive steady states of a Competitor-Competitor-Mutualist modelwith diffusion and homogeneous Dirichlet boundary conditions.We first give the necessary conditions,and thenestablish the sufficient conditions for the existence of positive steady states.

Non-constant Positive Steady States of the Epidemic Model with Non-monotonic Incidence Rate

In this paper, the positive steady states of the epidemic model with non-monotonic incidence rate are considered. Firstly, it is proved that the unique positive constant steady state is stable for the ODE system and the PDE system. Secondly, a priori estimate of positive steady states is given, and the non-existence of non-constant positive steady states is established by using Poincare inequality and Young inequality. Finally,the existence and bifurcation of non-constant positive steady states are studied by using the degree theory and the global bifurcation theorem.