POSITIVE CLASSICAL SOLUTIONS OF DIRICHLET PROBLEM FOR THE STEADY RELATIVISTIC HEAT EQUATION

In this paper,for a bounded C2 domain,we prove the existence and uniqueness of positive classical solutions to the Dirichlet problem for the steady relativistic heat equation with a class of restricted positive C2 boundary data.We have a non-existence result,which is the justification for taking into account the restricted boundary data.There is a smooth positive boundary datum that precludes the existence of the positive classical solution.

On the Fifth-Order Stokes Solution for Steady Water Waves

This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flexibilities on the definition of the perturbation parameter and on the determination of the wave celerity. The universal solution can be extended to that of Chappelear （1961）, confirming the correctness for the universal theory. Furthermore, a particular fifth-order solution is obtained where the wave steepness is used as the perturbation parameter. The applicable range of this solution in shallow depth is analyzed. Comparisons with the Fourier approximated results and with the experimental measurements show that the solution is fairly suited to waves with the Ursell number not exceeding 46.7.

Semi-analytic Solution of Steady Temperature Fields During Thin Plate Welding

Usually, it is very difficult to find out an analytical solution to thermal conduction problems during high temperature welding. Therefore, as an important numerical approach, the method of lines （MOLs） is introduced to solve the temperature field characterized by high gradients. The basic idea of the method is to semi-discretize the governing equation of the problem into a system of ordinary differential equations （ODEs） defined on discrete lines by means of the finite difference method, by which the thermal boundary condition with high gradients are directly embodied in formulation. Thus the temperature field can be obtained by solving the ODEs. As a numerical example, the variation of an axisymmetrical temperature field along the plate thickness can be obtained.

Analytical solutions of steady vibration of free rectangular plate on semi-infinite elastic foundation

The method of double Fourier transform Was employed in the analysis of the semi-infinite elastic foundation with vertical load. And an integral representations for the displacements of the semi-infinite elastic foundation was presented. The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semiinfinite elastic foundation. Some computational results and the analysis on the influence of parameters were presented.

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.

Effects of wind input and wave dissipation formulations on the steady Ekman current solution

The effects of different wind input and wave dissipation formulations on the steady Ekman current solution are described. Two formulations are considered: one from the wave modeling(WAM) program proposed by Hasselmann and Komen and the other provided by Tsagareli and Babanin. The solution adopted for our study was presented by Song for the wave-modifi ed Ekman current model that included the Stokes drift, wind input, and wave dissipation with eddy viscosity increasing linearly with depth. Using the Combi spectrum with tail effects, the solutions are calculated using two formulations for wind input and wave dissipation, and compared. Differences in the results are not negligible. Furthermore, the solution presented by Song and Xu for the eddy viscosity formulated using the K-Profi le Parameterization scheme under wind input and wave dissipation given by Tsagareli and Babanin is compared with that obtained for a depth-dependent eddy viscosity. The solutions are further compared with the available well-known observational data. The result indicates that the Tsagareli and Babanin scheme is more suitable for use in the model when capillary waves are included, and the solution calculated using the K-Profi le Parameterization scheme agrees best with observations.

A Simple Strategy for Capturing the Unstable Steady Solution of an Unsteady Flow

A simple strategy for capturing unstable steady solution is proposed in this paper. By enlarging the real time step, the unstable high frequency modes of the unsteady flow can be effectively suppressed because of the damping action on the real time level. The steady component will not be changed during real time marching. When the unsteady flow solution converges to a steady state, the partial derivatives of real time in unsteady governing equations will disappear automatically. The steady solution is the exacted unstable steady solution. The method is validated by the laminar flow past a circular cylinder and a transonic buffet of NACA0012 airfoil. This approach can acquire high-precision unstable steady solutions quickly and effectively without reducing the spatial discretization accuracy. This work provides the basis for unstable flow modeling and analysis.

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.

ANALYTICAL SOLUTION OF AXIAL SYMMETRICAL WALL TEMPERATURE DISTRIBUTION FOR HOLLOW CYLINDER

Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.

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.

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.

TRANSONIC SHOCK SOLUTIONS TO THE EULER SYSTEM IN DIVERGENT-CONVERGENT NOZZLES

In this paper,we study the transonic shock solutions to the steady Euler system in a quasi-one-dimensional divergent-convergent nozzle.For a given physical supersonic inflow at the entrance,we obtain exactly two non-isentropic transonic shock solutions for the exit pressure lying in a suitable range.In addition,we establish the monotonicity between the location of the transonic shock and the pressure downstream.

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.

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。

基坑二维稳态渗流场的解析解及简化解

在基坑工程中,地下水渗流对基坑稳定性的影响不可忽视,但现有的一维渗流理论无法完全满足渗流计算的安全性要求。针对现有理论的不足,对悬挂式不考虑厚度挡墙支护下的各向同性土层中基坑的二维稳态渗流场进行了解析。依据对称性取基坑半截面,将周围土层分成4个规则区域,利用叠加原理和分离变量法分别将4个区域内的水头表示为级数解的形式,结合区域间连续条件及级数解的正交性得出渗流场的显式解。对比解析解与PLAXIS 2D软件的水头计算结果,发现级数项取20的解收敛且取1时的解仍具有一定的精度,可分别视为精确解和简化解。提出的简化解计算方便,借助计算器即可快速完成对基坑任意一点水头的求解。对比一维静水压力、一维考虑渗流的水压力、流网法、简化解、精确解及数值解水压力计算结果,发现精确解与数值解吻合较好且较流网法精度更高,简化解较一维静水压力、一维考虑渗流的水压力精度更高。参数分析表明:精确解和简化解计算的水压力合力相对误差主要受基坑内侧水位和挡墙至不透水层距离的影响;简化解适用于基坑尺寸不大,尤其内侧水位线到挡墙底部距离大于7 m、底部不透水层到挡墙距离小于30 m的基坑,计算挡墙水压力合力作用点则适用于任意尺寸的基坑;与精确解相比,简化解误差主要出现在挡墙底部,其余位置在基坑尺寸不大时,水头误差小于5%。

渗透各向异性土层中考虑挡墙厚度的基坑稳态渗流解析解

本文对考虑厚度挡墙支护下渗透各向异性土层中基坑的二维稳态渗流进行了解析研究。根据对称性取基坑半截面,将周围土层划分为5个规则区域,采用坐标变换将渗透各向异性土层转换成等效各向同性土层,对各区域利用叠加法和分离变量法推导得到二维稳态渗流场、挡墙上水压力以及坑底出逸比降的显式解析解。对比保角变换和积分变换方法,本文解渗流场计算结果连续且无奇异点,且基坑水头和挡墙两侧水压力分布情况与数值软件分析一致性较好,说明本文解析解的正确性和优越性。本文解与不同计算方法得到的挡墙水压力结果对比分析发现,挡墙厚度d、竖直与水平向渗透系数比α对挡墙上水压力的影响不可忽略。分析α、d对挡墙底部水压力及出逸比降的影响,随着α和d的增大,基坑外侧挡墙底部水压力增大,基坑内侧挡墙底部水压力减小;随着α和d的逐渐减小,坑底出逸比降不断增大;当α和d较小时,考虑一维渗流情况得到的出逸比降安全性较低,且随着α和d的减小与本文解析解差距越来越大。

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。

非饱和成层土稳态渗流问题的解析计算

广泛存在的成层土非饱和稳态渗流的解析计算研究相对薄弱。基于达西渗流定律和土层界面的连续性条件,构建了描述非饱和成层土稳态渗流过程的数学模型。使用分离变量技术和数学归纳思想,获得了成层土同一剖面的基质吸力、有效饱和度与吸应力沿高程分布的解析表达式。基于COMSOL数值分析平台对解析算法进行了验证计算,从而实现了非饱和成层土稳态渗流过程的解析求解。而后,探讨了土层界面的存在对渗流过程的影响并开展了参数敏感度分析。分析表明:(1)相同入渗条件下相同高程处砂土的基质吸力最大,黏土最小;地表渗流速率的不同对粉土层有效饱和度分布影响最大,砂土最小。(2)黏土层中吸应力近乎线性增长,砂土的吸应力则沿高程先增大后减小;土层界面的存在会影响基质吸力沿高程的增长速率,可使有效饱和度和吸应力沿高程分布发生突变。(3)Gardner模型参数α值越小,相同高程处基质吸力值越大,饱和土渗透系数(ks值)越小,基质吸力增长速率越慢;α与k_(s)取值越小,有效饱和度降低速率越慢;α取值越小或ks取值越大,地表处的吸应力值越大。研究成果可为诸如边坡稳定等工程地质问题提供一定的理论支撑。

热泵型多联式空调系统稳态仿真

热泵型多联式空调系统(简称热泵型多联机)相对于单冷型多联机,在系统结构和系统控制上更复杂,使得对其进行性能仿真时,需要在系统描述和求解算法方面进行改进。本文对热泵型多联机进行稳态仿真。通过使用邻接矩阵的对角线元素来反映部件工作状态,变换邻接矩阵切换制冷制热模式的方法,对热泵型多联机的结构进行描述;根据热泵型多联机实际运行时的控制策略,采用基于过热度/过冷度的制冷剂流量分配算法对模型进行求解。对于样机的仿真及实验对照表明:在额定制冷和额定制热工况下,热泵型多联机仿真预测的系统能力、功率和系统能效的误差均在5%以内,系统温度和压力的误差分别在±3℃和±100 kPa以内,能够满足热泵型多联机设计的精度需求。

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.