A UNIFORMLY DIFFERENCE SCHEME OF SINGULAR PERTURBATION PROBLEM FOR A SEMILINEAR ORDINARY DIFFERENTIAL EQUATION WITH MIXED BOUNDARY VALUE CONDITION

In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condition. The uniform convergence on small parameter ε of order one for an IVin type difference scheme constructed is proved. At the end of the paper, a numerical example is given. The computing results coincide with the theoretical analysis.

Optimization of Culture Conditions and Medium Composition for the Marine Algicidal Bacterium Alteromonas sp. DH46 by Uniform Design

Harmful algal blooms(HABs) have led to extensive ecological and environmental issues and huge economic losses.Various HAB control techniques have been developed,and biological methods have been paid more attention.Algicidal bacteria is a general designation for bacteria which inhibit algal growth in a direct or indirect manner,and kill or damage the algal cells.A metabolite which is strongly toxic to the dinoflagellate Alexandrium tamarense was produced by strain DH46 of the alga-lysing bacterium Alteromonas sp.The culture conditions were optimized using a single-factor test method.Factors including carbon source,nitrogen source,temperature,initial pH value,rotational speed and salinity were studied.The results showed that the cultivation of the bacteria at 28℃ and 180 r min-1with initial pH 7 and 30 salt contcentration favored both the cell growth and the lysing effect of strain DH46.The optimal medium composition for strain DH46 was determined by means of uniform design experimentation,and the most important components influencing the cell density were tryptone,yeast extract,soluble starch,NaNO3 and MgSO4.When the following culture medium was used(tryptone 14.0g,yeast extract 1.63g,soluble starch 5.0 g,NaNO3 1.6 g,MgSO4 2.3 g in 1L),the largest bacterial dry weight(7.36 g L-1) was obtained,which was an enhancement of 107% compared to the initial medium;and the algal lysis rate was as high as 98.4% which increased nearly 10% after optimization.

PREDICTION OF THE AERODYNAMIC PERFORMANCE OF HORIZONTAL AXIS WIND TURBINES IN CONDITION OF UNIFORM WIND

The classical momentum-blade element theory is improved by using the empirical formula while part of rotor blades enters into the turbulent wake state, and the performance of a horizontal-axis wind turbine (HAWT) at all speed ratios can be predicted. By using an improved version of the so-called secant method, the convergent solutions of the system of two-dimensional equations concerning the induced velocity factors a and a' are guaranteed. Besides, a solving method of multiple solutions for a and a' is proposed and discussed. The method provided in this paper can be used for computing the aerodynamic performance of HAWTs both ofrlow solidity and of high solidity. The calculated results coincide well with the experimental data.

Novel wavelet-homotopy Galerkin technique for analysis of lid-driven cavity flow and heat transfer with non-uniform boundary conditions

In this paper, a brand-new wavelet-homotopy Galerkin technique is developed to solve nonlinear ordinary or partial differential equations. Before this investigation,few studies have been done for handling nonlinear problems with non-uniform boundary conditions by means of the wavelet Galerkin technique, especially in the field of fluid mechanics and heat transfer. The lid-driven cavity flow and heat transfer are illustrated as a typical example to verify the validity and correctness of this proposed technique. The cavity is subject to the upper and lower walls’ motions in the same or opposite directions.The inclined angle of the square cavity is from 0 to π/2. Four different modes including uniform, linear, exponential, and sinusoidal heating are considered on the top and bottom walls, respectively, while the left and right walls are thermally isolated and stationary.A parametric analysis of heating distribution between upper and lower walls including the amplitude ratio from 0 to 1 and the phase deviation from 0 to 2π is conducted. The governing equations are non-dimensionalized in terms of the stream function-vorticity formulation and the temperature distribution function and then solved analytically subject to various boundary conditions. Comparisons with previous publications are given,showing high efficiency and great feasibility of the proposed technique.

A UNIFORMLY CONVERGENT FINITE DIFFERENCE METHOD FOR A SINGULARLY PERTURBED INITIAL VALUE PROBLEM

Initial value problem for linear second order ordinary differential equation with small parameter by the first and second derivatives is considered. An exponentially fitted difference scheme with constant fitting factors is developed in a uniform mesh, which gives first_order uniform convergence in the sense of discrete maximum norm. Numerical results are also presented.

Sufficient conditions of the various stabilities of the linear time-varying delayed differential equations

Due to the appearance and the study of the ornithopter and flexible-wing micro air vehicles, etc., the time-varying systems become more and more important and ubiquitous in the study of the mechanics. In this letter, the sufficient conditions of the uniform asymptotic stability are first presented for the delayed time-varying linear differential equations with any time delay by employing the Dini derivative, Lozinskii measure and the generalized scalar Halanay delayed differential inequality. They are especially based on the estimation of the arbitrary solutions but not the fundamental solution matrix since their solutions＇ space is infinite-dimensional. Then some sufficient conditions of the stability, asymptotic stability and uniform asymptotic stability of the delayed time-varying linear system with a sufficiently small time delay are reported by employing Taylor expansion and Dini derivative. It implies that these stabilities can be guaranteed by the Lozinskii measure of the matrix composing of the time delay and the coefficient matrices of the system.

Longitudinal dispersion with constant source concentration along unsteady groundwater flow in finite aquifer: analytical solution with pulse type boundary condition

Analytical solution is obtained to predict the contaminant concentration with presence and absence of pollution source in finite aquifer subject to constant point source concentration. A longitudinal dispersion along unsteady groundwater flow in homogeneous and finite aquifer is considered which is initially solute free that is, aquifer is supposed to be clean. The constant source concentration in intermediate portion of the aquifer system is considered with pulse type boundary condition and at the other end of the aquifer, concentration gradient is supposed to be zero. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution of the formulated solute transport model with suitable initial and boundary conditions. The time varying velocities are considered. Analytical solutions are perhaps most useful for benchmarking the numerical codes and models. It may be used as the preliminary predictive tools for groundwater management.

The Uniformly Valid Solution for a Top System of Two Free Dimensions with Parameter

A general top system of two free dimensions with parameter is studied and the four cases satisfied by the frequency of the system are discussed.Using the multiple scale method,its uniformly valid asymptotic solution,which is expressed by complex amplitudes,of the first order is obtained.And solvable conditions satisfied by the complex amplitudes are given,and then the relative result is generalized.

Uniform isochronous center of a class of higher degree polynomial differential systems

In this paper,we give the necessary and sufficient conditions for a class of higher degree polynomial systems to have a uniform isochronous center.At the same time,we prove that for this system the composition conjecture is correct.

Mesoscale Simulation for Polymer Migration in Confined Uniform Shear Flow

The structure and dynamics of confined single polymer chain in a dilute solution, either in equilibrium or at different shear rates in the uniform shear flow fields, were investigated by means of dissipative particle dynamics simulations. The no-slip boundary condition without density fluctuation near the wall was taken into account to mimic the environment of a nanochannel. The dependences of the radius of gyration, especially in three different di- rections, and the density profile of the chain mass center on the strength of the confinement and the Weissenberg number（Wn） was studied. The effect of the interaction between polymer and solvent on the density profile was also investigated in the cases of moderate and strong Wn. In the high shear flow, the polymer migrates to the center of the channel with increasing Wn. There is only one density profile peak in the channel center in the uniform shear flow, which is in agreement with the results of the experiments and theory.

BLOW-UP RATE OF POSITIVE SOLUTION OF UNIFORMLY PARABOLIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

This paper deals with the blow-up of positive solutions of the uniformly pa-rabolic equations ut = Lu + a(x)f(u) subject to nonlinear Neumann boundary conditions . Under suitable assumptions on nonlinear functi-ons f, g and initial data U0(x), the blow-up of the solutions in a finite time is proved by the maximum principles. Moreover, the bounds of 'blow-up time' and blow-up rate are obtained.

More Properties of Semi-Linear Uniform Spaces

In this paper we shall generalize the definition given in [1] for Lipschitz condition and contractions for functions on a non-metrizable space, besides we shall give more properties of semi-linear uniform spaces.

Factors Impacting Corn (<i>Zea mays</i>L.) Establishment and the Role of Uniform Establishment on Yield

Information from actual farm fields can help corn producers understand the value and importance of establishing uniform crop emergence and within-row plant spacing. Thirty-eight fields planted with corn (Zea mays L.) by North Dakota producers were evaluated to determine the effects of uneven plant emergence timing and within-row plant space variability, as well as identifying contributing factors. Rows within a planter’s width with the most variability yielded 6% less than the least variable rows. Individual ear weights decreased as the number of days after normal emergence (date when 50% of plant stand emerged) increased. Ears next to within-row gaps (>30.5 cm) weighed 11% more than the normally spaced plants. Combined ears from both plants situated <5.1 cm apart weighed 36% more than from a single ear from normally spaced plants. Surface residue and planting speed impacted stand establishment variability more often than other factors measured. Producers should assess each field environment individually in order to identify best practices to achieve uniform stand establishment.

Thermal explosion of a reactive gas mixture at constant pressure for non-uniform and uniform temperature systems

In this study,the approximate and exact solutions for the stationary-state of the solids model with neglecting reactant consumption for both non-uniform and uniform temperature systems were applied on gas ignition under a constant pressure condition.The criticality conditions for a slab,an infinite cylinder,and a sphere are determined and discussed using dimensionless temperatures under constant ambient and surface temperatures for a non-uniform temperature system.Exact solution for a Semenov model with convection heat loss was also presented.The solution of the Semenov problem for constant volume or density as a solid and constant pressure were compared.The critical parameterδis calculated and compared with those of Frank-Kamenetskii solution values.The validation of the calculated ignition temperatures with other exact solution and experimental results were offered.The relation between critical parameters form Semenov and F.K.models solution was introduced.

汽车空调风道性能定量评价与结构优化

针对汽车空调风道压力损失大、出口风速不均匀、常用的CFD优化仿真方法存在因网格重复划分和几何模型重修而导致的效率低下问题,提出一种速度均匀性系数的定量评价方法,并在气流分离严重的管道位置创建了网格变形参数,形成了基于Isight的Sculptor网格变形和STAR-CCM+技术的集成优化方法,实现了空调风道的自动优化。对比分析结果表明:采用出风口速度均匀性系数和自动优化技术,在各出风口出风量不变的前提下,风道压力损失降低了26%~34%,出风口速度均匀性系数提高了16%~33%,优化效率大幅提升。

板坯宽度方向非均匀冷却条件下凝固模拟

利用多物理场仿真软件COMSOL模拟板坯连铸宽度方向非均匀冷却状态下的凝固过程的数值模拟。通过将各冷却区设定的铸坯表面目标温度作为约束条件代入傅里叶传热微分方程,反向推算板坯内弧表面中线上各冷却区的换热系数。在此基础上,根据二冷区喷嘴的布置及喷嘴喷雾分布试验数据将该换热边界条件沿铸坯宽度方向进行拓展,计算出板坯从MD弯月面开始到最末扇形段出口的整个铸流区间的3D温度场。通过该方法可模拟出相同冷却条件下不同铸坯宽度在厚度中性层剖面两相区区间范围的区别,并且也可以清晰地反映出喷嘴的布置对铸坯表面温度及凝固终点的影响,从而为生产中的凝固末端压下策略和喷嘴布置的设计提供有力的数据支撑。

论我国页岩油气的统一性

页岩油气是我国重要的油气战略资源,具有赋存于页岩层系中、自生自储的特征。2012年我国涪陵页岩气获得突破,形成了海相页岩气“二元富集”理论,即深水陆棚优质泥页岩发育是页岩气“成烃控储”的基础,良好的保存条件是页岩气“成藏控产”的关键。近年来,页岩油高效勘探开发实践表明,我国陆相页岩油同样具有“二元富集”特征。通过解剖我国典型页岩油气藏特征,将页岩油气纳入同一套成烃、成储、成藏体系中,进一步深化页岩油气“二元富集”理论内涵,形成页岩油气富集统一性新认识,并对未来深化研究趋势进行展望。研究表明:①以半深水—深水陆棚相和半深湖—深湖相为主的沉积环境是页岩油气成烃控储的基础,不仅控制着页岩的有机质丰度与类型,也控制着优质储层和有利岩相组合的分布;②稳定的构造条件、有效的顶底板封盖和页岩自封闭性共同形成的以地层超压为依据的良好的保存条件是页岩油气成藏控产的关键,为页岩油气的富集与高产提供关键保障;③页岩油气形成与富集是一个统一的动态演化体系,以热演化为主线,有序形成页岩油、凝析油和页岩气;④今后研究中重点加强常非一体化的评价思路,深化常非油气资源的分配系数,从整体的角度思考油气的分配规律。相关研究成果对深化页岩油气富集理论和指导页岩油气勘探开发具有重要的科学与实践意义。

矿用宽体车互联式油气悬架系统平顺性分析

采用钢板弹簧悬架的矿用宽体车难以获得良好的行驶平顺性,为此,提出了一种刚度阻尼可调的互联式油气悬架系统。首先,阐述了互联式油气悬架系统的工作原理,建立了油气悬架系统的数学模型;其次,运用AMESim软件搭建了互联式油气悬架系统和钢板弹簧悬架的仿真模型,确定了仿真模型中的主要参数;最后,在D级随机路面激励下进行了匀速和加速-制动运行工况的车辆行驶平顺性仿真研究,并对仿真结果进行了分析。研究结果表明:与钢板弹簧悬架相比,匀速和加速-制动的空载工况下,互联式油气悬架系统的车身加速度均方根值分别下降了38.7%和38.8%,车轮动载荷均方根值分别增加了3.1%和0.5%,不影响车轮的接地性,悬架动挠度均方根值分别增加了41.6%和39.7%,悬架撞击限位块的概率小于0.1%,满足设计要求;匀速和加速-制动的满载工况下,互联式油气悬架系统的车身加速度、车轮动载荷、悬架动挠度三项平顺性评价指标均得到改善。该结果证明互联式油气悬架系统可提升车辆的行驶平顺性,为矿用宽体车油气悬架系统设计提供参考。

温湿度箱不同湿度条件下温度分布实验研究

通过对温湿度箱不同湿度条件下温度均匀性的实际测量,可以确认温湿度箱在相同的温度下,湿度不相同,可导致温度均匀性不相同。同时,可以证实湿度越低,温度均匀性越差,湿度越高,温度均匀性越好,并从热传导角度,分析了不同湿度条件对温度均匀性产生影响的原因。

Uniform Lipschitz Estimates of Homogenization of Elliptic Systems in Divergence Form with Dini Conditions

The paper is devoted to the homogenization of elliptic systems in divergence form.We obtain uniform interior as well as boundary Lipschitz estimates in a bounded C1,γdomain when the coefficients are Dini continuous,inhomogeneous terms are divergence of Dini continuous functions and the boundary functions have Dini continuous derivatives.The results extend Avellaneda and Lin’s work[Comm.Pure Appl.Math.,40:803-847(1987)],where Holder continuity is the main assumption on smoothness of the data.