一类具有接种疫苗和再次感染的传染病模型分析

建立和研究了具有接种疫苗和再次感染的SEIRV传染病模型.给出了基本再生数的表达式,得到了模型存在后向分支的条件.     

具有垂直传染且总人口在变化的SIRS传染病模型的渐近分析

讨论了具有垂直传染且总人口在变化的连续预防接种SIRS传染病模型,给出了基本再生数R_0的表达式,并利用广义Bendixson-Dulac函数方法证明了无病平衡点和地方病平衡点的全局稳定性.     

部分线性回归模型变窗宽一步局部M-估计

讨论了部分线性回归模型的变窗宽一步局部M-估计.用一步局部M-估计给出未知函数的估计,用平均方法给出参数估计.进一步通过两个引理证明一步M-估计的渐近正态性.所提出的方法继承了局部多项式的优点并且克服了最小二乘法缺乏稳健性的缺点.     

带随机初值的随机偏微分方程整体解的存在性

研究了一类带随机初值并且由分数次Brownian运动驱动的随机偏微分方程.借助于Kolmogorov准则,建立了整体Lipschitz条件下此类随机偏微分方程的一个解.同时证明了局部Lipschitz条件下整体解的存在性.     

Support vector machines in water quality management

Support vector classification (SVC) and regression (SVR) models were constructed and applied to the surface water quality data to optimize the monitoring program. The data set comprised of 1500 water samples representing 10 different sites monitored for 15 years. The objectives of the study were to classify the sampling sites (spatial) and months (temporal) to group the similar ones in terms of water quality with a view to reduce their number; and to develop a suitable SVR model for predicting the biochemical oxygen demand (BOD) of water using a set of variables. The spatial and temporal SVC models rendered grouping of 10 monitoring sites and 12 sampling months into the clusters of 3 each with misclassification rates of 12.39% and 17.61% in training, 17.70% and 26.38% in validation, and 14.86% and 31.41% in test sets, respectively. The SVR model predicted water BOD values in training, validation, and test sets with reasonably high correlation (0.952, 0.909, and 0.907) with the measured values, and low root mean squared errors of 1.53, 1.44, and 1.32, respectively. The values of the performance criteria parameters suggested for the adequacy of the constructed models and their good predictive capabilities. The SVC model achieved a data reduction of 92.5% for redesigning the future monitoring program and the SVR model provided a tool for the prediction of the water BOD using set of a few measurable variables. The performance of the nonlinear models (SVM, KDA, KPLS) was comparable and these performed relatively better than the corresponding linear methods (DA, PLS) of classification and regression modeling.     

Fast and efficient size-based separations of polymers using ultra-high-pressure liquid chromatography

Ultra-high-pressure liquid chromatography (UHPLC) has great potential for the separations of both small molecules and polymers. However, the implementation of UHPLC for the analysis of macromolecules invokes several problems. First, to provide information on the molecular-weight distribution of a polymer, size-exclusion (SEC) columns with specific pore sizes are needed. Development of packing materials with large pore diameters and pore volumes which are mechanically stable at ultra-high-pressures is a technological challenge. Additionally, narrow-bore columns are typically used in UHPLC to minimize the problem of heat dissipation. Such columns pose stringent requirements on the extra-column dispersion, especially for large (slowly diffusing) molecules. Finally, UHPLC conditions generate high shear rates, which may affect polymer chains. The possibilities and limitations of UHPLC for size-based separations of polymers are addressed in the present study. We demonstrate the feasibility of conducting efficient and very fast size-based separations of polymers using conventional and wide-bore (4.6 mm I.D.) UHPLC columns. The wider columns allow minimization of the extra-column contribution to the observed peak widths down to an insignificant level. Reliable SEC separations of polymers with molecular weights up to ca. 50 kDa are achieved within less than 1 min at pressures of about 66 MPa. Due to the small particles used in UHPLC it is possible to separate high-molecular-weight polymers (50 kDa ≤ M(r) ≤ 1-3 MDa, upper limit depends on the flow rate) in the hydrodynamic-chromatography (HDC) mode. Very fast and efficient HDC separations are presented. For very large polymer molecules (typically larger than several MDa, depending on the flow rate) two chromatographic peaks are observed. This is attributed to the onset of molecular deformation at high shear rates and the simultaneous actions of hydrodynamic and slalom chromatography.     

平面P波在充满流体的任意形状孔洞上的散射

采用复变函数的保角映射方法和波函数展开法,根据孔洞与内部流体在界面上的应力和位移连续的边界条件,得到了充满流体的任意形状的孔洞对入射平面P波的散射问题的理论解,以椭圆形孔洞为例,着重分析了椭圆的长短轴之比、流体的存在与否以及入射频率对散射幅值的影响,结果表明:(1)圆形孔洞的分波波谱的峰值分布均匀,而椭圆形孔洞则不均匀;(2)散射P波的波谱主要集中于前进方向和背向一侧,而散射S波的波谱主要集中于与传播方向垂直的一侧;(3)入射波与孔洞的作用面积越大,散射P波的波谱也越大,而散射S波的波谱也越小;(4)当孔洞为圆形时,流体对散射P波和S波的波谱影响最小,即此时流体与孔壁的动力相互作用最小.     

Numerical simulation of viscous oscillatory flow past four cylinders in square arrangement

The results of a numerical study of the viscous oscillating flow past four circular cylinders, for a constant frequency parameter equal to 50 and KC ranging between 0.2 and 10, are presented. The cylinders were placed on the vertices of a square, two sides of which were perpendicular and two parallel to the oncoming flow, for pitch ratios, P/D, ranging between 2 and 5. The finite-element method was employed for the solution of the Navier-Stokes equations, in the formulation where the stream function and the vorticity are the field variables, whereas the pressure distribution throughout the computational domain was obtained from the solution of Poisson’s equation. When the Keulegan-Carpenter number is lower than 4, the flow remains symmetrical with respect to the horizontal axis of symmetry of the solution domain and periodic at consecutive cycles. As KC increases to 4, the flow becomes aperiodic in different cycles, although symmetry with respect to the horizontal central line of the domain is preserved. For KC equal to 5, asymmetries appear intermittently in the flow, which are eventually amplified as KC increases still further. These asymmetries, in association with the aperiodicity of flow in different cycles, lead to an almost chaotic configuration as KC grows larger. For characteristic cases the flow pattern and the time histories of the in-line and transverse forces exerted on the cylinders are presented. The mean transverse forces acting on the cylinders, the r.m.s. values of the in-line and transverse forces, together with the drag and inertia coefficients of the in-line force, were evaluated for each pitch ratio in the range of Keulegan-Carpenter numbers examined and are presented in diagrams.     

Flow field characteristics study of a flapping airfoil using computational fluid dynamics

The flow field of a flapping airfoil in Low Reynolds Number (LRN) flow regime is associated with complex nonlinear vortex shedding and viscous phenomena. The respective fluid dynamics of such a flow is investigated here through Computational Fluid Dynamics (CFD) based on the Finite Volume Method (FVM). The governing equations are the unsteady, incompressible two-dimensional Navier-Stokes (N-S) equations. The airfoil is a thin ellipsoidal geometry performing a modified figure-of-eight-like flapping pattern. The flow field and vortical patterns around the airfoil are examined in detail, and the effects of several unsteady flow and system parameters on the flow characteristics are explored. The investigated parameters are the amplitude of pitching oscillations, phase angle between pitching and plunging motions, mean angle of attack, Reynolds number (Re), Strouhal number (St) based on the translational amplitudes of oscillations, and the pitching axis location (x/c). It is shown that these parameters change the instantaneous force coefficients quantitatively and qualitatively. It is also observed that the strength, interaction, and convection of the vortical structures surrounding the airfoil are significantly affected by the variations of these parameters.     

Observations of acoustically generated cavitation bubbles within typical fluids applied to a scroll expander lubrication system

An experimental study to evaluate the dynamic performance of three different types of cavitation bubbles is conducted. An ultrasonic transducer submerged into the working fluids of a scroll expander is utilised to produce cavitation bubbles and a high speed camera device is used to capture their behaviour. Three critical regions around the ultrasonic source, between the source and the solid boundary, and across the solid boundary were observed. Experimental results revealed that refrigerant bubbles sustain a continuous oscillatory movement, referenced as “wobbling effect”, without regularly collapsing. Analytical results indicate the influence of several factors such as surface tension/viscosity ratio, Reynolds number and Weber number which interpret that particular behaviour of the refrigerant bubbles. Within the refrigerant environment the bubbles obtain large Reynolds numbers and low Weber numbers. In contrast, within the lubricant and the water environment Weber number is significantly higher and Reynolds number substantially lower. The bubble radius and velocity alterations are accurately calculated during the cavitation process. Lubricant bubbles achieve the highest jet velocity while refrigerant bubbles having the lowest jet velocity are not considered as a destructive mean of cavitation for scroll expander systems.