两种型面曲线方程的推导

本文详细推导了等距型面曲线方程和旋轮线（摆线）型面曲线方程，并确定了旋轮线型面曲线方程参数的合理选择范围。

单螺杆压缩机工作腔表面积的计算

根据微分几何及空间啮合的基本理论,对单螺杆压缩机圆台二次包络啮合副的型面方程及工作腔面积的计算作了系统的分析。它是单螺杆压缩机工作过程热传导计算及啮合副加工的基础。

圆盘密封单螺杆泵啮合特性研究

为了研究圆盘密封单螺杆泵的啮合特性,分析了圆盘密封单螺杆泵的结构特点和工作原理,根据空间啮合理论及三维坐标变换原理建立了螺杆转子-密封圆盘啮合副的型面方程。利用上述方程得到了密封圆盘任意转角位置处的啮合特性分析模型,研究了啮合副型面参数对螺杆转子-密封圆盘啮合副啮合特性的影响机理。结果表明:密封盘存在着较为严重的局部磨损且下半侧会先予磨损;不同截面上的密封盘其啮合角范围不同,当圆心角接近π时啮合部位最为集中;中心距、密封盘半径对啮合角变化影响较大,圆盘边缘倒角半径、偏心距的影响较小。通过对圆盘密封单螺杆泵啮合特性的研究,可为以后对其啮合副型面的优化设计提供一定的理论基础。

A Class of the Singularly Perturbed Boundary Value Problems for Elliptic Equation with a Super Surface of Turning Point in n-dimensional Space

In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theorem. The uniformly valid asymptotic approxmations of solutions for the boundary value problem is constructed.

Meshing Theoretical Study and Simulation on Cylindrical Tri-sine Oscillating Tooth Gear Drive

The structure of cylindrical tri-sine oscillating tooth gear drive is presented. Based on the space meshing theory, equations of meshing and tooth profile are established and its meshing theory is studied. Using Pro/E, this system is modeled and simulated,which is compared with the above-established equations.

One Class of Hyperbolic Function Equation and Its Application

In this paper,one class of transcendental function equation is considered. Using the metheds of one-dimensional search,series expansion of function and the property of infinite series,we obtain existence,distribution of solution for this equation,we also discuss it's some application.

Quantifying the Mean Sea Level Change at the Gulf of Finland Coast Caused by the Realistic Portion of the Global Warming Forcing

Quantifying the coastal mean sea level change causing by the winter positive phase of the North Atlantic oscillation index NAO＋ at the Gulf of Finland coast is of high priority for detecting and predicting the global warming impact in this region. Both boreal winter months and season of three long-term data station series of the coastal mean sea levels and the NAO indices were linked for two cases, i.e.： different periods and the 1977-1994 period. This study is dedicated to： （1） Detecting the exclusive impacts of the NAO＋; （2） Estimating the significant standard bivariate linear regression models; （3） Calculating the climatic linear trend coefficient by using three methods （OLS, GLS, Theil-Sen）; （4） Correcting the mean sea level series anomalies by using the significant linear regression equations as a function of NAO＋ anomalies, over the period 1977-1994; （5） Calculating the realistic linear trend caused as a function of NAO＋ for period 1977-1994 in the context of the realistic portion of the global warming. The results reveal that, the NAO＋ manifests their impacts on the coastal mean sea levels and its contribution in the configured linear trends. The realistic linear changes have detected and predicted. The Gulf of Finland coast showed the wannest regions in the context of the realistic portion of the global warming during the winters of the period 1977-1994.

CFD study of turbulent jet impingement on curved surface

The heat transfer and flow characteristics of air jet impingement on a curved surface are investigated with computational fluid dynamics(CFD)approach.The first applied model is a one-equation SGS model for large eddy simulation(LES)and the second one is the SST-SAS hybrid RANS-LES.These models are utilized to study the flow physics in impinging process on a curved surface for different jet-to-surface(h/B)distances at two Reynolds numbers namely,2960 and 4740 based on the jet exit velocity(U_e)and the hydraulic diameter(2B).The predictions are compared with the experimental data in the literature and also the results from RANS k-εmodel.Comparisons show that both models can produce relatively good results.However,one-equation model(OEM)produced more accurate results especially at impingement region at lower jet-to-surface distances.In terms of heat transfer,the OEM also predicted better at different jet-to-surface spacings.It is also observed that both models show similar performance at higher h/B ratios.

Design optimization of transonic compressor stage using CFD and response surface model

In order to shorten the design period, the paper describes a new optimization strategy for computationally expensive design optimization of turbomachinery, combined with design of experiment (DOE), response surface models (RSM), genetic algorithm (GA) and a 3-D Navier-Stokes solver(Numeca Fine). Data points for response evaluations were selected by improved distributed hypercube sampling (IHS) and the 3-D Navier-Stokes analysis was carried out at these sample points. The quadratic response surface model was used to approximate the relationships between the design variables and flow parameters. To maximize the adiabatic efficiency, the genetic algorithm was applied to the response surface model to perform global optimization to achieve the optimum design of NASA Stage 35. An optimum leading edge line was found, which produced a new 3-D rotor blade combined with sweep and lean, and a new stator one with skew. It is concluded that the proposed strategy can provide a reliable method for design optimization of turbomachinery blades at reasonable computing cost.

On a Strongly Damped Wave Equation for the Flame Front

In two-dimensional free-interface problems, the front dynamics can be modeled by single parabolic equations such as the Kuramoto-Sivashinsky equation (K-S). However, away from the stability threshold, the structure of the front equation may be more involved. In this paper, a generalized K-S equation, a nonlinear wave equation with a strong damping operator, is considered. As a consequence, the associated semigroup turns out to be analytic. Asymptotic convergence to K-S is shown, while numerical results illustrate the dynamics.

Analytical estimation of mixing coefficient induced by surface wave-generated turbulence based on the equilibrium solution of the second-order turbulence closure model

Based on the equations of motion and the assumption that ocean turbulence is of isotropy or quasi-isotropy, we derived the closure equations of the second-order moments and the variation equations for characteristic quantities, which describe the mechanisms of advection transport and shear instability by the sum of wave-like and eddy-like motions and circulation. Given that ocean turbulence generated by wave breaking is dominant at the ocean surface, we presented the boundary conditions of the turbulence kinetic energy and its dissipation rate, which are determined by energy loss from wave breaking and entrainment depth respectively. According to the equilibrium solution of the variation equations and available data of the dissipation rate, we obtained an analytical estimation of the characteristic quantities of surface-wave-generated turbulence in the upper ocean and its related mixing coefficient. The derived kinetic dissipation rate was validated by field measurements qualitatively and quantitatively, and the mixing coefficient had fairly good consistency with previous results based on the Prandtl mixing length theory.

Three Dimensional Interface Problems for Elliptic Equations

The author studies the structure of solutions to the interface problems for second order linear elliptic partial differential equations in three space dimension. The set of singular points consists of some singular lines and some isolated singular points. It is proved that near a singular line or a singular point, each weak solution can be decomposed into two parts, a singular part and a regular part. The singular parts are some finite sum of particular solutions to some simpler equations, and the regular parts are bounded in some norms, which are slightly weaker than that in the Sobolev space H^2.

Symmetries and solutions to geometrical flows

In this paper,we investigate group-invariant solutions to the hyperbolic geometric flow on Riemann surfaces,which include solutions of separation variables,traveling wave solutions,self-similar solutions and radial solutions.In the proceeding of reduction,there are elliptic,hyperbolic and mixed types of equations.For the first kind of equation,some exact solutions are found;while for the last two kinds,with implicit solutions found,we furthermore investigate whether there will be a global solution or blowing up.Referring to the work of Kong et al.(2009),the results come out perfectly.

Visible characteristics of space-based targets based on bidirectional reflection distribution function

A precise modeling method of visible characteristics of the space-based target was presented based on bidirectional reflection distribution function (BRDF). The background characteristics of the space-based target were represented to build models of direct solar radiation and reflected radiation of the Earth based on blackbody radiation theory. The geometry characteristics of the target were analyzed to establish a surface equation of each surface based on its body coordinate system. The material characteristics of the target surface were described by introducing a BRDF model which considers the character of surface Gauss statistics and self-shadow and is obtained by measurement and modeling in advance. The relative positions of the space-based target, the background radiation sources and the observation platform were determined based on coordinate con- version to judge contributing surface of the target to observation system. Then a mathematical model on visible characteristics of the space target for the given optical system was built by summing reflection components of all the surfaces. Simulation of visible characteristics of the space-based target in orbit was achieved according to its given geometrical dimensions, physical parameters and orbital parameters. The results show that the method is effective for analysis on visible characteristics of the space-based target when single reflection is considered and its surface is regularly described in a surface equation, which provides a way to real-time calculation of visible characteristics of the space-based target.

HIGH ACCURACY ANALYSIS OF TENSOR-PRODUCT LINEAR PENTAHEDRAL FINITE ELEMENTS FOR VARIABLE COEFFICIENT ELLIPTIC EQUATIONS

For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In addition, the estimate for the W1,1-seminorm of the discrete derivative Green＇s function is given. Finally, the authors show that the derivatives of the finite element solution uh and the corresponding interpolant Hu are superclose in the pointwise sense of the L∞-norm.

Hypergeometric equations and weighted projective spaces

We compute the Hodge numbers of the polarised(pure) variation of Hodge structure V = grn-1WRn-1f!Z of the Landau-Ginzburg model f:Y → C mirror-dual to a weighted projective space wPn in terms of a variant of Reid's age function of the anticanonical cone over wPn.This implies,for instance,that wPn has canonical singularities if and only if hn-1,0V = 1.We state a conjectural formula for the Hodge numbers of general hypergeometric variations.We show that a general fibre of the Landau-Ginzburg model is birational to a Calabi-Yau variety if and only if a general anticanonical section of wP is Calabi-Yau.We analyse the 104 weighted 3-spaces with canonical singularities,and show that a general anticanonical section is not a K3 surface exactly in those 9 cases where a generic fibre of the Landau-Ginzburg model is an elliptic surface of Kodaira dimension 1.

The spreading fronts in a mutualistic model with delay

This paper is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic eco- logical model. The local existence and uniqueness of a classical solution are obtained and the asymptotic behavior of the free boundary problem is studied. Our results indi- cate that two free boundaries tend monotonically to finite or infinite limits at the same time, and the free boundary problem admits a global slow solution with unbounded free boundaries if the intra-specific competitions are strong, while if the intra-specific competitions are weak, there exist the blowup solution and global fast solution.

The influence of rainfall on PR radar measurement of ocean surface wind speed and its calibration

Rain can significantly degrade the wind vector retrieval from Precipitation Radar （PR） by three mechanisms, namely, two-way rain attenuation, rain volume-backscattering, and ocean surface roughening from the rain splash effect. Here we first derive the radar equation for PR in rainy conditions. Then we use the rain attenuation model for Ku band, volume backscatter model for spherical raindrops and PR-TMI （TRMM Microwave Imager, TMI） matchup datasets from June to August in 2010 to solve the radar equation, and quantitatively analyze the influence of rainfall on PR radar measurement of ocean surface wind speed. Our results show that the significant effect of rain on radar signal is dominated by two-way rain attenuation and rain splash effect, and the effect of rain volume-backscattering is relatively the weakest, which can even be neglected in rain-weak conditions. Moreover, both the two-way rain attenuation and rain splash effect increase with the increasing of integration rain rate and in- cident angle. Last, we combine volume-backscattering effect and splash effect into a simple phenomenological model for rain calibration and select three typhoon cases from June to August in 2012 to verify the accuracy of this model. Before calibration, the mean difference and mean square error （MSE） between PR-observed σ0 and wind-induced σσ are about 2.95 dB and 3.10 dB respectively. However, after calibration, the mean difference and MSE are reduced to 0.64 dB and 1.61 dB respectively. The model yields an accurate calibration for PR near-nadir normalized radar cross section （NRCS） in rainy conditions.