A corrected particle method with high-order Taylor expansion for solving the viscoelastic fluid flow

In this paper, a corrected particle method based on the smoothed particle hydrodynamics (SPH) method with high-order Taylor expansion (CSPH-HT) for solving the viscoelastic flow is proposed and investigated. The validity and merits of the CSPH-HT method are first tested by solving the nonlinear high order Kuramoto-Sivishinsky equation and simulating the drop stretching, respectively. Then the flow behaviors behind two stationary tangential cylinders of polymer melt, which have been received little attention, are investigated by the CSPH-HT method. Finally, the CSPH-HT method is extended to the simulation of the filling process of the viscoelastic fluid. The numerical results show that the CSPH-HT method possesses higher accuracy and stability than other corrected SPH methods and is more reliable than other corrected SPH methods.

Q estimation using multifrequency point average method based on the Taylor series expansion with a different order

The quality factor Q is an important parameter because it can refl ect the reservoir attenuated features and can be used for inverse-Q filtering to compensate for the seismic wave energy.The accuracy of the Q estimation is greatly significant for improving the precision of the reservoir prediction and the resolution of seismic data.In this paper,the Q estimation formulas of the single-frequency point are derived on the basis of a diff erent-order Taylor series expansion of the amplitude attenuated factor.Moreover,the multifrequency point average(MFPA)method is introduced to obtain a stable Q estimation.The model tests demonstrate that the MFPA method is less aff ected by the frequency band,travel time diff erence,time window width,and noise interference than the logical spectrum ratio(LSR)method and the energy ratio(ER)method and has a higher Q estimation accuracy.In addition,the proposed method can be applied to post-stack seismic data and obtain eff ective Q values of complex models.When the MFPA method was applied to real marine seismic data,the Q values estimated by the MFPA method with the 1st–4th order showed good consistency with each other.In contrast,the Q values obtained by the ER method were larger than those of the proposed method,while those estimated by the LSR method signifi cantly deviated from the average values.In conclusion,the MFPA method has superior stability and practicability for the Q estimation.

TAYLOR EXPANSION METHOD FOR NONLINEAR EVOLUTION EQUATIONS

A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0_th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1_st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example, namely, the two_dimensional Navier_Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.

THE TAYLOR EXPANSION OF A FUNCTION OF FUNCTIONS

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Numerical Solution of Differential Equations by Direct Taylor Expansion

A variation of the direct Taylor expansion algorithm is suggested and applied to several linear and nonlinear differential equations of interest in physics and engineering, and the results are compared with those obtained from other algorithms. It is shown that the suggested algorithm competes strongly with other existing algorithms, both in accuracy and ease of application, while demanding a shorter computation time.

参数曲线光滑处理的双向四阶Taylor拟合方法

为了使数控轨迹更加光滑,以进一步提高加工效率,提出一种基于空间轴的光滑曲线双向四阶Taylor拟合方法,通过优化使曲率更平缓来进一步降低拟合曲线的轮廓误差。首先,在参数曲线上选取有限均匀的数据点计算参数各阶导数以及曲率、挠率等微分几何量,以建立Frenet坐标系;然后,在第i区间始末两个数据点分别进行前向和后向四阶Taylor展开,根据刀位点在始末两个数据点形成的参数空间的相对距离确定耦合权重的拟合曲线;最后,通过坐标反变换得到机床坐标系XYZ下的优化轨迹。通过对原始轨迹和双向四阶Taylor拟合进行比较表明,随着阶数的提高,轮廓误差逐渐降低,曲率均值、曲率极差和曲率的导数极差均趋近原始曲线。通过对标准圆和高速列车车轮踏面LM-32进行拟合测试表明,相比拟合曲线,所提方法得到的优化曲线曲率变化连续,轮廓误差小4μm~5μm。

车辆主动悬架自适应变论域T-S模糊控制研究

针对传统变论域模糊控制存在过度依赖专家经验、伸缩因子参数不能自适应调整的问题,提出一种车辆主动悬架自适应变论域T-S模糊控制策略,从而提高车辆的行驶平顺性。结合神经网络和T-S模糊推理建立基于自适应神经模糊推理的一阶T-S模糊控制器,利用神经网络的自学习特性产生完善的模糊规则,进而在传统函数型伸缩因子的基础上,将系统误差和误差变化率作为动态参数引入伸缩因子中,实现伸缩因子参数的自适应调整,解决了传统函数型伸缩因子因参数确定难度大导致控制效果差的问题。通过随机工况下的仿真分析和基于相似理论的缩尺实验,对所提出算法的有效性和工况自适应性进行了验证。结果表明,所提出的自适应变论域T-S模糊控制策略具有较强的工况适应性,在不同车速、路面激励下均可有效提高车辆的平顺性并保证轮胎接地安全性。

Thermal Expansion Coefficients of Thin Crystal Films

The formulas for atomic displacements and Hamiltonian of a thin crystal film in phonon occupation number representation are obtained with the aid of Green's function theory. On the basis of these results, the formulas for thermal expansion coefficients of the thin crystal film are derived with the perturbation theory, and the numerical calculations are carried out. The results show that the thinner films have larger thermal expansion coefficients.

ON AN EXTENSION OF ABEL-GONTSCHAROFF'S EXPANSION FORMULA

We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.

Unifying the theory of integration within normal-,Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.

Thermal Expansion Behavior of Precursor-Derived Amorphous Si-C-N and Si-B-C-N Ceramics

Thermal expansion behaviors of some precursor-derived amorphous Si-C-N and Si-B-C-N ceramics, which were shaped by plastic forming after crosslink, were studied. To complete the shrinkage and densification, after thermolysis specimens were heat treated at a temperature of 1400℃ for 10 h in nitrogen atmosphere. The thermal expansion coefficient of VT50-derived amorphous Si-C-N ceramic increases from 1.98×10-6/K at 400℃ to 3.09×10-6/K at 1000℃, of NCP200-derived amorphous Si-C-N ceramic increases from 2.35×10-6/K at 400℃ to 3.45×10-6/K at 1000℃, and of T2-l-derived amorphous Si-B-C-N ceramic increases from 2.08×10-6/K at 400℃ to 3.18×10-6/K at 1000℃. No glass transition for these amorphous ceramic materials was detected, indicating that as-thermolyzed precursor-derived Si-(B-)C-N ceramic materials are amorphous solids, but not glasses.

Exact solutions for the coupled Klein-Gordon-Schrǒdinger equations using the extended F-expansion method

The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.

ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson’s extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson’s extrapolation.

电源网络低频段S参数拓展方法

电源网络S参数与芯片电源模型(Chip Power Module,CPM)级联可实现电源时域噪声仿真,完成电源完整性设计签核。当下部分仿真工具在AC阻抗优化过程中导出的S参数存在低频段无法覆盖的问题,影响时域纹波仿真精度,如果重新对S参数进行提取,又会增加仿真时间降低仿真效率。针对AC阻抗优化过程中导出的S参数无法覆盖低频段的问题,提出了一种电源网络S参数低频段拓展方法,结合电压调节模块(Voltage Regulator Module,VRM)的R-L模型,推导出低频段的S参数可以借用抽取的S参数中最低频点处的S参数实现低频段S参数的拓展。仿真和实验结果表明,通过对低频段S参数进行拓展,电源时域纹波噪声仿真的精度提升31%。同时,低频段的S参数直接借用已抽取的S参数中低频点的数值无须重复提取,在8 GB内存的配置下,仿真时间节约14%左右,提高了仿真效率。

Proof of Hubble’s Law and the Truth about the Expansion of the Universe as Well as Dark Matter and Dark Energy

In 1929,American astronomer Hubble first discovered that the recessional velocity of a galaxy increases with its distance from the earth,and therefore put forward Hubble’s law.It is considered the first observational basis for the expansion of the universe and today serves as one of the pieces of evidence most often cited in support of the Big Bang model.Since then the astrophysics community has believed that the universe is in a constant rate of expansion until Saul Permutter,Brian Paul Schmit and Adam Guy Riees discovered the accelerating expansion of the universe through observation of several dozen distant supernovas in 1998,who then won the Nobel Prize in Physics 2011.But human still cannot completely explain the phenomenon that the universe is expanding at an ever-accelerating rate.Thus the author of this paper studied the origin and evolution of galaxies again,and revealed the structure of galaxy and proved Hubble’s law,then revealed the truth about the expansion of the universe as well as dark matter and dark energy.

ZTE Corporation Selected for Telkom Indonesia's CDMA Network Expansion

August 30,2007,Shenzhen,China-ZTE Corporation ("ZTE"),a leading global provider of telecommunications equipment and network solutions,announced that it has recently signed an agreement with Telkom Indonesia ("Telkom"),the largest InfoCom company and full-service network provider in Indonesia,to help expand the CDMA2000 network capacity for national coverage. Under the contract,the network expansion will cover the four main cities of the eastern part of Sulawesi,Indonesia.

含[1+1/x]^(x)极限式的Taylor展开求解方法

泰勒展开式可以有效地用来求解一些极限问题.本文用一些例子展现这一过程.

Pinched Material Einstein Space-Time Produces Accelerated Cosmic Expansion

An instructive analogy between the deformation of a pinched elastic cylindrical shell and the anti-gravity behind accelerated cosmic expansion is established. Subsequently the entire model is interpreted in terms of a hyperbolic fractal Rindler space-time leading to the same robust results regarding real energy and dark energy being 4.5% and 95.5% respectively in full agreement with all recent cosmological measurements.