精确稳定的时域积分方程方法在求解复杂线面结合问题中的应用

本文采用了时间步进算法(MOT)求解时域线面结合积分方程(TDSWIE),以解决金属平台和复杂线天线结合这种组合目标问题.为了提高该算法的精度和数值稳定性,文中采用了精确计算阻抗矩阵元素值的方式.对单级子天线放置在金属球面以及螺旋天线放置在圆台形天线基座等进行数值仿真,获得了天线与基座结合处的瞬态电流值、天线的回波损耗(S11)、天线的输入导纳以及方向图等重要参数.数值结果验证了本文方法的有效性和精确性.

同轴线馈电的球面共形微带天线的数值分析

采用基于矩量法(method of moments,MoM)的面-线积分方程法分析了同轴线馈电的球面共形微带天线的输入阻抗。面-线积分法在分析过程中具有未知量少,计算时间短的优势。天线贴片电流和探针电流分别采用Rao-Wilton-Glisson(RWG)基函数与三角基函数来模拟。在线面连接处,提出一种新型的连接基函数以保证探针与贴片的电流连续性。激励源采用磁流环模型,并且结合球表面磁并矢格林函数求解激励源在天线表面产生的场。最后,通过实例验证了连接基函数的可行性,并分析了两副球面共形微带天线的输入阻抗,证明所提分析处理的正确性。

一种在三个医学解剖面上任意切面图像提取的有效方法

针对在三个正交医学图像切面上任意斜切面的提取问题,通过空间几何知识,把抽象的切面空间位置关系进行描述,对不同的正交面上的提取切面采用相应的插值方式以获取较高质量的图片结果,从而为医生的临床提供更多和有效的图像视角。通过提取结果对采用的方法和原理进行了验证。

A new algorithm for designing developable Bézier surfaces

A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper.

3D Modeling and Born approximation inversion for the borehole surface electromagnetic method

We present a 3D approach to numerical modeling of the borehole-surface electromagnetic （BSEM） method. The 3D electromagnetic response created by a vertical line current source in a layered medium is modeled using the 3D integral equation method. The modeling results are consistent with analytical solutions. 3D Born approximation inversion of BSEM data is also conducted for reservoir delineation. The inversion method is verified by a synthetic reservoir model.

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.

Water Profile over an Ogee-Shaped Crest and the Reynolds Fractional Equations

Weir crest must have the correct shape in the concave side of an ogee-shaped crest to diminish erosion. This shape can be obtained using an approximation of the fractional Reynolds equations when the water interacts with the surface. A model is introduced for the Reynolds stresses complemented with a closure relation of fractional origin. A power type solution is obtained for the main velocity and stress. Velocity profile is found based on the assumption of a steady flow and the energy conservation equation. A Froude number and the cubic equation of the weir are built. The dimensionless upstream velocity head is also determined which allow graphically showing the exponent and coefficient of the water-profile over an ogee-shaped crest. It is possible to estimate the occupied-space index trough an exponents＇ ratio of profile over the velocity head.

Scattering of Oblique Surface Waves by the Edge of Small Deformation on a Porous Ocean Bed

The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. Using perturbation analysis, the corresponding problem governed by modified Helmholtz equation is reduced to a boundary value problem for the first-order correction of the potential function. The first-order potential and, hence, the reflection and transmission coefficients are obtained by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number along x-direction and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the free-surface, and the reflection coefficient becomes a multiple of the number of ripples. Again, for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. It is also observed that the reflected energy is somewhat sensitive to the changes in the porosity of the ocean bed. From the derived results, the solutions for problems with impermeable ocean bed can be obtained as particular cases.

Scattering of Plane P Waves by Circular-arc Canyon Topography:High-frequency Solution

Through the Fourier-Bessel series expansion of wave functions,the analytical solution to the two-dimensional scattering problem of incidental plane P waves by circular-arc canyon topography with different depth-to-width ratio is deduced.Unlike other existing analytical solutions,in order to ensure that the analytical solution is valid for higher frequency incident waves,the asymptotic properties of cylindrical functions are in this paper introduced to directly determine the unknown coefficients of scattering waves,avoiding the solution of linear equation systems and corresponding numerical issues,which in turn expand the frequency band in which the analytical solution is valid.Comparison with other existing analytical solutions demonstrates that the proposed analytical solution is correct.Furthermore,the scattering effects of a circular-arc canyon on the incident plane P wave are analyzed in a comparatively broad frequency band.

Free Surface Flow Generated by Submerged Twin-cylinders in Forward Motion Using a Fully Nonlinear Method

The free surface flow generated by twin-cylinders in forced motion submerged beneath the free surface is studied based on the boundary element method. Two relative locations, namely, horizontal and vertical, are examined for the twin cylinders. In both cases, the twin cylinders are starting from rest and ultimately moving with the same constant speed through an accelerating process. Assuming that the fluid is inviscid and incompressible and the flow to be irrotational, the integral Laplace equation can be discretized based on the boundary element method. Fully-nonlinear boundary conditions are satisfied on the unknown free surface and the moving body surface. The free surface is traced by a Lagrangian technique. Regriding and remeshing are applied, which is crucial to quality of the numerical results. Single circular cylinder and elliptical cylinder are calculated by linear method and fully nonlinear method for accuracy checking and then fully nonlinear method is conducted on the twin cylinder cases, respectively. The generated wave elevation and the resultant force are analysed to discuss the influence of the gap between the two cylinders as well as the water depth. It is found that no matter the kind of distribution, when the moving cylinders are close to each other, they suffer hydrodynamic force with large absolute value in the direction of motion. The trend of force varying with the increase of gap can be clearly seen from numerical analysis. The vertically distributed twin cylinders seem to attract with each other while the horizontally distributed twin cylinders are opposite when they are close to each other.

Aerodynamic Performances of Wind Turbine Airfoils Using a Panel Method

One of the key features of Laplace＇s Equation is the property that allows the equation governing the flow field to be converted from a 3D problem throughout the field to a 2D problem for finding the potential on the surface. The solution is then found using this property by distributing ＂singularities＂ of unknown strength over discretized portions of the surface： panels. Hence the flow field solution is found by representing the surface by a number of panels, and solving a linear set of algebraic equations to determine the unknown strengths of the singularities. In this paper a Hess-Smith Panel Method is then used to examine the aerodynamics of NACA 4412 and NACA 23015 wind turbine airfoils. The lift coefficient and the pressure distribution are predicted and compared with experimental result for low Reynolds number. Results show a good agreement with experimental data.

EXISTENCE OF MINIMIZING SOLUTIONSAROUND“EXTENDED STATES”FOR A NONLINEARLY ELASTICCLAMPED PLANE MEMBRANE

The formal asymptotic analysis of D. Fox, A. Raoult & J.C. Simo[10] has justified the twodimensional nonlinear "membrane" equations for a plate made of a Saint Venant-Kirchhoff material.This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of R3, is equivalent to finding the critical points of a functional whose nonlinear part depends on the first fundamental form of the unknown deformed surface.The author establishes here, by the inverse function theorem, the existence of an injective solution to the clamped membrane problem around particular forces corresponding physically to an "extension" of the membrane. Furthermore, it is proved that the solution found in this fashion is also the unique minimizer to the nonlinear membrane functional, which is not sequentially weakly lower semi-continuous.

Sensitivity studies of a high accuracy surface modeling method

The sensitivities of the initial value and the sampling information to the accuracy of a high accuracy surface modeling(HASM) are investigated and the implementations of this new modeling method are modified and enhanced. Based on the fundamental theorem of surface theory, HASM is developed to correct the error produced in geographical information system and ecological modeling process. However, the earlier version of HASM is theoretically incomplete and its initial value must be produced by other surface modeling methods, such as spline, which limit its promotion. In other words, we must use other interpolators to drive HASM. According to the fundamental theorem of surface theory, we modify HASM, namely HASM.MOD, by adding another important nonlinear equation to make it independent of other methods and, at the same time, have a complete and solid theory foundation. Two mathematic surfaces and monthly mean temperature of 1951–2010 are used to validate the effectiveness of the new method. Experiments show that the modified version of HASM is insensitive to the selection of initial value which is particular important for HASM. We analyze the sensitivities of sampling error and sampling ratio to the simulation accuracy of HASM.MOD. It is found that sampling information plays an important role in the simulation accuracy of HASM.MOD. Another feature of the modified version of HASM is that it is theoretically perfect as it considers the third equation of the surface theory which reflects the local warping of the surface. The modified HASM may be useful with a wide range of spatial interpolation as it would no longer rely on other interpolation methods.

An improved HASM method for dealing with large spatial data sets

Surface modeling with very large data sets is challenging. An efficient method for modeling massive data sets using the high accuracy surface modeling method(HASM) is proposed, and HASM_Big is developed to handle very large data sets. A large data set is defined here as a large spatial domain with high resolution leading to a linear equation with matrix dimensions of hundreds of thousands. An augmented system approach is employed to solve the equality-constrained least squares problem(LSE) produced in HASM_Big, and a block row action method is applied to solve the corresponding very large matrix equations.A matrix partitioning method is used to avoid information redundancy among each block and thereby accelerate the model.Experiments including numerical tests and real-world applications are used to compare the performances of HASM_Big with its previous version, HASM. Results show that the memory storage and computing speed of HASM_Big are better than those of HASM. It is found that the computational cost of HASM_Big is linearly scalable, even with massive data sets. In conclusion,HASM_Big provides a powerful tool for surface modeling, especially when there are millions or more computing grid cells.

Optimal four-impulse rendezvous between coplanar elliptical orbits

Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden＇s primer vector theory is favored by many researchers with its clear physical concept and simplicity in solu- tion. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital ren- dezvous in a near circular orbit and achieved great success. Extending Prussing＇s work, this paper will employ the primer vec- tor theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit （referred to as T-H equations）, the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large ec- centricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden＇s necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentric- ity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution.

The semi-global isometric embedding of surfaces with Gaussian curvature changing sign cleanly

A new method to solve the Gauss-Codazzi system is given in which we transform the linearized system to a partial differential equation of second order, and by the method we solve the problem of semi-global isometric embedding of surfaces with Gaussian curvature changing sign cleanly.

TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS

The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.

On the universal third order Stokes wave solution

This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and determining the Fourier coefficients by solving a set of nonlinear algebraic equations through the Taylor expansion and perturbation method. The universal solution is expressed upon the still water depth with the still water level as datum and retains a global perturbation parameter. The wave set-up term generated by the self-interaction of oscillatory waves is explicitly included in the free surface function. With the use of different definitions for the wave celerity, different water levels as the datum, different non-dimensional variables as the perturbation parameter, and different treatments for the total head, the universal solution can be reduced to the existing various Stokes solutions, thus explaining the reasons and the physical significance of different non-periodic terms in them, such as the positive or negative constant term in the free surface expression and the time-or space-proportional term in the potential function.

LIMIT BEHMIOUR OF SOLUTIONS TOEQUIVALUED SURFACE BOUNDAny VALUEPROBLEM FOR PARABOLIC EQUATIONS

Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension of the domain is two or more.

A Study on Dynamic Response of Cable-Seabed Interaction

A numerical method is developed to investigate the dynamic response of cable-seabed interaction in this paper. The motion of cable is described by the Lumped Parameter Method, while the seabed, unlike the prevailing simplified model of elastic foundation, is modeled as an irregular continuous rigid surface with rebound and friction existing, and the forces exerted by the seabed consist of normal counterforce and isotropic tangential Coulomb friction resistance. To describe the detailed dynamic response, two coefficients are introduced by analogy with the theory of rigid body collision with friction. The cable-seabed kinematic and dynamic contact conditions are formulated subsequently, and are used to incorporate the seabed effect into the cable dynamics to produce a set of ordinary differential governing equations. In this paper, we employ 4th order Runge-Kutta method to solve these equations. Several simulation cases are presented to illustrate the seabed effect. The results show that friction and impact have a prominent influence on the statics and dynamics of the cable.