Improved absorbing boundary condition based on linear interpolation for ADI-FDTD method

With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.

HIGH RESOLUTION POSITIVITY-PRESERVING DIFFERENCE SCHEMES FOR TWO DIMENSIONAL EULER EQUATIONS

A class of high resolution positivity preserving Boltzmann type difference schemes for one and two dimensional Euler equations is studied. First, the relation between Boltzmann and Euler equations is analyzed. By using a kind of special interpolation, the high resolution Boltzmann type difference scheme is constructed. Finally, numerical tests show that the schemes are effective and useful.

New algorithm for solving 3D incompressible viscous equations based on projection method

A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.

A novel adjustable multiple cross-hexagonal search algorithm for fast block motion estimation

In this paper,we propose a novel adjustable multiple cross-hexagonal search(AMCHS) algorithm for fast block motion estimation. It employs adjustable multiple cross search patterns(AMCSP) in the first step and then uses half-way-skip and half-way-stop technique to determine whether to employ two hexagonal search patterns(HSPs) subsequently. The AMCSP can be used to find small motion vectors efficiently while the HSPs can be used to find large ones accurately to ensure prediction quality. Simulation results showed that our proposed AMCHS achieves faster search speed,and provides better distortion performance than other popular fast search algorithms,such as CDS and CDHS.

The Stability Research for the Finite Difference Scheme of a Nonlinear Reaction-diffusion Equation

In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.

Improving the Stability Problem of the Finite Difference Scheme for Reaction-diffusion Equation

This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.

Calculation of earth pressure based on disturbed state concept theory

The theoretical formulations of Coulomb and Rankine still remain as the fundamental approaches to the analysis of most gravity-type retaining wall,with the assumption that sufficient lateral yield will occur to mobilize fully limited conditions behind the wall.The effects of the magnitude of wall movements and different wall-movement modes are not taken into consideration.The disturbance of backfill is considered to be related to the wall movement under translation mode.On the basis of disturbed state concept(DSC),a general disturbance function was proposed which ranged from-1 to 1.The disturbance variables could be determined from the measured wall movements.A novel approach that related to disturbed degree and the mobilized internal frictional angle of the backfill was also derived.A calculation method benefited from Rankine's theory and the proposed approach was established to predict the magnitude and distribution of earth pressure from the cohesionless backfill under translation mode.The predicted results,including the magnitude and distribution of earth pressure,show good agreement with those of the model test and the finite element method.In addition,the disturbance parameter b was also discussed.

Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid

Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically.

Meshfree First-order System Least Squares

We prove convergence for a meshfree first-order system least squares(FOSLS) partition of unity finite element method(PUFEM).Essentially,by virtue of the partition of unity,local approximation gives rise to global approximation in H(div)∩H(curl). The FOSLS formulation yields local a posteriori error estimates to guide the judicious allotment of new degrees of freedom to enrich the initial point set in a meshfree dis- cretization.Preliminary numerical results are provided and remaining challenges are discussed.

Deriving Vibration Modes of Semi-infinite Chain Model by “Invariant Eigen-operator”Method

For the first time, we introduce a fully quantum mechanical Hamiltonian for a semi-infinite chain model of atoms. We then derive the vibration modes of this model by virtue of the ＂invariant eigen-operator＂ method in two different cases, which is concise and revealing.

Analyzing Parabolic Profile Path for Underwater Towed-Cable

This article discusses the dynamic state analysis of underwater towed-cable when tow-ship changes its speed in a direction making parabolic profile path. A three-dimensional model of underwater towed system is studied. The established governing equations for the system have been solved using the central implicit finite-difference method. The obtained difference non-linear coupled equations are solved by Newton＇s method and satisfactory results were achieved. The solution of this problem has practical importance in the estimation of dynamic loading and motion, and hence it is directly applicable to the enhancement of safety and the effectiveness of the offshore activities.

Mathematical Model for Takeoff Simulation of a Wing in Proximity to the Ground

Aircraft flying close to the ground benefit from enhanced efficiency owing to decreased induced drag and increased lift. In this study, a mathematical model is developed to simulate the takeoff of a wing near the ground using an Iterative Boundary Element Method （IBEM） and the finite difference scheme. Two stand-alone sub-codes and a mother code, which enables communication between the sub-codes, are developed to solve for the self-excitation of the Wing-In-Ground （WIG） effect. The aerodynamic force exerted on the wing is calculated by the first sub-code using the IBEM, and the vertical displacement of the wing is calculated by the second sub-code using the finite difference scheme. The mother code commands the two sub-codes and can solve for the aerodynamics of the wing and operating height within seconds. The developed code system is used to solve for the force, velocity, and displacement of an NACA6409 wing at a 4° Angle of Attack （AoA） which has various numerical and experimental studies in the literature. The effects of thickness and AoA are then investigated and conclusions were drawn with respect to generated results. The proposed model provides a practical method for understanding the flight dynamics and it is specifically beneficial at the pre-design stages of a WIG effect craft.

COMPUTATION OF TURBULENCE FLOW ON HYBRID GRIDS USING k-ω TURBULENCE MODEL AND OSHER SCHEME

An unstructured Reynolds-averaged Navier-Stokes flow solver using the finite volume method is studied. The spatial discretisation is based on the Osher approximate Riemann solvers. A two-equation turbulence model (k-ω model) is also developed for hybrid grids to compute the turbulence flow. The turbulence flow past NACA0012 airfoil and the double ellipsolids are computed, and the numerical results show that the above methods are very efficient.

Threshold Ring Signature Scheme Based on TPM

The conventional ring signature schemes cannot address the scenario where the rank of members of the ring needs to be distinguished, for example, in electronically commerce application. To solve this problem, we presented a Trusted Platform Module （TPM）-based threshold ring signature schen. Employing a reliable secret Share Distribution Center （SDC）, the proposed approach can authenticate the TPM-based identity rank of members of the ring but not track a specific member＇s identity. A subset including t members with the same identity rank is built. With the signing cooperation of t members of the subset, the ring signature based on Chinese remainder theorem is generated. We proved the anonymity and unforgeability of the proposed scheme and compared it with the threshold ring signature based on Lagrange interpolation polynomial. Our scheme is relatively simpler to calculate.

Three-Step Difference Scheme for Solving Nonlinear Time-Evolution Partial Differential Equations

In this paper, a special three-step difference scheme is applied to the solution of nonlinear time-evolution equations, whose coefficients are determined according to accuracy constraints, necessary conditions of square conservation, and historical observation information under the linear supposition. As in the linear case, the schemes also have obvious superiority in overall performance in the nonlinear case compared with traditional finite difference schemes, e.g., the leapfrog(LF) scheme and the complete square conservation difference(CSCD) scheme that do not use historical observations in determining their coefficients, and the retrospective time integration(RTI) scheme that does not consider compatibility and square conservation. Ideal numerical experiments using the one-dimensional nonlinear advection equation with an exact solution show that this three-step scheme minimizes its root mean square error(RMSE) during the first 2500 integration steps when no shock waves occur in the exact solution, while the RTI scheme outperforms the LF scheme and CSCD scheme only in the first 1000 steps and then becomes the worst in terms of RMSE up to the 2500th step. It is concluded that reasonable consideration of accuracy, square conservation, and historical observations is also critical for good performance of a finite difference scheme for solving nonlinear equations.

Numerical Computation of Hard Excitation in an Autocatalytic Biochemical System

An autocatalytic biochemical system in the presence of recycling enzyme is solved numerically using two numerical methods based on finite difference schemes. The first method is the well known Euler method which is an explicit method, whereas the second method is implicit. Although the implicit method, method 2, is first-order accurate in time it converges to the fixed point（s） for large time step, L Numerical results show the existence of hard excitation and birhythmicity.

Asymptotic Solution for Coupled Heat and Mass Transfer During the Solidification of High Water Content Materials

This paper focuses on obtaining an asymptotic solution for coupled heat and mass transfer problem during the solidification of high water content materials. It is found that a complicated function involved in governing equations can be approached by Taylor polynomials unlimitedly, which leads to the simplification of governing equations. The unknown functions involved in governing equations can then be approximated by Chebyshev polynomials. The coefficients of Chebyshev polynomials are determined and an asymptotic solution is obtained. With the asymptotic solution, the dehydration and freezing fronts of materials are evaluated easily, and are consistent with numerical results obtained by using an explicit finite difference method.

A Modified Polynomial Preserving Recovery and Its Applications to A Posteriori Error Estimates

A modified polynomial preserving gradient recovery technique is proposed. Unlike the polynomial preserving gradient recovery technique,the gradient recovered with the modified polynomial preserving recovery(MPPR) is constructed element-wise, and it is discontinuous across the interior edges.One advantage of the MPPR technique is that the implementation is easier when adaptive meshes are involved.Superconvergence results of the gradient recovered with MPPR are proved for finite element methods for elliptic boundary problems and eigenvalue problems under adaptive meshes. The MPPR is applied to adaptive finite element methods to construct asymptotic exact a posteriori error estimates.Numerical tests are provided to examine the theoretical results and the effectiveness of the adaptive finite element algorithms.

法律修辞学的旨趣和意义

法律修辞学(legal rhetoric)是20世纪六七十年代以来在欧美法学界逐渐兴起并取得一定影响的法学理论,其产生的背景是20世纪修辞学的复兴以及"充分的论证"成为法律判断正当性的重要依据。法律修辞学,顾名思义是法律与修辞学的结合,但是法律与修辞学的关联实际上有一个比较长远的发展背景。研究法律修辞学对我们进一步探究价值判断在法律判断形成过程中的重要作用以及如何通过法律论辩和主体之间相互说服的方式限制法律判断的恣意都具有重要意义。在考察法律修辞学的概念及意义之前我们必须首先厘清修辞学的发展和演变过程,因为在修辞学发展的坎坷过程中法律与修辞学的关联也经历着考验。

Arch-dam crack deformation monitoring hybrid model based on XFEM

An extended finite element method incorporated with the cohesive crack model(CCM-based XFEM) is developed in consideration of crack tip enrichment.It could improve the accuracy and is introduced into dam safety monitoring for the first time.Firstly,the proposed method is verified for a benchmark concrete beam by comparing the results with those of numerical investigations obtained by other researchers.Furthermore,it is adopted as an alternative method for building the deformation hybrid models of non-stable cracks in an arc dam,for the reason that classical FEMs are cumbersome in modeling the cohesive crack growth due to the need of remeshing the moving discontinuities.Case study proves that the fitted results of the mentioned deformation hybrid model,better than the classical statistical model,are well consistent with the measured data and reliable to forecast the development tendency of crack deformation.Therefore,the present CCM-based XFEM could provide a practical way to simulate and monitor the cracking process in concrete arch dam.