Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation

In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.

A study on the numerical prediction method for the vertical thermal structure in the Bohai Sea and the Huanghai Sea-I.One-dimensional numerical prediction model

In this paper, on the basis of the heat conduction equation without consideration of the advection and turbulence effects, one-dimensional model for describing surface sea temperature ( T1), bottom sea temperature ( Tt ) and the thickness of the upper homogeneous layer ( h ) is developed in terms of the dimensionless temperature θT and depth η and self-simulation function θT - f(η) of vertical temperature profile by means of historical temperature data.The results of trial prediction with our one-dimensional model on T, Th, h , the thickness and gradient of thermocline are satisfactory to some extent.

An efficient locally one-dimensional finite-difference time-domain method based on the conformal scheme

An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D transverse-electric（TE） case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit（ADI） CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field（TF/SF） boundary and the perfectly matched layer（PML）, the radar cross section（RCS） of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.

Algebraic Calculation Method of One-Dimensional Steady Compressible Gas Flow

This paper describes a new method of calculation of one-dimensional steady compressible gas flows in channels with possible heat and mass exchange through perforated sidewalls. The channel is divided into small elements of a finite size for which mass, energy and momentum conservation laws are written in the integral form, assuming linear distribution of the parameters along the length. As a result, the calculation is reduced to finding the roots of a quadratic algebraic equation, thus providing an alternative to numerical methods based on differential equations. The advantage of this method is its high tolerance to coarse discretization of the calculation area as well as its good applicability for transonic flow calculations.

Alternating Group Explicit Iterative Methods for One-Dimensional Advection-Diffusion Equation

The finite difference method such as alternating group iterative methods is useful in numerical method for evolutionary equations and this is the standard approach taken in this paper. Alternating group explicit (AGE) iterative methods for one-dimensional convection diffusion equations problems are given. The stability and convergence are analyzed by the linear method. Numerical results of the model problem are taken. Known test problems have been studied to demonstrate the accuracy of the method. Numerical results show that the behavior of the method with emphasis on treatment of boundary conditions is valuable.

Controlling the Bandgaps of One-Dimensional TiO2/SiO2, TiO2/SnO2, and SiO2/SnO2 Photonic Crystals Using the Transfer Matrix Method

One-dimensional photonic crystals (1D PhCs) have a unique ability to control the propagation of light waves, however certain classes of 1D oxides remain relatively unexplored for use as PhCs. Specifically, there has not been a comparative study of the three different 1D PhC structures to compare the influence of layer thickness, number, and refractive index on the ability of the PhCs to control light transmission. Herein, we use the transfer matrix method (TMM) to theoretically examine the transmission of 1D PhCs composed of layers of TiO2/SiO2, TiO2/SnO2, SiO2/SnO2, and combinations of the three with various top and bottom layer thicknesses to cover a substantial region of the electromagnetic spectrum (UV to NIR). With increasing layer numbers for TiO2/SiO2 and SiO2/SnO2, the edges became sharper and wider and the photonic bandgap width increased. Moreover, we demonstrated that PhCs with significantly thick TiO2/SiO2 layers had a high transmittance for a wide bandgap, allowing for wide-band optical filter applications. These different PhC architectures could enable a variety of applications, depending on the properties needed.

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.

One-dimensional nonlinear consolidation analysis of soil with continuous drainage boundary

Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution is derived by using finite difference method and its correctness is assessed by comparing with existing analytical and numerical solutions.Based on the present solution,the effects of interface parameters,stress ratios(i.e.,final effective stress over initial effective stress,N_(σ))and the ratio c_(c)/c_(k)of compression index to permeability index on the consolidation behavior of soil are studied in detail.The results show that,the characteristics of one-dimensional nonlinear consolidation of soil are not only related to c_(c)/c_(k)and N_(σ),but also related to boundary conditions.In the engineering practice,the soil drainage rate of consolidation process can be designed by adjusting the values of interface parameters.

Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy pro jection technique

This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method （FEM） by recursive application of the one-dimensional （1D） element energy projection （EEP） technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully discretized standard finite element （FE） model is reached. This conceptual dimension-by- dimension （D-by-D） discretization procedure is entirely equivalent to a full FE discretization. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional （2D） and three-dimensional （3D） problems can be obtained over the domain. Numerical examples of 3D Poisson＇s equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy.

Effective elastic properties of one-dimensional hexagonal quasicrystal composites

The explicit expression of Eshelby tensors for one-dimensional(1D) hexagonal quasicrystal composites is presented by using Green’s function method. The closed forms of Eshelby tensors in the special cases of spheroid, elliptic cylinder, ribbon-like,penny-shaped, and rod-shaped inclusions embedded in 1 D hexagonal quasicrystal matrices are given. As an application of Eshelby tensors, the analytical expressions for the effective properties of the 1 D hexagonal quasicrystal composites are derived based on the Mori-Tanaka method. The effects of the volume fraction of the inclusion on the elastic properties of the composite materials are discussed.

ONE-DIMENSIONAL CONSOLIDATION OF LAYERED SOILS WITH IMPEDED BOUNDARIES UNDER TIME-DEPENDENT LOADINGS

On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method of Laplace transform, the solution was presented. Influences of different kinds of cyclic loadings and impeded boundaries conditions were discussed. Through numerical inversion of Laplace transform, useful illustrations were given considering several common time-dependent loadings. Pervious or impervious boundary condition is just the special case of the problem considered here. Compared with average index method,the results from the method illustrated are more accurate.

Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating

In this paper, the three-dimensional(3D) interfacial fracture is analyzed in a one-dimensional(1D) hexagonal quasicrystal(QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape is studied by a displacement discontinuity method. Fundamental solutions of interfacial concentrated displacement discontinuities are obtained by the Hankel transform technique, and the corresponding boundary integral-differential equations are constructed with the superposition principle.Green’s functions of constant interfacial displacement discontinuities within a rectangular element are derived, and a boundary element method is proposed for numerical simulation.The singularity of stresses near the crack front is investigated, and the stress intensity factors(SIFs) as well as energy release rates(ERRs) are determined. Finally, relevant influencing factors on the fracture behavior are discussed.

A Numerical Study of One-Dimensional Hyperbolic Telegraph Equation

In this paper, an approximate solution for the one-dimensional hyperbolic telegraph equation by using the q-homotopy analysis method （q-HAM） is proposed.The results shows that the convergence of the q- homotopy analysis method is more accurate than the convergence of the homotopy analysis method （HAM）.

改良Brent法全耳再造术治疗先天性小耳畸形的临床分析

目的 探讨改良Brent法全耳再造术治疗先天性小耳畸形的临床效果及经验。方法 选取2018年11月—2021年4月湖南省儿童医院耳鼻咽喉头颈外科收治的用改良Brent法全耳再造术治疗先天性小耳畸形的患儿20例,患儿均为单侧耳畸形,年龄6.5~15岁,平均年龄8.7岁。一期手术首先处理残耳,分离耳后乳突区形成囊腔,同时行耳垂转位。取患耳对侧的肋软骨雕刻成耳廓支架,在传统雕刻的基础上,同时雕刻出耳屏,将耳屏处的基底垫高,尽可能的加深耳舟、三角窝,耳屏、耳屏间切迹的深度,在修剪耳轮时,将耳轮脚的前端尽可能垫高,尖端留置的更长,以凸显耳轮脚的深度。将耳廓支架埋置于耳后囊腔内;二期手术行“立耳”,颅耳角成形;三期手术行耳甲腔成形。结果 20例再造耳一期手术出现血肿1例,二期手术出现感染1例,支架外露1例,通过局部处理均恢复,并继续进行下一期手术。所有患儿三期手术术后随访3~9个月,再造耳双耳对称性佳,耳轮脚、耳屏处形态佳,颅耳沟加深,耳垂与耳廓下部接合处的线条流畅,再造耳总体外观满意。结论 改良Brent法全耳再造术,可更凸显耳屏、耳轮脚、三角窝及耳垂等部位的细微结构,更能呈现出再造耳的立体感,该方法可为先天性小耳畸形手术方式的选择提供参考。

改良Brent法外耳再造的临床应用研究

目的总结改良Brent法外耳再造的临床应用效果。方法2009年6月至2012年7月，共20例小耳畸形患者就诊于海军总医院医学整形科，均为单侧小耳畸形，其中右侧13例，左侧7例。采用Brent法行外耳再造并加以改良，观察手术效果。结果20例患者经过手术治疗均获得了比较满意的再造耳。两侧耳廓形态相似，耳轮、对耳轮、耳舟、耳甲腔等结构清晰。结论改良Brent法外耳再造效果逼真。

基于Brent算法的轴偏置虎克铰型Hexapod平台位置反解

针对Newton-Raphson算法求解轴偏置虎克铰型并联六自由度Hexapod平台位置反解时高精度计算会降低平台响应速度的问题,提出了一种新的基于Brent算法的位置反解求解方法。首先,根据平台几何特性和轴偏置虎克铰结构运动特性,建立了基于空间圆辅助模型的运动学模型;接着,提出了基于空间圆距离求解方法的位置反解算法,并针对丝杠螺母副产生的衍生运动,提出了补偿方案;然后,介绍了Brent求根算法,并将Brent算法应用于位置反解算法;最后,通过实验验证了衍生运动误差补偿方案的必要性,同时与采用Newton-Raphson算法的位置反解进行了对比,并测试了该算法控制下的Hexapod平台的响应速度和精度。实验结果表明:在保证平台重复精度低于10μm和5″的工作需求下,基于Brent算法的位置反解与Newton-Raphson算法相比,综合响应速度提高了约0.5 s。因此,基于Brent算法的位置反解求解方法相对改善了Hexapod平台的响应速度。

A Numerical Method on Inverse Determination of Heat Transfer Coefficient Based on Thermographic Temperature Measurement

The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dimensional correction method （MODCM）, along with the finite volume method, is employed for both two- and three-dimensional inverse problems. A series of numerical experiments are conducted in order to verify the effectiveness of the method. In addition, the effect of the temperature measurement error, the ending criterion of the iteration, etc. on the result of the inverse problem is investigated. It is proved that the method is a simple, stable and accurate one that can solve successfully the inverse heat conduction problem.

Computation of one—dimensional consolidation of double layered ground using differential quadrature method

The authors give the solution to the problem of one-dimensional conso l idation of double-layered ground with the use of the differential quadrature me t hod. Case studies showed that the computational results for pore-water pressure in soil layer agreed with those of analytical solution; and that in the computat ional results for the interface of soil layer also agreed with those of the anal ytical solution except for the small discrepancies during shortly after the star t of computation. The advantages of the solution presented in this paper are tha t compared with the analytical solution, it avoids the cumbersome work in solvin g the transcendental equation for eigenvalues, and in the case of the Laplace transform s olution, it can resolve the precision problem in the numerical solution of long time inverse Laplace transform. Because of the matrix form of the solution in th is paper, it is convenient for formulating computational program for engineering practice. The formulas for calculating double-layered ground consolidation may be easily extended to the case of multi-layered soils.

Infrared radiation method for measuring ice segregation temperature of artificially frozen soils

In order to study the evolution of the freezing fringe and final lenses of frost susceptible soils and advance the understanding of frost heave and mechanism of frost heave control, we used an open one-dimensional frost heave test system of infrared radiation technology, instead of a traditional thermistor method. Temperatures of the freezing fringe and segregated ice were measured in a non-contact mode. The results show that accurate and precise temperatures of ice segregation can be obtained by infrared thermal imaging systems. A self-developed inversion program inverted the temperature field of frozen soils. Based on our analysis of temperature variation in segregated ice and our study of the relationship between temperature and rate of ice segregation in cooling and warming processes during intermittent freezing, the mechanism of decreasing frost heave of frozen soils by controlling the growth of final lenses with an intermittent freezing mode, can be explained properly.

EFFECTS OF A CLOUD FILTERING METHOD FOR FENGYUN-3C MICROWAVE HUMIDITY AND TEMPERATURE SOUNDER MEASUREMENTS OVER OCEAN ON RETRIEVALS OF TEMPERATURE AND HUMIDITY

For Microwave Humidity and Temperature sounder(MWHTS) measurements over the ocean, a cloud filtering method is presented to filter out cloud-and precipitation-affected observations by analyzing the sensitivity of the simulated brightness temperatures of MWHTS to cloud liquid water, and using the root mean square error(RMSE)between observation and simulation in clear sky as a reference standard. The atmospheric temperature and humidity profiles are retrieved using MWHTS measurements with and without filtering by multiple linear regression(MLR),artificial neural networks(ANN) and one-dimensional variational(1DVAR) retrieval methods, respectively, and the effects of the filtering method on the retrieval accuracies are analyzed. The numerical results show that the filtering method can improve the retrieval accuracies of the MLR and the 1DVAR retrieval methods, but have little influence on that of the ANN. In addition, the dependencies of the retrieval methods upon the testing samples of brightness temperature are studied, and the results show that the 1DVAR retrieval method has great stability due to that the testing samples have great impact on the retrieval accuracies of the MLR and the ANN, but have little impact on that of the 1DVAR.