Topology Optimization of Sound-Absorbing Materials for Two-Dimensional Acoustic Problems Using Isogeometric Boundary Element Method

In this work,an acoustic topology optimizationmethod for structural surface design covered by porous materials is proposed.The analysis of acoustic problems is performed using the isogeometric boundary elementmethod.Taking the element density of porousmaterials as the design variable,the volume of porousmaterials as the constraint,and the minimum sound pressure or maximum scattered sound power as the design goal,the topology optimization is carried out by solid isotropic material with penalization(SIMP)method.To get a limpid 0–1 distribution,a smoothing Heaviside-like function is proposed.To obtain the gradient value of the objective function,a sensitivity analysis method based on the adjoint variable method(AVM)is proposed.To find the optimal solution,the optimization problems are solved by the method of moving asymptotes(MMA)based on gradient information.Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems.Furthermore,the optimal distribution of sound-absorbingmaterials is highly frequency-dependent and usually needs to be performed within a frequency band.

Two-Dimensional Riemann Problems:Transonic Shock Waves and Free Boundary Problems

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation

This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

THE CHEBYSHEV PSEUDOSPECTRAL DOMAIN DECOMPO SITION METHOD FOR SOLVING TWO-DIMENSIONAL ELLIPTIC EQUATION

This paper ix devoted to establishment of the Chebyshev pseudospectral domain de-composition scheme for solving two-dimensional elliptic equation. By the generalized equivalent variatiunal form, we can get the stability and convergence of this new scheme.

Solution of two-dimensional scattering problem in piezoelectric/piezomagnetic media using a polarization method

Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic ＂comparison body＂ is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green＇s function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.

Eigenfunction expansion method of upper triangular operator matrixand application to two-dimensional elasticity problems based onstress formulation

This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.

A Local Discontinuous Galerkin Method for Two-Dimensional Time Fractional Diffusion Equations

For two-dimensional(2D)time fractional diffusion equations,we construct a numerical method based on a local discontinuous Galerkin(LDG)method in space and a finite differ-ence scheme in time.We investigate the numerical stability and convergence of the method for both rectangular and triangular meshes and show that the method is unconditionally stable.Numerical results indicate the effectiveness and accuracy of the method and con-firm the analysis.

High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation

In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.

Effects of external fields on a two-dimensional Klein-Gordon particle under pseudo-harmonic oscillator interaction

We study the effects of the perpendicular magnetic and Aharonov-Bohm （AB） flux fields on the energy levels of a two-dimensional （2D） Klein Gordon （KG） particle subjected to an equal scalar and vector pseudo-harmonic oscillator （PHO）. We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential param- eter, magnetic field strength, AB flux field, and magnetic quantum number by means of the Nikiforov Uvarov （NU） method. The non-relativistic limit, PHO, and harmonic oscillator solutions in the existence and absence of external fields are also obtained.

Interfacial fracture analysis for a two-dimensional decagonal quasi-crystal coating layer structure

The interface crack problems in the two-dimensional(2D)decagonal quasicrystal(QC)coating are theoretically and numerically investigated with a displacement discontinuity method.The 2D general solution is obtained based on the potential theory.An analogy method is proposed based on the relationship between the general solutions for 2D decagonal and one-dimensional(1D)hexagonal QCs.According to the analogy method,the fundamental solutions of concentrated point phonon displacement discontinuities are obtained on the interface.By using the superposition principle,the hypersingular boundary integral-differential equations in terms of displacement discontinuities are determined for a line interface crack.Further,Green’s functions are found for uniform displacement discontinuities on a line element.The oscillatory singularity near a crack tip is eliminated by adopting the Gaussian distribution to approximate the delta function.The stress intensity factors(SIFs)with ordinary singularity and the energy release rate(ERR)are derived.Finally,a boundary element method is put forward to investigate the effects of different factors on the fracture.

Variational Monte Carlo analysis of Bose-Einstein condensation in a two-dimensional trap

The ground-state properties of a system with a small number of interacting bosons over a wide range of densities are investigated. The system is confined in a two-dimensional isotropic harmonic trap, where the interaction between bosons is treated as a hard-core potential. By using variational Monte Carlo method, we diagonalize the one-body density matrix of the system to obtain the ground-state energy, condensate wavefunction and the condensate fraction. We find that in the dilute limit the depletion of central condensate in the 2D system is larger than in a 3D system for the same interaction strength; however as the density increases, the depletion at the centre of 2D trap will be equal to or even lower than that at the centre of 3D trap, which is in agreement with the anticipated in Thomas-Fermi approximation. In addition, in the 2D system the total condensate depletion is still larger than in a 3D system for the same scattering length.

GENERALIZED FATIGUE CONSTANT LIFE CURVE AND TWO-DIMENSIONAL PROBABILITY DISTRIBUTION OF FATIGUE LIMIT

According to the traditional fatigue constant life curve, the concept and the universal expression of the generalized fatigue constant life curve were proposed. Then, on the basis of the optimization method of the correlation coefficient, the parameter estimation formulas were induced and the generalized fatigue constant life curve with the reliability level p was given. From P-S-a-S-m curve, the two-dimensional probability distribution of the fatigue limit was derived. After then, three se, of tests of LY11 CZ corresponding to the different average stress were carried out in terms of the two-dimensional up-down method. Finally, the methods are used to analyze the test results, and it is found that the analyzed results with the high precision may be obtained.

Comment on “Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals” by Si-Qi Zhang et al.

Recently, Zhang et al. （Chin. Phys. B 26 024208 （2017）） investigated the band gap structures and semi-Dirac point of two-dimensional function photonic crystals, and the equations for the plane wave expansion method were induced to obtain the band structures. That report shows the band diagrams with the effects of function coefficient k and medium column ra under TE and TM waves. The proposed results look correct at first glance, but the authors made some mistakes in their report. Thus, the calculated results in their paper are incorrect. According to our calculations, the errors in their report are corrected, and the correct band structures also are presented in this paper.

Three-Dimensional Numerical Simulation of Stably Stratified Flows over a Two-Dimensional Hill

Stably stratified flows over a two-dimensional hill are investigated in a channel of finite depth using a three-dimensional direct numerical simulation (DNS). The present study follows onto our previous two-dimensional DNS studies of stably stratified flows over a hill in a channel of finite depth and provides a more realistic simulation of atmospheric flows than our previous studies. A hill with a constant cross-section in the spanwise (y) direction is placed in a 3-D computational domain. As in the previous 2-D simulations, to avoid the effect of the ground boundary layer that develops upstream of the hill, no-slip conditions are imposed only on the hill surface and the surface downstream of the hill;slip conditions are imposed on the surface upstream of the hill. The simulated 3-D flows are discussed by comparing them to the simulated 2-D flows with a focus on the effect of the stable stratification on the non-periodic separation and reattachment of the flow behind the hill. In neutral (K = 0, where K is a non-dimensional stability parameter) and weakly stable (K = 0.8) conditions, 3-D flows over a hill differ clearly from 2-D flows over a hill mainly because of the three-dimensionality of the flow, that is the development of a spanwise flow component in the 3-D flows. In highly stable conditions (K = 1, 1.3), long-wavelength lee waves develop downstream of the hill in both 2-D and 3-D flows, and the behaviors of the 2-D and 3-D flows are similar in the vicinity of the hill. In other words, the spanwise component of the 3-D flows is strongly suppressed in highly stable conditions, and the flow in the vicinity of the hill becomes approximately two-dimensional in the x and z directions.

Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg–de Vries equation

Within the(2+1)-dimensional Korteweg–de Vries equation framework,new bilinear B¨acklund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation.By introducing an arbitrary functionφ(y),a family of deformed soliton and deformed breather solutions are presented with the improved Hirota’s bilinear method.By choosing the appropriate parameters,their interesting dynamic behaviors are shown in three-dimensional plots.Furthermore,novel rational solutions are generated by taking the limit of the obtained solitons.Additionally,twodimensional(2D)rogue waves(localized in both space and time)on the soliton plane are presented,we refer to them as deformed 2D rogue waves.The obtained deformed 2D rogue waves can be viewed as a 2D analog of the Peregrine soliton on soliton plane,and its evolution process is analyzed in detail.The deformed 2D rogue wave solutions are constructed successfully,which are closely related to the arbitrary functionφ(y).This new idea is also applicable to other nonlinear systems.

Numerical Analysis of Upwind Difference Schemes for Two-Dimensional First-Order Hyperbolic Equations with Variable Coefficients

In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.

Corrigendum to“Atomic-scale electromagnetic theory bridging optics in microscopic world and macroscopic world”

The signs of the electric field markers in Figs.2 and 4 of the paper[Chin.Phys.B 32104211(2023)]have been corrected.These modifications do not affect the results derived in the paper.

基于SWOT-AHP模型的蓬莱丘山谷葡萄酒庄旅游发展战略研究

葡萄酒庄旅游作为葡萄酒产业和旅游业相结合的产物,能够促进一二三产业的融合发展,是极具发展潜力的旅游项目。蓬莱区作为国内较早发展酒庄旅游的产区之一,酒庄旅游业已取得初步进展,但如今也面临如何更好整合资源以实现可持续发展的问题。该文基于态势分析法(SWOT)模型分析蓬莱丘山谷葡萄酒庄旅游业发展的优势、劣势、机遇以及威胁,设置发展因素指标体系,利用层次分析法(AHP)计算各个因素的权重,构建战略四边形。结果表明:蓬莱丘山谷酒庄旅游发展的优势大于劣势,机遇高于威胁,应采取实力型战略。根据上述分析,从自身优势、区位影响力和特色旅游体验等方面提出相应建议,以期实现可持续发展。

象限法评估椎体成形术后骨水泥分布类型与骨质疏松性椎体新发骨折的关系

目的 象限法评估骨水泥在椎体内弥散分布情况,分析骨水泥弥散分布类型与椎体强化术后新发椎体骨折的相关性。方法 2020年1月~2021年12月收治满足条件的病人170例。根据脊柱正侧位片将伤椎分成4个象限,根据术后骨水泥在伤椎内弥散分布情况分为弥散均匀组和弥散不均组。比较两组术后再骨折发生率及再骨折类型,以及术后及末次随访VAS评分及Cobb角变化情况。结果 170例病人均获得至少12个月的随访,其中弥散均匀组90例、弥散不均组80例。发生再骨折33例,发生率为19.41%;弥散均匀组发生再骨折12例,发生率为13.33%;弥散不均组发生再骨折21例,发生率26.25%,组间比较,差异具有统计学意义(P<0.05)。弥散均匀组发生再骨折部位以邻椎骨折为主,而弥散不均型邻椎及术椎发生再骨折概率相近。弥散均匀组病人术后骨水泥泄漏发生率低于弥散不均组,差异有统计学意义(P<0.05)。两组术后及末次随访时VAS评分及Cobb角较术前均显著改善,但组间比较差异无统计学意义(P>0.05)。结论 椎体成形术后新发椎体骨折的发生率与骨水泥弥散类型相关,通过象限法定义为骨水泥弥散不均型再骨折风险较高。