Green's functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials

In this paper,we obtain Green’s functions of two-dimensional(2D)piezoelectric quasicrystal(PQC)in half-space and bimaterials.Based on the elastic theory of QCs,the Stroh formalism is used to derive the general solutions of displacements and stresses.Then,we obtain the analytical solutions of half-space and bimaterial Green’s functions.Besides,the interfacial Green’s function for bimaterials is also obtained in the analytical form.Before numerical studies,a comparative study is carried out to validate the present solutions.Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force,the line dislocation,the line charge,and the phason line force.As a result,the coupling effect among the phonon field,the phason field,and the electric field is prominent,and the butterfly-shaped contours are characteristic in 2D PQCs.In addition,the changes of material parameters cause variations in physical quantities to a certain degree.

GREEN FUNCTION ON TWO-PHASE SATURATED MEDIUM BY CONCENTRATED FORCE IN TWO-DIMENSIONAL DISPLACEMENT FIELD

The Green function on two-phase saturated medium by concentrated force has a broad and important use In seismology, seismic engineering, soil mechanics, geophysics, dynamic foundation theory and so on. According to the Green function on two-phase saturated medium by concentrated force in three-dimentional displacement field obtained by Ding Bo-yang et al., it gives out the Green function in two-dimensional displacement field by infinite integral method along x(3)-direction derived by De Hoop and Manolis. The method adopted in the thesis is simpler. The result will be simplified to the boundary element method of dynamic problem.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Mathematic Model of Green Function with Two-Dimensional Free Water Surface

Adopting complex number theory, a mathematic model of Green function is built for two dimension free water surface, and an analytic expression of Green function is obtained by introducing two parameters. The intrinsic properties of Green function are discussed on vertical line and horizontal line. At last, the derivation expression of Green function is obtained from the formula of Green function.

Magnetic Properties of a Mixed Spin-2 and Spin-5/2 Heisenberg Ferrimagnetic System on a Two-Dimensional Honeycomb Lattice： Green＇s Function Approach

multisublattice 格林“ s 功能技术被使用学习磁性一。混合 spin-2 和 spin-5/2 海森堡含铁 atwo 维的蜂房格子上的磁性的系统。在 Hamiltonian 的不同相互作用的角色被探索。当仅仅近邻居的相互作用和单个离子的 anisotropy 被包括时，我们的结果显示在有限温度有赔偿点。当 thenext-nearest-neighbor 相互作用超过在 Hamiltonian 取决于另外的参数的最小的价值时，赔偿点消失。next-nearest-neighbor 相互作用有改变赔偿温度的效果。

Assessment of Regional Left Ventricular Myocardial Function in Rats after Acute Occlusion of Left Anterior Descending Artery by Two-dimensional Speckle Tracking Imaging

This study evaluated the change in regional left ventricular myocardial function in rats following acute occlusion of the left anterior descending coronary artery （LAD） by using two-dimensional speckle tracking imaging （2D-STI）. Sixty Wistar rats were randomly divided into two groups, a myocardial infarction （MI） group, in which 50 rats were subjected to LAD occlusion for 30–45 min, and a sham-operated （SHAM） group that contained 10 rats serving as control. Echo-cardiography was performed at baseline and 1, 4 and 8 week（s） after the operation. High frequency two-dimensional images of left ventricular short axis at papillary muscle level were recorded. Peak systolic radial strain （PRS） and circumferential strain （PCS） were measured in the mid-ventricle in short-axis view by using EchoPAC workstation. Left ventricular internal diameter at diastole （LVIDd） and systole （LVIDs）, fractional shortening （FS）, ejection fraction （EF） and left ventricular mass （LVM） were measured by anatomical M-model echocardiography. Infarct size was measured using triphenyl tetrazolium chloride （TTC） staining 1 week and 8 weeks after the operation. Fibrosis of left ventricu-lar myocardium was displayed using Van Gieson staining 1 week after the infarction. In terms of the TTC staining results, the left ventricle fell into three categories： infarcted, peri-infarcted and remote myocardial regions. Compared with those at baseline and in the SHAM group, （1） PRS and PCS in the infarcted, peri-infarcted and remote myocardial regions were significantly decreased in the MI group within 1 week after the operation （P〈0.05） and the low levels lasted 8 weeks; （2） Compared with those at baseline, LVIDd, LVIDs, FS, EF and LVM in the MI group showed no significant dif-ference 1 week after the operation （P〉0.05）. However, LVIDd, LVIDs and LVM were increased sig-nificantly 4 and 8 weeks after the operation （P〈0.05）, and FS and EF were decreased substantially （P〈0.05）. Van Gieson staining showed that fibrosis developed in all the three myocardial regions to varying degrees. It is concluded that 2D-STI is non-invasive and can be used to assess regional func-tion of myocardium with different blood supply in rats following acute occlusion of the LAD, and can be used as a sensitive and reliable means to follow up the process of left ventricular remodeling.

Assessment of Myocardial Perfusion and Systolic Function in Patients with Coronary Artery Disease after Coronary Artery Bypass Surgery by Myocardial Contrast Echocardiography and Two-dimensional Strain Echocardiography

The clinically applied value of myocardial perfusion and systolic function in patients with coronary artery disease after coronary artery bypass surgery using real-time myocardial contrast echocardiography （RT-MCE） combined with two-dimensional strain echocardiography was assessed. Twenty patients underwent intravenous RT-MCE by intravenous injections of SonoVue before and after coronary artery bypass surgery. Two-dimensional images were recorded from the left ventricular four-chamber view, two-chamber view and the apical view before, and two weeks and three months after coronary artery bypass surgery, and the peak systolic longitudinal strain was measured. The results showed that myocardial perfusion was significantly increased after coronary artery bypass surgery in about 71.6% segments. In the group that myocardial perfusion was improved, the peak systolic longitu- dinal strain three months after bypass surgery was significantly higher than that before operation [（-15.78±5.91）% vs （-10.45±8.31）%, P〈0.05]. However, the parameters did not change in the group without myocardial perfusion improvement [（-10.33±6.53）% vs （-9.41±6.09）%, P〉0.05]. It was concluded that whether or not the improvement of myocardial perfusion can mirror the recovery trend of regional systolic function, two-dimensional strain echocardiography can observe dynamic change of regional systolic function. The combination of myocardial perfusion with two-dimensional strain echocardiography can more accurately assess the curative effectiveness of coronary artery bypass surgery.

约束Green函数与非线性地基梁模态分析

在生物和医学领域,微机电系统(MEMS)中的微梁结构在植入人体的使用时,由于体内的细胞环境类似于水凝胶,在这种环境下工作,设备和仪器的精度和稳定性很大程度上受到细胞弹性的影响.为了分析此类地基梁的动力学问题,本文建立了非线性基础上的梁振动模型,研究了任意位置弹簧和非线性弹簧基础上的梁模态.通过Laplace变换和线性叠加原理,得到了一种约束Green函数,利用数值计算验证方案的有效性,并研究了各种重要物理参数的影响,发现弹簧位置向跨中移动时,模态对称性被打破,弹簧刚度增加,模态阶数改变.

Experimental and theoretical studies on two-dimensional vanadium carbide hybrid nanomaterials derived from V_(4)AlC_(3) as excellent catalyst for MgH_(2)

Hydrogen is considered one of the most ideal future energy carriers.The safe storage and convenient transportation of hydrogen are key factors for the utilization of hydrogen energy.In the current investigation,two-dimensional vanadium carbide(VC) was prepared by an etching method using V_(4)AlC_(3) as a precursor and then employed to enhance the hydrogen storage properties of MgH_(2).The studied results indicate that VC-doped MgH_(2) can absorb hydrogen at room temperature and release hydrogen at 170℃. Moreover,it absorbs 5.0 wt.%of H_(2) within 9.8 min at 100℃ and desorbs 5.0 wt.% of H_(2) within 3.2 min at 300℃.The dehydrogenation apparent activation energy of VC-doped MgH_(2) is 89.3 ± 2.8 kJ/mol,which is far lower than that of additive-free MgH_(2)(138.5 ± 2.4 kJ/mol),respectively.Ab-initio simulations showed that VC can stretch Mg-H bonds and make the Mg-H bonds easier to break,which is responsible for the decrease of dehydrogenation temperature and conducive to accelerating the diffusion rate of hydrogen atoms,thus,the hydrogen storage properties of MgH_(2) are remarkable improved through addition of VC.

GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM

The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space,and the singular kinetic waves which become smooth for all(t,x,v)when t>0.Furthermore,we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function.

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green’s function method for neutron-rich Ca,Ni,Zr,and Sn isotopes

The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.

Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals

Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.

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.

THE IMPROVEMENT OF THE GENERAL EXPRESSION FOR THE STRESS FUNCTION φ OF THE TWO-DIMENSIONAL PROBLEM

In this paper, it is pointed that the general expression for the stress function of the plane problem in polar coordinates is incomplete. The problems of the curved bar with an arbitrary distributive load at the boundries can't he solved by this stress function. For this reason, we suggest two new stress functions and put them into the general expression. Then, the problems of the curved bar applied with an arbitrary distributive load at r=a,b boundaries can be solved. This is a new stress function including geometric boundary constants.

Static response of functionally graded multilayered two-dimensional quasicrystal plates with mixed boundary conditions

The unusual properties of quasicrystals(QCs)have attracted tremendous attention from researchers.In this paper,a semi-analytical solution is presented for the static response of a functionally graded(FG)multilayered two-dimensional(2 D)decagonal QC rectangular plate with mixed boundary conditions.Based on the elastic theory of FG 2 D QCs,the state-space method is used to derive the state equations composed of partial differential along the thickness direction.Besides,the Fourier series expansion and the differential quadrature technique are utilized to simulate the simply supported boundary conditions and the mixed boundary conditions,respectively.Then,the propagator matrix which connects the field variables at the upper interface to those at the lower interface of any homogeneous layer can be derived based on the state equations.Combined with the interface continuity condition,the static response can be obtained by imposing the sinusoidal load on the top surfaces of laminates.Finally,the numerical examples are presented to verify the effectiveness of this method,and the results are very useful for the design and understanding of the characterization of FG QC materials in their applications to multilayered systems.

Value of myocardial function in children with Kawasaki disease by two-dimensional and three-dimensional ultrasound speckle tracking

Objective:To investigate the value of two-dimensional ultrasound speckle tracking(2D-STI)and three-dimensional ultrasound speckle tracking(3D-STI)in evaluating myocardial function in children with Kawasaki disease.Methods 92 children with Kawasaki disease admitted to our hospital from February 2017 to February 2019 were retrospectively analyzed.50 children who underwent 3D-STI examination were taken as observation group and 42 children who underwent 2D-STI examination were taken as control group.The left ventricular systolic function index,storage time and analysis time of the image,the diameter of coronary artery,the strain difference of left ventricular basal segment,middle segment,apical segment and whole segment were observed.Results The levels of left ventricular end-diastolic volume(LVEDV),left ventricular end-systolic volume(LVESV),left ventricular myocardial mass(LVMI)in the observation group were higher than those in the control group(P<0.05),but there was no statistical difference in left ventricular ejection fraction(LVEF)between the two groups(P>0.05).The storage time and analysis time of the image in the observation group were significantly lower than those in the control group(P<0.05).The left coronary artery(LCA)and right coronary artery(RCA)in the observation group were higher than those in the control group(P<0.05).There was no statistical difference between left anterior descending(LAD)in the two groups(P>0.05).The longitudinal peak systolic strain(LS),circumferential peak systolic strain(CS)and radial peak systolic strain(RS)in the observation group were higher than those in the control group(P<0.05).The global longitudinal peak strain(GLS),global circumferential peak strain(GCS)and global radial peak strain(GRS)in the observation group were higher than those in the control group(P<0.05).LS and CS in the middle segment of the observation group were higher than those in the control group(P<0.05).Conclusions Compared with 2D-STI,3D-STI can objectively and accurately reflect the myocardial function of children with Kawasaki disease.

Evaluation of the Effect of Sigmoid-Shaped Interventricular Septum on Left Ventricular Systolic Function in Patients with Essential Hypertension by Two-Dimensional Speckle Tracking Echocardiography

Objective: To evaluate left ventricular regional and global systolic function by measuring left ventricular longitudinal strain (LS) in hypertensive patients with sigmoid-shaped interventricular septum (SIS) by two-dimensional speckle tracking (2D-STE);in order to explore whether the sigmoid-shaped interventricular septum affects the left ventricular systolic function in patients with hypertension. Methods: Routine echocardiographic parameters were measured in 30 hypertensive patients with SIS (SIS group) and 30 hypertensive patients without SIS (non-SIS group). The left ventricular segments and global LS were measured by 2D-STE, and the two sets of parameters were compared. Results: The value of the thickness of the basal segment of the interventricular septum (IVSBT), the thickness of the middle segment of the interventricular septum (IVSMT) and the ratio of the basal segment of the ventricular septum to the middle segment of the interventricular septum (IVSBT/IVSMT) in SIS group was higher than that in non-SIS group. However, the value of left ventricular outflow tract diameter (LVOTD) in SIS group was lower than that in non-SIS group. There was a significant difference between the two groups (all P Conclusion: SIS affects left ventricular regional systolic function of patients with hypertension. 2D-STE can early evaluate left ventricular longitudinal systolic function in hypertensive patients with SIS.

Value of two-dimensional speckle tracking imaging in quantitative assessment of left ventricular function in patients with OSAS

Objective: To research the clinical application of two-dimensional speckle tracking imaging (2D-STI) in quantitative assessment of left ventricular function in patients with obstructive sleep apnea-hypopnea syndrome (OSAS). Method: From July 2016 to December 2018, 86 patients with OSAS were selected as OSAS group. According to sleep apnea hypopnea index (AHI), they were divided into mild OSAS group (24 cases), moderate OSAS group (29 cases) and severe OSAS group (33 cases). Another 50 healthy volunteers who underwent physical examination in our hospital during the same period were selected as the control group. The left ventricular function of all patients was quantitatively assessed by 2D-STI. The left ventricular function of all patients was quantitatively assessed by 2D-STI. The results of routine echocardiography and left ventricular global strain parameters of the OSAS group, the control group and the OSAS patients with different severity were compared and analyzed. Result: There were no significant differences in the levels of left ventricular ejection fraction (LVEF), left ventricular end diastolic diameter (LVEDd), left ventricular end systolic diameter (LVESd) between the two groups and OSAS patients with different severity (P>0.05). The levels of IVST, LVPW and LVMI in the OSAS group were significantly higher than those in the control group, the levels of end-diastolic interventricular septal thickness (IVS), left ventricular posterior wall thickness (LVPW), left ventricular mass index (LVMI) in the severe OSAS group were significantly higher than those in the mild and moderate OSAS group, and the levels of IVST, LVPW and LVMI in the moderate OSAS group were significantly higher than those in the mild OSAS group, there were significant differences between groups (P<0.05). The levels of GLS, GRS and GCS in the OSAS group were significantly lower than those in the control group (P<0.05). GLS, GRS and GCS levels in the severe OSAS group were significantly lower than those in the mild OSAS group and the moderate OSAS group, while the levels of global longitudinal strain (GLS), global radial strain (GRS) and global circumferential strain (GCS) in the moderate OSAS group were significantly lower than those in the mild OSAS group (P<0.05). Conclusion: The left ventricular systolic function of OSAS patients is obviously impaired. Left ventricular function in OSAS patients can be assessed timely and accurately by two-dimensional speckle tracking imaging.

The Green's function of the harmonic horizontal force applied at the interior of the saturated half-space soil

By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.

纳米分子器件量子传导中的Green's Function模型

将纳米分子器件的电极和分子本体作为一个系统,考虑到入射电子在原子电极和分子本体中的传导,在电极与分子之间界面上的透射的量子状态,在满足Fisher-Lee关系式的基础上,一个新型的Green’sFunction被设计出来。这一理论模型把三个区域上的不同量子状态完整地表达在一个方程式里,符合物理学基本原理,可以系统地用来研究纳米分子器件的量子传导特性。