ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS

We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.

Comparison of transport coefficients before and after density pump-out induced by resonant magnetic perturbation using a BOUT++ six-field model on the EAST tokamak

Many experiments have demonstrated that resonant magnetic perturbation(RMP) can affect the turbulent transport at the edge of the tokamak. Through the Experimental Advanced Superconducting Tokamak(EAST) density modulation experiment, the particle transport coefficients were calculated using the experimental data, and the result shows that the particle transport coefficients increase with RMP. In this study, the six-field two-fluid model in BOUT++ is used to simulate the transport before and after density pump-out induced by RMP,respectively referred as the case without RMP and the case with RMP. In the linear simulations,the instabilities generally decreases for cases with RMP. In the nonlinear simulation, ELM only appears in the case without RMP. Additionally, the particle transport coefficient was analyzed,and the result shows that the particle transport coefficient becomes larger for the case with RMP,which is consistent with the experimental conclusion. Moreover, its magnitude is comparable to the results calculated from experimental data.

Molecular Dynamics, Diffusion Coefficients and Activation Energy of the Electrolyte (Anode) in Lithium (Li and Li+), Sodium (Na and Na+) and Potassium (K and K+)

This work is a simulation modelling with the LAMMPS calculation code of an electrode based on alkali metals (lithium, sodium and potassium) using the MEAM potential. For different multiplicities, two models were studied;with and without gap. In this work, we present the structural, physical and chemical properties of the lithium, sodium and potassium electrodes. For the structural properties, the cohesive energy and the mesh parameters were calculated, revealing that, whatever the chemical element selected, the compact hexagonal hcp structure is the most stable, followed by the face-centred cubic CFC structure, and finally the BCC structure. The most stable structure is lithium, with a cohesion energy of -6570 eV, and the lowest bcc-hcp transition energy of -0.553 eV/atom, followed by sodium. For physical properties, kinetic and potential energies were calculated for each of the sectioned chemical elements, with lithium achieving the highest value. Finally, for the chemical properties, we studied the diffusion coefficient and the activation energy. Only potassium followed an opposite order to the other two, with the quantities with lacunae being greater than those without lacunae, whatever the multiplicity. The order of magnitude of the diffusion coefficients is given by the relationship DLi > DNa > Dk for the multiplicity 6*6*6, while for the activation energy the order is reversed.

Normalized glandular dose coefficients for digital breast tomosynthesis using detailed Chinese breast models

The rise in breast cancer diagnoses among Chinese women has necessitated the use of X-ray breast screening,which carries a radiation risk.This study aimed to provide a dosimetry protocol for the Chinese female population to replace the traditional standard that utilizes simplified breast models,for the accurate estimation of the mean glandular dose of a patient undergoing digital breast tomosynthesis(DBT).The first set of detailed Chinese female breast models and representative breast parameters was constructed.Considering backscatter radiation and computational efficiency,we improved the combination of these models and the Chinese reference adult female whole-body voxel phantom.Image acquisition for four commercial DBT systems that are widely employed in China was simulated using the Monte Carlo method to obtain the normalized glandular dose coefficients of DBT(D_(gN)^(DBT))and the glandular depth dose(D_(g)^(dep)(z))for different breast characteristics and X-ray spectra.We calculated a series of D_(gN)^(DBT) values for breasts with different percentage mass glandularities(5%,25%,50%,75%,and 100%)and compressed breast thicknesses(2,3,4,5,6,and 7 cm)at various tube potentials(25,28,30,32,35,and 49 kV)and target/filter combinations(W/Rh,W/Al,Mo/Mo,Rh/Rh,and Rh/Ag).The parameter dependence of the breast characteristics and beam conditions on D_(gN)^(DBT) in detailed breast models was investigated.The D_(gN)^(DBT) results were 14.6-51.0%lower than those of the traditional dosimetry standard in China.The difference in D_(gN)^(DBT) was mainly due to a decrease in the depth of the main energy deposition area caused by the glandular distribution along the depth direction.The results obtained in this study may be used to improve breast dosimetry in China and provide more detailed information on risk assessment during DBT.

Adaptive Random Effects/Coefficients Modeling

Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.

Molecular Dynamics, Physical Properties, Diffusion Coefficients and Activation Energy of the Lithium Oxide (Li-O) and Sodium Oxide (Na-O) Electrolyte (Cathode)

This work is a simulation model with the LAMMPS calculation code of an electrode based on alkali metal oxides (lithium, sodium and potassium) using the Lennard Jones potential. For a multiplicity of 8*8*8, we studied a gap-free model using molecular dynamics. Physical quantities such as volume and pressure of the Na-O and Li-O systems exhibit similar behaviors around the thermodynamic ensembles NPT and NVE. However, for the Na2O system, at a minimum temperature value, we observe a range of total energy values;in contrast, for the Li2O system, a minimum energy corresponds to a range of temperatures. Finally, for physicochemical properties, we studied the diffusion coefficient and activation energy of lithium and potassium oxides around their melting temperatures. The order of magnitude of the diffusion coefficients is given by the relation Dli-O >DNa-O for the multiplicity 8*8*8, while for the activation energy, the order is well reversed EaNa-O > EaLi-O.

Identification of the Diffusion Coefficients of Pollutants ( N O 3 - and Mn2+) through the Walls of Concrete Tank and Vulnerability of the Stored Water Quality

The populations of urban centers in Congo-Brazzaville have decided to develop various methods of water storage (concrete or masonry underground tanks) for domestic use, due to shortages in the distribution of water through the public network. However, questions remain as to the physico-chemical quality of the water stored in these tanks, when these structures are built in wet and relatively polluted areas. This paper presents a model of pollutant diffusion through the cementitious matrix (concrete) of tank walls simulated at a buried reservoir. The results of the experimental and numerical simulations show that certain concrete parameters, such as porosity, permeability and diffusivity, have a significant influence on the transfer of pollutants through the concrete walls, thus altering the physico-chemical quality of the stored water. The numerical models (1D) used to predict pollutant transfer and the quality of the stored water are consistent with those of the optimal control for identifying the diffusion coefficient. Major ion concentrations appear to be correlated with system porosity and diffusion coefficient. Nevertheless, the identification of the diffusion coefficient from the optimal control method, based on an explicit numerical resolution of a finite volume PDE for the approximation of the experiment, is not consistent with that of the optimal control method.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

High-Order Solitons and Hybrid Behavior of (3 + 1)-Dimensional Potential Yu-Toda-Sasa-Fukuyama Equation with Variable Coefficients

In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton solution. By using the long wave limit method, the N-order rational solution can be obtained from N-order soliton solution. Then, through the paired complexification of parameters, the lump solution is obtained from N-order rational solution. Meanwhile, we obtained a hybrid solution between 1-lump solution and N-soliton (N=1,2) by using the long wave limit method and parameter complex. Furthermore, four different sets of three-dimensional graphs of solitons, lump solutions and hybrid solutions are drawn by selecting four different sets of coefficient functions which include one set of constant coefficient function and three sets of variable coefficient functions.

THE FEKETE-SZEG?INEQUALITY AND SUCCESSIVE COEFFICIENTS DIFFERENCE FOR A SUBCLASS OF CLOSE-TO-STARLIKE MAPPINGS IN COMPLEX BANACH SPACES

Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.

Impacts of Surface Exchange Coefficients on Simulations of Super Typhoon Megi(2010)Using a Coupled Ocean-Atmosphere-Wave Model

In this study,the effects of surface exchange coefficients on simulations of Super Typhoon Megi(2010)are investigated using a fully coupled ocean-atmosphere-wave model.Several experiments are conducted using different parameterization schemes for the drag(C_(D))and enthalpy exchange(C_(K))coefficients.For the selected case,considering only the leveling-off of C_(D)at high wind speeds does not effectively improve the simulated typhoon track,intensity,or size.We found that increasing C_(K)monotonically with wind speed(Komori et al.,2018)yields stronger winds and deeper pressures by enhancing latent and sensible heat fluxes,but typhoon intensity remains underestimated.We propose a new higher C_(K)than that from Komori et al.(2018)based on the theory of Emanuel(1995).This approach produces a greater modeled typhoon intensity that is in good agreement with the best track data and effectively improves the track error for the simulation.Improved accuracy for modeled typhoon intensity is achieved with the new coefficient because C_(K)/C_(D)reaches the threshold of about 0.75 predicted by Emanuel(1995).The new proposed C_(K)also results in a reasonably accurate modeled sea surface temperature.However,typhoon size and surface wave height are overestimated.This finding implies that more numerical tests for tropical cyclones of different nature(such as strong,weak,dissipating,rapidly intensifying,or weakening tropical cyclones)should be studied,and more physical processes should be explored in future coupled models.

Theoretical calculations on Landé g-factors and quadratic Zeeman shift coefficients of nsnp ^(3)P_(0)^(o) clock states in Mg and Cd optical lattice clocks

The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce.In this work,the hyperfine-induced Landég-factors and quadratic Zeeman shift coefficients of the nsnp ^(3)P_(0)^(o) clock states for ^(111,113)Cd and ^(25)Mg were calculated by using the multi-configuration Dirac–Hartree–Fock theory.To obtain accurate values of these parameters,the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements,and energy separations were investigated in detail.We also estimated the contributions from perturbing states to the Landég-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy.Our calculations provide important data for estimating the first-and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.

Darboux transformation,infinite conservation laws,and exact solutions for the nonlocal Hirota equation with variable coefficients

This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation,along with the expression for N-soliton solutions.Influence of coefficients that are taken as a function of time instead of a constant,i.e.,coefficient functionδ(t),on the solutions is investigated by choosing the coefficient functionδ(t),and the dynamics of the solutions are analyzed.This article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations.The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.

Nondegenerate solitons of the(2+1)-dimensional coupled nonlinear Schrodinger equations with variable coefficients in nonlinear optical fibers

We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.

不同温度下再生骨料沥青混凝土动态抗压性能研究

为进一步研究再生骨料沥青混凝土在水工建筑物中的适用性,本文在不同温度环境中对再生骨料水工沥青混凝土的动态力学特性进行试验研究。对再生骨料水工沥青混凝土在温度为-10℃~10℃和应变速率为10^(-5)~10^(-2)s^(-1)的条件下进行动态抗压性能试验研究。试验结果表明:再生骨料水工沥青混凝土的抗压强度和弹性模量与温度成反比关系,与加载速率成正比关系;峰值应变与温度成正比关系,与加载速率成反比关系。通过温度影响因子和相关性系数分析,发现抗压强度和弹性模量随着温度升高逐渐减小并趋于某一定值。

Review of All Possible Conversion Equations of Influence Coefficients with Different Formats on Two-Plane Balancing

This article lists all possible conversion equations of influence coefficients(ICs)with different formats when some of these are known to handle two-plane balancing tasks with no or less trial weight runs.There are two approaches for two-plane balancing.One can treat it as a multi-plane balance problem involving a 2×2 matrix of complex ICs where two direct ICs along with two cross-effect ICs are generated so that correction weights at one or two balance planes can be determined.One can also apply a static pare(in-phase)and/or couple pair(180 degrees out-of-phase)weights for balancing.The latter approach has been used quite often in the field,especially on steam turbine and generator rotors.Dependent on vibration mode shapes and combinations as well as balance plane accessibility,sometimes applying static or couple pair weights can be a wise choice;other times weights at one or two end planes are needed.There are totally 4 possible sets of IC data due to weights at plane 1,plane 2,static pair,and couple pair.IC data would typically be obtained by applying trial weights followed by trial weight runs.It is found,however,that all these IC data can be converted easily without trial weight runs once any two of 4 sets are known.The above findings and conversion equations have been obtained analytically and verified by experimental results.Real cases are given to demonstratetheirapplications.

云南松苗木萌枝能力对截干高度的响应

【目的】探讨截干高度对云南松苗木萌枝能力的影响,为采穗圃穗条生产和适宜截干高度的确定提供技术支撑。【方法】以1年生云南松播种苗为试验材料,采用单因素完全随机区组试验,设置截干高度(即留桩高度)5,10和15 cm 3个处理,以不截干为对照,截干后每月测定萌枝数量和萌枝生长量,年底测算萌枝保存率和母株保存率,分析不同截干高度下萌枝数量和萌枝生长量的变化进程及累积数量的变化规律,并结合萌枝和母株保存率,探讨萌枝能力对截干高度的响应规律。【结果】不同截干高度萌枝发生的进程有所差异,截干高度5 cm萌枝数量速生期开始最早(截干后15 d)、持续时间最短(22 d),而截干高度10 cm萌枝数量速生期开始最晚(截干后22 d)、持续时间最长(39 d);净萌枝数量增加集中在截干后1~2个月的速生期内,占理论极值的57.51%~58.55%;不同截干高度的净萌枝数量和累积萌枝数量在生长前期、速生期、生长后期均表现为截干高度5 cm<截干高度10 cm<截干高度15 cm;截干高度5,10和15 cm的平均单株累积萌枝数量分别为12.82,19.72和22.71枝/株,不同处理间存在显著差异(P<0.05)。不同截干高度云南松苗木的萌枝平均生长量积累过程呈现“慢-快-慢”的节律,截干高度5,10和15 cm的萌枝生长量分别为6.094,5.486和7.868 cm,处理间无显著差异(P>0.05);云南松萌枝生长量增加集中在截干处理后1~3个月,占总萌枝生长量的70%以上。截干高度5,10和15 cm的萌枝存活率分别为86.14%,76.26%和63.48%,不同处理间差异显著(P<0.05);母株保存率分别为95.83%,100%和100%,不同处理间无显著差异(P>0.05)。综合来看,截干高度5 cm的萌枝数量少,但存活率最高;截干高度10 cm的萌枝数量多,且存活率较高;截干高度15 cm的萌枝数量多,但存活率最低。【结论】截干高度10 cm的处理既利于枝条萌发和萌枝生长,又具有较高的萌枝存活率,可较好权衡萌枝数量、生长量和存活率之间的关系,因此确定其为最有利于萌枝潜力发挥的适宜留桩高度。

中国数字经济发展水平的地区差异、空间集聚与状态转移

文章基于TOPSIS法,通过CRITIC权与灰色关联理论构建CRITIC权灰色关联TOPSIS法,并将其在空间与时间上应用两次,从而可对面板数据进行短期评价。根据新评价法测算2015—2020年中国31个省份的数字经济发展水平并展开分析,结果显示:中国数字经济发展水平地区差异显著,主要取决于三大地区间的差异,且有扩大趋势;北京、上海稳居前2名,浙江、广东、福建、天津、江苏稳居第3至第7名;贵州、青海数字经济发展进步较大,东北三省排名退步显著;省域数字经济发展水平状态转移较难,跨级状态转移基本不会发生,较低水平状态为贫困陷阱,陷于其中的省份很难靠自身得到提升;中国数字经济发展水平存在空间集聚现象,基于配对t检验的结果表明,数字经济可以在一定程度上打破地理限制。

沈阳恒隆市府广场超高层塔楼风荷载分析研究

为了确定高度350.6m沈阳恒隆市府广场塔楼结构设计的风荷载,采用刚性风洞试验与风洞数值模拟相结合的方法分析塔楼的风荷载,风洞试验研究给出楼层剪力与扭矩及风致加速度。采用四种湍流模型进行风洞数值模拟,分析建筑平均风压系数、体型系数、基底剪力及倾覆力矩,并与风洞试验进行比较,得出适用于超高层建筑风洞模拟的湍流分析模型,利用该分析模型的数值风洞模拟技术,分析塔楼13个风向角的风压系数、体型系数和基底剪力,为结构风荷载取值提供依据。研究结果表明:相比于《建筑结构荷载规范》(GB 50009—2012)对近似矩形平面建筑物的体型系数的规定,RSM模型迎风面0.83、背风面-0.56,与规范矩形截面迎风面0.8、背风面-0.6最为接近;RSM模型与试验吻合最好;选取RSM模型来分析超高层等大型复杂结构风荷载,能够得到较为准确的结果。

阀后管道突扩对控制阀门流阻特性的影响

为准确地描述非均匀流条件下控制阀门阀后采用突扩管道后的流阻特性,针对典型控制阀门(活塞式调流阀与固定式锥形阀),采用物理模型试验与理论分析方法,基于阀后突扩管道内的流场结构及试验段压力特性,研究阀后管道突扩对典型控流调压阀门流阻特性的影响规律。结果表明,不同阀型采用相同突扩体时的流阻特性变化程度不同,阀型的影响主要体现在改变了突扩体的入流、出流条件。在规范公式的基础上,考虑阀门出流流场结构(突扩体入流条件)与水流缩脉(突扩体出流条件)的影响,分析得到管道突扩比与阀门流量系数的定量关系,规范计算值与试验值的最大差异约为8%,优化公式计算值与试验值最大差异约为1%,说明改进后的突扩体流阻系数公式的计算精度较规范公式有所提高。研究结果可为高压差、大流量调流调压系统管路设计提供参考。