Nonnegative solutions to reaction–diffusion system with cross-diffusion and nonstandard growth conditions

We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross-diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition and nonstandard growth conditions and prove that the existence of weak solutions using Galerkin's approximation technique.     

Quantum to classical crossover under dephasing effects in a two-dimensional percolation model

Scaling theory predicts complete localization in d = 2 in quantum systems belonging to the orthogonal class(i.e., with timereversal symmetry and spin-rotation symmetry). The conductance g behaves as g^exp(-L/l) with system size L and localization length l in the strong disorder limit. However, classical systems can always have metallic states in which Ohm’s law shows a constant g in d=2. We study a two-dimensional quantum percolation model by controlling dephasing effects. The numerical investigation of g aims at simulating a quantum-to-classical percolation evolution. An unexpected metallic phase, where g increases with L, generates immense interest before the system becomes completely classical. Furthermore, the analysis of the scaling plot of g indicates a metal-insulator crossover.     

安培环路定理的拓扑学描述

近年来拓扑学在量子力学中得到了广泛的运用.本文将安培环路定理积分式重新表达为一矢量场在轮胎参数面上的第一类陈数积分.数值模拟展示了该积分值为一整数即第一陈数,其代表矢量场的整体性质:当经历连续变换时,矢量场的局部数值发生改变但整体积分值即陈数仍保持不变;若陈数发生改变,则表明矢量场变换的连续性条件发生破坏,矢量场出现奇点.进一步通过高斯映射将该矢量场从参数轮胎面映射到单位球面上,并给出了第一陈数的直观几何意义.理论和数值结果揭示了安培环路定理的拓扑学本质,表明拓扑概念在经典物理学中也会有广泛应用.     

Finite element computations of viscoelastic two-phase flows using local projection stabilization

A three-field local projection stabilized (LPS) finite element method is developed for computations of a three-dimensional axisymmetric buoyancy driven liquid drop rising in a liquid column where one of the liquid is viscoelastic. The two-phase flow is described by the time-dependent incompressible Navier-Stokes equations, whereas the viscoelasticity is modeled by the Giesekus constitutive equation in a time-dependent domain. The arbitrary Lagrangian-Eulerian (ALE) formulation with finite elements is used to solve the governing equations in the time-dependent domain. Interface-resolved moving meshes in ALE allows to incorporate the interfacial tension force and jumps in the material parameters accurately. A one-level LPS based on an enriched approximation space and a discontinuous projection space is used to stabilize the numerical scheme. A comprehensive numerical investigation is performed for a Newtonian drop rising in a viscoelastic fluid column and a viscoelastic drop rising in a Newtonian fluid column. The influence of the viscosity ratio, Newtonian solvent ratio, Giesekus mobility factor, and the Eötvös number on the drop dynamics are analyzed. The numerical study shows that beyond a critical Capillary number, a Newtonian drop rising in a viscoelastic fluid column experiences an extended trailing edge with a cusp-like shape and also exhibits a negative wake phenomena. However, a viscoelastic drop rising in a Newtonian fluid column develops an indentation around the rear stagnation point with a dimpled shape.     

A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

Uncertainty quantification for dynamics of geometrically nonlinear structures coupled with internal acoustic fluids in presence of sloshing and capillarity

In this paper, we propose an uncertainty quantification analysis, which is the continuation of a recent work performed in a deterministic framework. The fluid–structure system under consideration is the one experimentally studied in the sixties by Abramson, Kana, and Lindholm from the Southwest Research Institute under NASA contract. This coupled system is constituted of a linear acoustic liquid contained in an elastic tank that undergoes finite dynamical displacements, inducing geometrical nonlinear effects in the structure. The liquid has a free surface on which sloshing and capillarity effects are taken into account. The problem is expressed in terms of the acoustic pressure field in the fluid, of the displacement field of the elastic structure, and of the normal elevation field of the free surface. The nonlinear reduced-order model constructed in the recent work evoked above is reused for implementing the nonparametric probabilistic approach of uncertainties. The objective of this paper is to present a sensitivity analysis of this coupled fluid–structure system with respect to uncertainties and to use a classical statistical inverse problem for carrying out the experimental identification of the hyperparameter of the stochastic model. The analysis show a significant sensitivity of the displacement of the structure, of the acoustic pressure in the liquid, and of the free-surface elevation to uncertainties in both linear and geometrically nonlinear simulations.     

Can Anti-Aufbau DFT Calculations Estimate Singlet Excited State Aromaticity? Correspondence on “Dibenzoarsepins: Planarization of 8π-Electron System in the Lowest Singlet Excited State”

The simple anti-aufbau DFT approach for estimating singlet excited state aromaticity suggested in a recent Communication published in this journal is shown to produce incorrect results because it targets a linear combination of the singlet and triplet configurations involving the HOMO and LUMO rather than the first singlet excited state. If the S₁ state of a molecule is dominated by the HOMO→LUMO excitation, a comparably simple but theoretically consistent and qualitatively correct approximation to the S₁ wavefunction can be achieved by performing a small “two electrons in two orbitals” CASSCF(2,2) calculation which can be followed by the evaluation of magnetic aromaticity criteria such as NICS.     

基于无人机多光谱图像的土壤水分检测方法研究

以表层土壤为对象,探究土壤的多光谱反射率与土壤水分含量相关性,进行基于无人机多光谱图像的土壤水分含量预测模型方法的探究。选取中国农业大学通州实验站为研究区域,实地采集试验田的土壤样本100组,按照一定梯度配制土壤含水量,配成的土壤含水率为10%~50%之间,土壤含量的真实值采用土壤烘干法进行测定。多光谱相机灵巧便捷,可搭载在无人机上对土壤进行监测。将RedEdged-M型多光谱相机搭载在Phantom 3型无人机上,选择阳光充足的采集环境,实时采集土壤样本的多光谱图像,建立土壤多光谱信息与水分含量之间的模型。利用处理光谱数据的ENVI5.3软件提取土壤样本多光谱信息,以多光谱相机自带的标准白板反射率为100%,计算出土壤样本在蓝、绿、红、红边、近红外五个波段的光谱反射率。采用BP神经网络算法、支持向量机算法、偏最小二乘算法分别建立基于无人机多光谱图像的土壤水分含量的预测模型。以80组土壤样本数据作为训练集,建立基于多光谱图像的土壤水分含量预测模型。采用莱文贝格-马夸特算法对BPNN进行改进,提高了其训练速度,当网络结构为5-10-1时,训练效果最好,本文选择该网络结构;SVM采取高斯核函数,当参数为0.56时,模型效果最好。本研究采用归一化均方根误差(NRMSE)和决策系数(R 2)对三种土壤水分含量的预测模型进行定量对比。以20组土壤样本数据作为测试集,结果可知,基于BP神经网络土壤水分含量预测模型的NRMSE为0.268,R 2为0.872;基于支持向量机的土壤水分含量预测模型的NRMSE为0.298,R 2为0.821;基于偏最小二乘土壤水分含量预测模型的NRMSE为0.316,R 2为0.789。对三种模型分析可知,基于BPNN的土壤水分含量预测模型效果均较好。结果可知,土壤的光谱反射率与含水率间存在较密切的相关性,将多光谱相机搭载在无人机上可以对土壤水分含量进行有效的实时监测,对监测土壤墒情提供技术支持和理论支撑。