Second order estimates for large solutions of elliptic equations

This paper deals with the second term asymptotic behavior of large solutions to the problems Δu=b(x)f(u), x∈Ω, subject to the singular boundary condition u(x)=∞, x∈∂Ω, where Ω is a smooth bounded domain in R^N, and b(x) is a non-negative weight function. The absorption term f is regularly varying at infinite with index ρ>1 (that is lim_u→∞f(ξu)/f(u)=ξ^ρ for every ξ>0) and the mapping f(u)/u is increasing on (0,+∞). Our analysis relies on the Karamata regular variation theory.     

广义Dedekind函数误差项的加权平方积分均值

研究了和式∑↑n≤x（n/ψ（n））^r的渐近公式中的误差项E（x;r）的加权平方积分均值。其中，r是正整数，ψ(n)是Dedekind函数。     

On application of asymptotic generalized discrepancy principle to the analysis of epidemiology models

Various implementations of the discrepancy principle (DP) for linear ill-posed problems are given in a large number of papers. In all of these papers, the DP has been justified for special types of regularization strategies. In our paper, a unified approach to the construction of the DP is presented that does not require any special structure of the regularizing operator. In that respect, the new method generalizes all prior results on the DP principle for linear irregular operator equations with noisy data. The efficiency of the proposed scheme is demonstrated for a parameter identification problem in avian influenza. In solving this particular inverse problem, it turned out to be beneficial to use some regularization strategies, for which the earlier (structure-based) discrepancy principles were not applicable. This motivated the development of a novel DP put forth in the current paper.     

变分模态分解在爆破信号趋势项去除中的应用

爆破工程中,信号趋势项的准确去除对提高爆破振动信号分析的精度具有重要意义。针对经验模态分解（empirical mode decomposition,EMD）识别法存在的模态混叠和端头效应等缺陷,提出了基于变分模态分解（variational mode decomposition,VMD）去除信号趋势项的方法,即VMD法。叙述了VMD法识别爆破信号趋势项原理,并进行了仿真实验,结果表明：趋势项频率对分解效果的影响相对较小,当趋势项频率处于1～5 Hz之间时,频率对分解效果的影响基本保持不变;振幅对分解效果影响显著,且振幅越小,VMD法的分解效果越差。当趋势项振幅超过原始爆破信号最大振幅的1/3时,VMD法分解效果较好。最后,应用VMD法和EMD法对含有趋势项的实测爆破振动信号进行处理,认为相比于EMD法,VMD法处理后的信号基本一致且不存在端点效应,在爆破信号趋势项去除领域中具有更加广泛的适用性。

     

The Local Conditional Stability Estimate for an Inverse Contact Problem in the Elasticity

In this paper, we consider an inverse problem in elasticity of determining stress on a contact domain from measurements outside the contact domain. The local conditional stability estimate for determining the stress vector is obtained. This conditional stability can give the convergence rate for Tikhonov's regularized solutions. This revised version was published online in July 2006 with corrections to the Cover Date.     

T-STRESS IN PIEZOELECTRIC SOLID

The non-singular and bounded terms for stresses near the crack tip were investigated. The crack problem in a transversely isotropic piezoelectric solid for the plane problem was dealt with. The principle of superposition and the Plemelj formulation were introduced. The non-singular terms are given by solving Rieman-Hilbert problem. It is shown that the non-singular terms are influenced by the elastic and electric constants.     

用同伦方法反演非饱和土中溶质迁移参数

非饱和土中溶质迁移参数反演问题可以归结为非线性算子方程的求解问题. 将同伦方法 引入该问题的求解，通过构造线性同伦将原问题转化为求解同伦函数最小值的无约束优化问 题. 同时在分析了同伦参数正则化效应的基础上，提出一种两段同伦参数修正方法. 即在求 解的初始阶段，根据拟Sigmoid函数调整同伦参数，以追踪同伦路径，保证计算稳定地进行； 在迭代的后期，采用与残差相关的同伦参数修正方法，以抵抗观测噪声对求解的影响. 数值 算例为求解带有平衡及非平衡吸附效应的一维非饱和土中溶质迁移模型参数反演问题，计算 结果表明了该方法的大范围收敛性及较强的抵抗观测噪声的能力.     

On the stability and dissipation of wall boundary conditions for compressible flows

Characteristic formulations for boundary conditions have demonstrated their effectiveness to handle inlets and outlets, especially to avoid acoustic wave reflections. At walls, however, most authors use simple Dirichlet or Neumann boundary conditions, where the normal velocity (or pressure gradient) is set to zero. This paper demonstrates that there are significant differences between characteristic and Dirichlet methods at a wall and that simulations are more stable when using walls modelled with a characteristic wave decomposition. The derivation of characteristic methods yields an additional boundary term in the continuity equation, which explains their increased stability. This term also allows to handle the two acoustic waves going towards and away from the wall in a consistent manner. Those observations are confirmed by stability matrix analysis and one‐ and two‐dimensional simulations of acoustic modes in cavities. Copyright © 2009 John Wiley & Sons, Ltd.     

Experimental study on correlation between turbulence and sound in a subsonic wind tunnel

In this paper, the effects of turbulence on sound generation and velocity fluctuations due to pressure waves in a large subsonic wind tunnel are studied. A trip strip located at different positions in the contraction part or at one position in the diffuser of a large wind tunnel is used to investigate the aforementioned phenomenon, and the results indicate that the trip strip has significant effects on sound reduction. The lowest turbulence intensity and sound are obtained from a trip strip with a diameter of 0.91 mm located either at X/L = 0.79 or at X/L = 0.115 in the wide portion of the contraction. Furthermore, the effect of monopole, dipole and quadrupole sources of aerodynamic noise at different velocities is investigated, and it is demonstrated that the contribution of the monopole is dominant, while the shares due to the dipole and quadrupole remain less important. In addition, it is found that the sound waves have a modest impact on the measured longitudinal turbulence and are generated essentially by eddies.     

Effect of quadratic pressure gradient term on a one-dimensional moving boundary problem based on modified Darcy’s law

A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations. Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model, a corresponding numerical solution method is presented. First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equations with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be stably numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy’s flow problem, the exact analytical solution for the case of Darcy’s flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform. A comparison of these model solutions leads to the conclusion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equations; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pressure gradient increasing for the one-dimensional problem.