New class of solutions for water infiltration problems in unsaturated soils

This paper presents the results of approximate analytical solutions to Richards' equation, which governs the problem of unsaturated flow in porous media. The existing methods generally fall within the category of numerical and analytical methods, often having many restrictions for practical situations. In the present study, two approximate analytical methods known as the differential transform method (DTM) and homotopy perturbation method (HPM) were employed to find analytical solutions to Richards' equation. The methods were found to be robust in finding solutions practically identical to those from the existing analytical and numerical methods. Two representative examples were considered in order to evaluate the accuracy of the solutions obtained by DTM and HPM, revealing high level of accuracy in both cases.     

Weakly nonlinear analysis of the α effect

We address mathematical issues raised by the so-called α?effect of dynamo theory, which is a dynamo mechanism arising in conducting flows with small scale fluctuations. Analytical results on the α?effect concern the linear induction equation, and are usually claimed to hold for the whole magnetohydrodynamics (MHD) system, as long as the amplitude of the perturbations is small. We discuss the justification of that claim, in the case of periodic fluctuations of the fields. We show a nonlinear instability result on the MHD system, that predicts dynamo action for a large class of high frequency periodic flows, up to the fully nonlinear regime.     

侧向应力扰动对断层摩擦影响的实验研究

利用双向伺服控制装置,对含有与最大主压应力σ1呈45°夹角的预切面的花岗闪长岩标本进行了摩擦实验,结果表明,在σ1方向位移速率恒定、侧向应力σ2恒定的条件下,粘滑间隔随滑动面上正应力的增加而增加,粘滑应力降也随滑动面上正应力的增加而呈线性增加。但当σ2叠加了高频小振幅的正弦波扰动时,这种相关性发生了明显的变化,应力降大小和粘滑间隔的离散度均显著提高,特别是应力降可能会大幅度增加。与σ1扰动的实验结果相比,σ2扰动对断层粘滑的影响更为显著,这主要归因于正应力变化使滑动面的非均匀性加剧     

Third Order Effect of Rotation on Stellar Oscillations of a B Star

We aim at investigating the effect of rotation up to the third order in the angular velocity of a star on the p and g modes, based on the formalism developed by Soufi et al. Our ultimate goal is the study of oscillations of β Cephei stars which are often rapidly rotating stars. Our results show that the third-order perturbation formalism presented by Soufi et al. should be corrected for some missing terms and some misprints in the equations. As a first step in our study of β Cephei stars, we quantify by numerical calculations the effect of rotation on the oscillation frequencies of a uniformly rotating zero-age main-sequence star with 12 M<,??>. For an equatorial velocity of 100km s-1, it is found that the second-and third-order corrections for (l, m)=(2, 2), for instance, are of the order of 0.01% of the frequency for radial order n=6 and reaches up to 0.5% for n=14.     

A Singular Perturbation Method for Parametric Investigation on J-lay Installation of Deepwater Pipelines

The maximum bending moment or curvature in the neighborhood of the touch down point (TDP) and the maximum tension at the top are two key parameters to be controlled during deepwater J-lay installation in order to ensure the safety of the pipe-laying operation and the normal operation of the pipelines. In this paper, the non-linear governing differential equation for getting the two parameters during J-lay installation is proposed and solved by use of singular perturbation technique, from which the asymptotic expression of stiffened catenary is obtained and the theoretical expression of its static geometric configuration as well as axial tension and bending moment is derived. Finite element results are applied to verify this method. Parametric investigation is conducted to analyze the influences of the seabed slope, unit weight, flexural stiffness, water depth, and the pipe-laying tower angle on the maximum tension and moment of pipeline by this method, and the results show how to control the installation process by changing individual parameters.     

Dynamic simulation of beam-like structure with a crack subjected to a random moving mass oscillator

In this paper,dynamic simulation of a beam-like structure with a transverse open crack subjected to a random moving mass oscillator is investigated.The simultaneous effect of a crack and a random oscillator has not been addressed up to now.The crack in the beam at different locations and with different depths is considered as one group of damage,each as an individual imperfection.In addition,bearing immobility is considered as another type of problem in the beam.Mass, stiffness,damping and velocity of th...     

Inducing Unstable Grassland Equilibrium States Due to Nonlinear Optimal Patterns of Initial and Parameter Perturbations: Theoretical Models

Due to uncertainties in initial conditions and parameters,the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern.Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models.We used a nonlinear optimization approach,i.e.,a conditional nonlinear optimal perturbation related to initial and parameter perturbations (CNOP) approach,in our work.Numerical results indicated that the CNOP showed a special and nonlinear optimal pattern when the initial state variables and multiple parameters were considered simultaneously.A visibly different complex optimal pattern characterizing the CNOPs was obtained by choosing different combinations of initial state variables and multiple parameters in different physical processes.We propose that the grassland modeled ecosystem caused by the CNOP-type perturbation is unstable and exhibits two aspects:abrupt change and the time needed for the abrupt change from a grassland equilibrium state to a desert equilibrium state when the initial state variables and multiple parameters are considered simultaneously.We compared these findings with results affected by the CNOPs obtained by considering only uncertainties in initial state variables and in a single parameter.The numerical results imply that the nonlinear optimal pattern of initial perturbations and parameter perturbations,especially for more parameters or when special parameters are involved,plays a key role in determining stabilities and uncertainties associated with a simulated or predicted grassland ecosystem.     

层状土中群桩非线性沉降的摄动分析

采用包含一个内变量的连续化St Venant模型,即连续的Masing-Iwan模型,模拟桩-土界面扰动区土体的非线性行为。基于两种分析单桩的荷载传递模型,假设桩-土-桩相互作用为弹性且服从叠加原理,推导出了适用于群桩中基桩的两种荷载传递新模型。采用荷载传递法建立了单桩和群桩的非线性控制方程,提出了近似求解该控制方程的摄动分析法,得出了单桩和群桩的荷载沉降和轴力分布方程。所得结果表明,在低荷载水平下严格趋近于弹性解;而在高荷载水平下,能够反映直到破坏阶段的桩的荷载-沉降特性。通过一个现场试验的理论预测结果与实测数据的对比分析,验证了方法的有效性和适用性。     

基于流变体模型的波恩近似方程地震正演模拟

常规τ值法假设应力松弛时间与应变延迟时间近似相等, 造成了常Q模型拟合精度低. 本文利用精确的广义流变体模型Q值计算公式, 研究改进的τ值法求解常Q模型参数. 根据地震波散射理论, 推导了基于广义流变体模型的黏滞性介质一阶波恩近似方程, 结合位移-速度关系得到了含卷积完全匹配层边界条件的黏滞性介质应力-速度方程的一阶波恩近似表达式. 通过数值实验验证并对比了黏滞性介质中全波波动方程、 一阶波恩近似方程以及单程波波动方程的波场特征, 讨论了基于流变体模型的黏滞性介质一阶波恩近似方程对速度扰动和Q扰动的适应性, 以及对旅行时和振幅精度的影响.