Torsion simple modules over the quantum spatial ageing algebra

Various classes of simple torsion modules are classified over the quantum spatial ageing algebra (this is a Noetherian algebra of Gelfand-Kirillov dimension 4). Explicit constructions of these modules are given and for each module its annihilator is found.     

Internal gravity–capillary solitary waves in finite depth

We consider a two‐dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and interfacial tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a spatial dynamics approach and formulate the steady Euler equations as a Hamiltonian system, where we consider the unbounded horizontal coordinate x as a time‐like coordinate. The linearization of the Hamiltonian system is studied, and bifurcation curves in the (β,α)‐plane are obtained, where α and β are two parameters. The curves depend on two additional parameters ρ and h, where ρ is the ratio of the densities and h is the ratio of the fluid depths. However, the bifurcation diagram is found to be qualitatively the same as for surface waves. In particular, we find that a Hamiltonian‐Hopf bifurcation, Hamiltonian real 1:1 resonance, and a Hamiltonian 0²‐resonance occur for certain values of (β,α). Of particular interest are solitary wave solutions of the Euler equations. Such solutions correspond to homoclinic solutions of the Hamiltonian system. We investigate the parameter regimes where the Hamiltonian‐Hopf bifurcation and the Hamiltonian real 1:1 resonance occur. In both these cases, we perform a center manifold reduction of the Hamiltonian system and show that homoclinic solutions of the reduced system exist. In contrast to the case of surface waves, we find parameter values ρ and h for which the leading order nonlinear term in the reduced system vanishes. We make a detailed analysis of this phenomenon in the case of the real 1:1 resonance. We also briefly consider the Hamiltonian 0²‐resonance and recover the results found by Kirrmann. Copyright © 2016 John Wiley & Sons, Ltd.     

Regularized Principal Component Analysis for Spatial Data

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations and n time points with the possibility that p > n. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when p is large relative to n. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical examples.     

Dynamics of a Diffusion Malaria Model With Vector-Bias北大核心CSCD

为了探讨季节性、蚊子叮咬的偏好性和人类的扩散对疟疾传播的影响,该文提出了一个部分退化的周期反应扩散模型.利用动力系统的持续性理论,研究了模型关于基本再生数R₀的阈值动力学.即当R₀<1时,疾病灭绝;而当R₀>1时,疾病一致持续,且会发生季节性的流行.数值上发现了忽略空间异质性和蚊子叮咬的偏好性会低估疾病传染的风险.     

岩体质量分级的风险分析方法

提出了基于RMR岩体质量分级系统的岩体质量研究风险分析方法。该方法分析步骤如下 :(1)通过岩芯样品的现场观测和实验室试验获得分类所需的变量 ;(2 )统计分析拟合得出各变量的分布函数及参数 ;(3)运用Monte Carlo模拟方法获得 2万个RMR值 ,并将结果绘成岩体质量描述图 ;(4)利用以上结果作出岩体质量风险分析评价。该方法用于润扬长江公路大桥岩体质量评价研究获得良好效果     

基于拓扑描述函数的连续体结构拓扑优化方法

提出了一种利用拓扑描述函数(TDF)作为拓扑设计变量求解连续体结构拓扑优化问题 的新方法. 优化问题的目标函数是结构的整体柔顺性，约束条件为对于可利用材料的体积限 制. 这种方法不仅可以消除拓扑优化中经常出现的棋盘格式等数值不稳定现象，而且能够有 效地抑制传统算法处理此类优化问题时所引发的边界扩散效应. 与其它的基于水平集描述函 数的拓扑优化方法相比，所提出的算法不仅无需求解控制水平集函数演化的双曲守恒方 程，而且合理地考虑了目标函数的拓扑导数信息，因而使得算法的计算效率有了显著的提高.     

Studying the Effect of the Spatial Frequency and Amplitude of Corrugation on the Stress–Strain State of Cylindrical Shells

An approach developed earlier to solve two-dimensional static problems for noncircular cylindrical shells is used to analyze the effect of the spatial frequency and amplitude of corrugation on the stress–strain state of shells. The results of the analysis are presented in the form of plots and tables     

Spatial chaos in boundary layer transition

Experiments have been performed on a laminar flat plate boundary layer undergoing transition to turbulence. Reproducible disturbances were introduced via a loudspeaker embedded at some upstream location and their evolution over the plate measured using hot-wire anemometry. A new technique has been used to estimate the number of nonlinearly independent modes in the reconstructed phase portraits. Nonlinear maps were then fitted that explicitly model the spatial evolution of disturbances. These maps are consistent with classical linear stability theory for small disturbances, and give rise to Smale horse-shoe like behaviour for larger amplitude distrubances. Thus a mechanism for generating chaos has been uncovered.     

Stochastic Analysis of Macrodispersion in a Semi‐Confined Aquifer

In this paper, the macroscopic dispersion resulting from one and twodimensional flows through a semiconfined aquifer with spatially variable hydraulic conductivity K which is represented by a stationary (statistically homogeneous) random process is analyzed using the spectral representation technique. Stochastic fluctuation equations of the steady flow and solute transport are solved to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of the leakage factor and input covariances describing the hydraulic conductivity in a semiconfined aquifer bounded by a leaky layer above and an impervious stratum below. The macrodispersivity tensor is studied using some convenient forms of the log hydraulic conductivity process. The sensitivity of the resulting macrodispersivity to the input covariances is discussed along with the influence of the leakage factor for both one and twodimensional flows. It is found that the longitudinal macrodispersivities are increased due to the presence of leakage, while the transverse macrodispersivities are reduced due to leakage.     

Spatial Estimates for the Constrained Anisotropic Elastic Cylinder

This paper establishes spatial estimates in a prismatic (semi-infinite) cylinder occupied by an anisotropic homogeneous linear elastic material, whose elasticity tensor is strongly elliptic. The cylinder is maintained in equilibrium under zero body force, zero displacement on the lateral boundary and pointwise specified displacement over the base. The other plane end is subject to zero displacement (when the cylinder is finite, say). The limiting case of a semi-infinite cylinder is also considered and zero displacement on the remote end (at large distance) is not assumed in this case. A first approach is developed by considering two mean-square cross-sectional measures of the displacement vector whose spatial evolution with respect to the axial variable is studied by means of a technique based on a second-order differential inequality. Conditions on the elastic constants are derived that show the cross-sectional measures exhibit alternative behaviour and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay. A second approach considers cross-sectional integrals involving the displacement and its gradient and furnishes information upon the spatial evolution, without restricting the range of strongly elliptic elastic constants. Such models are principally based upon a first-order differential inequality as well as on one of second order. The general results are explicitly presented for transversely isotropic materials and graphically illustrated for a cortical bone.