Isotropic Homogeneous Universe with a Bulk Viscous Fluid in Lyra Geometry

Exact solutions are obtained for an isotropic homogeneous universe with a bulk viscous fluid in the cosmological theory based on Lyra’s geometry. The viscosity coefficient of the bulk viscous fluid is assumed to be a power function of the mass density. Cosmological models with time dependent displacement field have been discussed for a constant value of the deceleration parameter. Finally some possibilities of further problems and their investigations have been pointed out.     

Breakdown of the slow manifold in the Shallow-Water equations

Abstract

Numerical solutions are obtained by implicit multigrid solvers for initial-value problems in the rotating Shallow-Water Equations (SWE) with spatially complex initial conditions. Companion solutions are also obtained with the Shallow-Water Balance Equations (SWBE), both to determine the initial conditions for the SWE and to provide a comparison solution that lies entirely on the slow, advective manifold. We make use of a control parameter (here the Rossby number, R) to regulate the degree of slowness and balance. While there are measurable discrepancies between the evolving SWE and SWBE solutions for all R, there is a distinct, spatially local breakdown both of the slow manifold in the SWE solution and in the closeness of correspondence between the SWE and SWBE solutions. This critical value for breakdown is only slightly smaller than the R values at which, first, the SWE evolution becomes singular (i.e., the fluid depth vanishes), or second, a consistent initial condition for the SWBE cannot be defined. This breakdown is most clearly evident in a sudden increase in vertical velocity near the center of a strong, cyclonic vortex; its behavior is primarily associated with an enhanced dissipation rather than an initiation of gravity-wave propagation. The numerical performance of the multigrid solvers is satisfactory even in the difficult circumstances near solution breakdown or singularity.     

高维数据非参数密度估计的低维流形代表点法

非参数核方法由于采用统一的度量标准,在大数据中利用高维样本数据学习时容易遭遇维数灾难问题.挖掘高维空间中的低维几何特性,有助于揭示数据分布的流形结构,进而利用有限样本的高维数据在低维子空间逼近数据的真实分布.基于此,提出一种新的高维数据密度非参数估计的低维流形代表点法,通过从高维空间中挖掘数据分布的几何结构来估计密度....     

Energy‐work‐based numerical manifold seepage analysis with an efficient scheme to locate the phreatic surface

A major challenge in seepage analysis is to locate the phreatic surface in an unconfined aquifer. The phreatic surface is unknown and assumed as a discontinuity separating the seepage domain into dry and wet parts, thus should be determined iteratively with special schemes. In this study, we systematically developed a new numerical manifold method (NMM) model for unconfined seepage analysis. The NMM is a general numerical method for modeling continuous and discontinuous deformation in a unified mathematical form. The novelty of our NMM model is rooted in the NMM two‐cover‐mesh system: the mathematical covers are fixed and the physical covers are adjusted with iterations to account for the discontinuity feature of the phreatic surface. We developed an energy‐work seepage model, which accommodates flexible approaches for boundary conditions and provides a form consistent with that in mechanical analysis with clarified physical meaning of the potential energy. In the framework of this energy‐work seepage model, we proposed a physical concept model (a pipe model) for constructing the penalty function used in the penalty method to uniformly deal with Dirichlet, Neumann, and material boundaries. The new NMM model was applied to study four example problems of unconfined seepage with varying geometric shape, boundary conditions, and material domains. The comparison of our simulation results to those of existing numerical models for these examples indicates that our NMM model can achieve a high accuracy and faster convergence speed with relatively coarse meshes. This NMM seepage model will be a key component of our future coupled hydro‐mechanical NMM model. Copyright © 2014 John Wiley & Sons, Ltd.     

岩体黏弹性蠕变计算的高阶数值流形法研究

数值流形法（numerical manifold method）是一种新型的数值计算方法,已成功应用于岩土工程的诸多领域,但该方法尚未应用于岩土工程蠕变分析。近年来对高阶流形法的研究表明,对复杂的岩土工程问题,使用高阶覆盖函数可明显提高流形法的计算精度。为此,开展了用高阶流形法模拟蠕变的研究,在高阶流形法中引入“时步-初应变”法计算蠕变,以广义开尔文体为基础,推导了相关的计算公式,并编制了相应的计算程序,同时还通过算例,验证了方法的可行性和合理性。结果表明,高阶流形可以方便地与“时步-初应变”法结合用于蠕变计算,可较好地模拟蠕变变形。算例分析表明,在不改变网格密度情况下,仅通过采用高阶覆盖函数,高阶流形法可大幅提高传统流形法的计算精度。     

Exact solutions of some cosmological models in Lyra geometry

Bianchi type-V anisotropic cosmological models have been studied in the theory based on Lyra’s geometry in normal gauge. The physical and kinematical behaviors of the models have been discussed in the presence and absence of the magnetic field.      

高阶流形方法模拟裂纹扩展研究

在物理覆盖上采用一阶覆盖函数（即单元上位移函数为二阶）模拟裂纹扩展,并且基于采用的覆盖函数给出了一种裂纹尖端停留在单元内部的算法,从而,可控制每一步裂纹扩展的长度。该方法可弥补物理覆盖上使用常覆盖函数模拟裂纹扩展时无法准确控制扩展长度的不足。     

微分流形及其在测绘科学中的应用初探

本文用通俗的语言介绍了微分流形中几个最基本的概念,并对其在测绘科学中的应用作了初步探讨。     

Higher dimensional thick domain wall in Lyra geometry

An exact solution is obtained for a thick domain wall in a five dimensional Kaluza-Klein space time within the framework of Lyra geometry. The space time is nonsingular both in its spatial and temporal behavior. It is shown that the domain wall has no particle horizon and the gravitational force due to them is attractive. This revised version was published online in July 2006 with corrections to the Cover Date.