地球的重力聚点与参数椭球的地球重力学性质

本文研究了“参数椭球”的地球重力学性质 ,在纬度 3 5°2 1′3 2″处 ,发现了地球的“重力聚点”,给出了适用于地球的“密度分布定理”、“物质流动定理”和“重力聚点定理”;为研究地球密度的整体变化 ,提供了有用的理论工具。     

A Method to Estimate Length Distributions from Outcrop Data

Dimensions of shales and other geologic bodies that affect fluid flow through reservoirs and aquifers are often estimated from analogous deposits exposed in outcrops. Shale lengths observed in outcrops are biased because the finite length of outcrops truncates longer shales and long shales tend to be overrepresented in the sample. Shale length distributions can be modeled using an Erlangian probability density function based on termination frequency. Termination frequency can be calculated from outcrop observations even if the shales are incompletely exposed. Termination frequency is unbiased regardless of underlying shale length distribution and outcrop size and shape. Complex length distributions can be represented by a weighted sum of Erlangian models, each with a distinct termination frequency. The proportions and termination frequencies of the component models can be estimated using Bayes' theorem. Subsamples of the outcrop area can be analyzed to quantify spatial trends in termination frequency and thus shale length. These methods can be applied to estimate length distributions of any geologic object exposed in outcrops or other spatially limited samples. In many cases estimated termination frequency is normally distributed, and its variance can be estimated using closed-form expressions. Shale length distributions for the Frewens Sandstone were modeled using one- and two-component Erlangian probability density functions. The Frewens Sandstone is a tide-influenced deltaic sandstone body within the Cretaceous-age Frontier Formation, exposed in central Wyoming, USA. Length observations and Erlangian models agree reasonably well. Because the models correct for the effects of shale truncation in limited outcrop exposures, predicted means and proportions of long shales are substantially greater than observed values. There is a vertical trend and pronounced vertical cyclicity in termination frequency, indicating that shales become shorter upward and intervals of longer and shorter shales alternate. Along strike, termination frequency decreases away from the sandstone-body axis, reflecting greater preserved shale lengths toward sandstone-body margins. No correlation was observed between distance along dip and termination frequency. Termination frequencies and histograms of shale length for adjacent, perpendicular walls are similar, indicating that there is no anisotropy in shale length.     

G-S变换的快速算法

在电磁场瞬变响应的数值计算中 ,常采用G S变换法作逆拉氏变换 .它是纯实数运算 ,而且只需对较少的拉氏变换变量s值作计算 （通常对每一采样时间选用 1 2个s值 ） ,因而是一种计算速度较快的算法 .但是 ,要对大量采样时间作计算 ,其计算量仍太大 .本文基于拉氏变换的延迟定理 ,建立了一种新的G S变换算法 .数值检验结果表明 ,新算法可成级次地减少对大量采样时间作G S变换的计算量 ,显著提高电磁场瞬变响应的计算速度 .     

非线性破坏准则与岩土材料地基承载力研究

根据线性Mohr-Coulomb破坏准则,前人运用极限平衡法、滑移线理论或极限分析等方法求解地基承载力问题,但实际上岩土在剪切破坏过程中破坏准则具有非线性。因此,为了研究非线性破坏准则对地基承载力的影响,基于上限定理,通过“切线法”引进变量,根据能量耗散情况,将承载力问题转变为非线性规划问题,运用“序列二次规划算法”求出地基承载力的最优解。数值计算结果表明,当非线性破坏准则转变为线性破坏准则时,非线性参数对地基承载力有重要影响。     

An improved return‐map stress update algorithm for finite deformation analysis of general isotropic elastoplastic geomaterials

This paper develops a novel return mapping algorithm for the numerical integration of general isotropic finite strain elastoplastic constitutive models for geomaterials. The constitutive formulation is founded on multiplicative decomposition of the deformation gradient. The logarithmic strain measure as well as the exponential approximation of the plastic flow rule is utilized to restore the standard infinitesimal format return mapping algorithm. Central to the algorithm is the exploitation of a set of three mutually orthogonal unit base tensors for the representation of constitutive relations and the corresponding integration of the rate form of the constitutive equations. The base tensors constitute a local cylindrical coordinate system in the principal space, which allows to formulate the return mapping algorithm in the three‐dimensional space and reduce the dimension of the problem to be analyzed from six down to three. With the proposed approach, direct determination of the principal axes and the transformation procedure between the general space and the principal space, as required in traditional spectral decomposition, are avoided. Furthermore, the matrices that are involved in the inversion evaluation take simple forms, leading to extremely easy inverse computation. As a result, the consistent tangent operator can be streamlined into a form simpler and more compact than those by conventional integration methods. Following the formulation of the integration procedure, a numerical experiment is performed to assess the accuracy and efficiency of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamic modeling and motion simulation for a winged hybrid-driven underwater glider

PETREL,a winged hybrid-driven underwater glider is a novel and practical marine survey platform which combines the features of legacy underwater glider and conventional AUV (autonomous underwater vehicle).It can be treated as a multi-rigid-body system with a floating base and a particular hydrodynamic profile.In this paper,theorems on linear and angular momentum are used to establish the dynamic equations of motion of each rigid body and the effect of translational and rotational motion of internal masses on the attitude control are taken into consideration.In addition,due to the unique external shape with fixed wings and deflectable rudders and the dual-drive operation in thrust and glide modes,the approaches of building dynamic model of conventional AUV and hydrodynamic model of submarine are introduced,and the tailored dynamic equations of the hybrid glider are formulated.Moreover,the behaviors of motion in glide and thrust operation are analyzed based on the simulation and the feasibility of the dynamic model is validated by data from lake field trials.     

Stability of L4 for radiated rigid primaries in resonant cases

The non-linear stability of the triangular libration point L₄ of the restricted three-body problem is studied under the presence of third- and fourth-order resonances, when the more massive primary is a triaxial rigid body and source of radiation. In this study, Markeev's theorems are applied with the help of Moser's theorem. It is found that the stability of the triangular libration point is unstable in the third-order resonance case and in the fourth-order resonance case, this is stable or unstable depending on A₁ and A₂, and a source of radiation parameter α, where A₁, A₂ depend upon the lengths of the semi-axes of the triaxial rigid body.     

Estimation of areal specific yield in sands using the central limit theorem

A new approach is demonstrated that permits a reliable estimate of specific yield using published values of the van Genuchten water retention parameters and effective grain sizes and the measured effective grain sizes of soil samples. The specific yield distribution of the soil texture was computed using the published values of the van Genuchten parameters. The specific yield values and the published values of effective grain sizes were then used to construct a specific yield–effective grain size curve, which estimates the ‘point’ specific yield of the soil samples. Applying the central limit theorem, the point specific yields could be transformed into an ‘areal’ specific yield for a study area. Compared with other commonly used approaches, the present procedure requires relatively low computational efforts and readily obtainable data. It is cost effective and does not depend on soil texture classification. More importantly, it incorporates the depth to water table and the variations in grain sizes inherent in natural soil conditions in the estimation. The approach developed was applied for estimating the specific yield of an unconfined sandy aquifer created by land reclamation in the equatorial region. The values obtained were compared with field measurements and the typical ranges of specific yield from the literature. Instead of a single estimate of the specific yield, the method yields a confidence interval with a high confidence level of 95% and with a narrower range than the typical ranges from the literature. In addition, the estimated values are close to the field measurements; hence, the procedure provides a cost‐effective alternative to field measurement. The applicability of the present approach could be extended to sites with heterogeneity in the horizontal direction. Nevertheless, the applicability of the present approach for layered soil profiles requires further evaluations. Copyright © 2006 John Wiley & Sons, Ltd.     

Bounding greybody and deflection angle of improved Schwarzschild black hole

In this paper, we study the weak deflection angle in the spacetime of improved Schwarzschild black hole using the method derived by Gibbons and Werner. To do so, we derive the optical curvature from the optical metric and calculate deflection angle in weak field limits by using the Gauss–Bonnet theorem. Moreover, we study the effect of the plasma medium on the weak gravitational lensing using the Gauss–Bonnet theorem. Furthermore, we also study the graphical analysis of the deflection angle in both the plasma and non-plasma mediums. Moreover, we obtain the bound on greybody for improved Schwarzschild black hole.     

Magnetic field generation by the motion of a highly conducting fluid

Abstract

Using an asymptotic expansion of Green's function for the problem of magnetic field generation by 3D steady flow of highly conducting fluid a general antidynamo theorem is proved in the case of no exponential stretching of liquid particles. Explicit formulae connecting the spectrum of the magnetic modes with the geometry of the Lagrangian trajectories are obtained. The existence of the fast dynamo action for special flows with exponential stretching is proved under the condition of smoothness of the fields of stretching and non-stretching directions.