The Roche Limit

The role of tides in deforming and possibly disrupting a secondary body orbiting about a primary body has been known for a considerable time. This was first inspired by the observations of ocean tides on Earth and then seen as playing an important role in the formation and evolution of the Earth–Moon system. Finally, in the beginning of the 20th century it was generally thought to have a significant role in the formation of the solar system through the tidal disruption of the Sun. Here, an overview of the historical developments of the ideas concerned with tidal disruption of a secondary body that can lead to mass loss is given. Some discussion of possible extensions to consider more realistic situations where the secondary body may not be moving on a circular orbit and may not rotate so as to maintain the phase-on configuration to the primary body is also given.     

Reliability assessment of serviceability performance of braced retaining walls using a neural network approach

In urban environments, one major concern with deep excavations in soft clay is the potentially large ground deformations in and around the excavation. Excessive movements can damage adjacent buildings and utilities. There are many uncertainties associated with the calculation of the ultimate or serviceability performance of a braced excavation system. These include the variabilities of the loadings, geotechnical soil properties, and engineering and geometrical properties of the wall. A risk‐based approach to serviceability performance failure is necessary to incorporate systematically the uncertainties associated with the various design parameters. This paper demonstrates the use of an integrated neural network–reliability method to assess the risk of serviceability failure through the calculation of the reliability index. By first performing a series of parametric studies using the finite element method and then approximating the non‐linear limit state surface (the boundary separating the safe and ‘failure’ domains) through a neural network model, the reliability index can be determined with the aid of a spreadsheet. Two illustrative examples are presented to show how the serviceability performance for braced excavation problems can be assessed using the reliability index. Copyright © 2005 John Wiley & Sons, Ltd.     

Equilibrium constants of triethanolamine in major seawater salts

Acid–base equilibrium constants of triethanolamine (TEA) have been determined by potentiometric titrations with a glass electrode, at 25 °C. Ionic strength was kept constant with only one electrolyte (using one of these salts: NaCl, KCl, MgCl₂ or CaCl₂), with binary mixtures of MgCl₂ and CaCl₂, and finally, in a solution with a composition approximately similar to that of natural seawater without sulfate. Equilibrium constants have been expressed in function of ionic strength by means of Pitzer equations and interaction parameters proposed in this theory have been obtained. It has been found that acid–base behaviour of TEA depends greatly on the salt used: basicity of TEA is decreased by CaCl₂, while it is increased by the other electrolytes used in this work.     

An integrable case of a rotational motion analogous to that of Lagrange and Poisson for a gyrostat in a Newtonian force field

The scope of the present paper is to provide analytic solutions to the problem of the attitude evolution of a symmetric gyrostat about a fixed point in a central Newtonian force field when the potential function isV ⁽²⁾.We assume that the center of mass and the gyrostatic moment are on the axis of symmetry and that the initial conditions are the following: (t ₀)=₀, (t ₀)=₀, (t ₀)=(t ₀)=₀, ₁(t ₀)=0, ₂(t ₀)=0 and ₃(t ₀)= ₃ ⁰ .The problem is integrated when the third component of the total angular momentum is different from zero (B ₁ 0). There now appear equilibrium solutions that did not exist in the caseB ₁=0, which can be determined in function of the value ofl ₃ ^r (the third component of the gyrostatic momentum).The possible types of solutions (elliptic, trigonometric, stationary) depend upon the nature of the roots of the functiong(u). The solutions for Euler angles are given in terms of functions of the timet. If we cancel the third component of the gyrostatic momentum (l ₃ ^r =0), the obtained solutions are valid for rigid bodies.     

Some breakage characteristics of ultra-fine wet grinding with a centrifugal mill

A centrifugal mill is a high-power intensity media mill that can be used for ultra-fine grinding, employing centrifugal forces generated by gyration of the axis of the mill tube in a circle. The mill charge motion is quite different depending on the ratio of the gyration diameter to the mill diameter (G / D ratio), varying from a motion similar to that of a conventional tumbling media mill to that of a vibration mill. In this study, a centrifugal mill was constructed with an arrangement where the gyration diameter could be readily adjusted. The batch grinding characteristics of three different minerals (limestone, talc and illite) in water with dispersing agent were investigated at various G / D ratios. It was found that the optimum G / D ratio in terms of the specific energy consumption to give a desired fineness of product was different for the three minerals. This was due to their different reactions to the breakage mechanisms provided by the mill charge motion at varying G / D ratios. The size distributions became progressively narrower at increased grinding times, and particles finer than about 0.1 μm were not detected even for prolonged grinding times. Measurement of specific surface areas indicated that this was not due to an artifact of the size measurements by laser diffractometry. This implies that there is a limitation in which particles finer than 0.1 μm are not produced under the conditions tested in this type of mill, but further investigation is needed for experimental verification of this limit of comminution.     

Analysis of a rigid footing lying on three-layered soil using the finite difference method

A numerical procedure is described for the analysis of the vertical deformation and the stress distribution of the strip footings on layered soil media. Three layers of soil with different stiffness are considered with the middle soil layer the thinnest and most stiff layer. The soil media is discretized and using the theory of elasticity, the governing differential equations are obtained in terms of vertical and horizontal displacements. These equations along with appropriate boundary and continuity conditions are solved by using the finite difference method. The vertical and horizontal displacements, strains and stresses are found at various nodes in the soil media. Parametric studies are carried out to study the effect of the placement depth of the middle soil layer, the relative ratios of the moduli of deformation of the soil layers on the vertical displacement of the footing and the vertical stress distribution. These studies reveal that the middle thin but very stiff layer acts like a plate and redistributes the stresses on the lower soft soil layer uniformly. The displacement on the top and bottom of the middle soil layer is almost the same showing that the compression of the middle layer is negligible as it is very stiff.     

福建平潭虎潮山滑坡成因机理分析与评价

虎潮山滑坡位于平宏公路12k 704~12k 884段北侧山坡体上,是平潭海岛通往陆地的唯一公路通道。论文通过定性的工程地质分析和定量计算评价了虎潮山坡体稳定性的变化趋势,提出改建公路超挖深切坡脚和持续长时间强降雨导致的孔隙水压力作用是边坡发生滑动破坏的主要因素。     

Disequilibrium for Ca during growth of pelitic garnet

Compositional zoning in hundreds of almandine-rich garnets in amphibolite by facies micaceous quartzites from the Picuris Range, north-central New Mexico USA, indicates that although Mn, Mg and Fe achieve chemical equilibrium at hand-sample scale during garnet growth, Ca does not. Instead, Ca concentrations at the surface of growing garnets appear to depend strongly on kinetic factors that govern the local chemical environment, yielding disequilibrium for Ca at scales larger than the region immediately surrounding an individual porphyroblast. Detailed zoning profiles were obtained for 371 garnet crystals in a small volume of a single sample of garnetiferous quartzite, and core analyses were made of 97 additional crystals. Each analysis was made on a section that passed precisely through the morphological centre of the crystal, located by means of 3-D imagery from computed X-ray tomography. The data reveal strong correlations between crystal size and concentrations of Mn, Mg and Fe (but not Ca) in garnet cores; a relationship between crystal size and isolation; rigorous cross-correlations among concentrations of Mn, Mg and Fe (but not Ca); and systematic variations in Ca concentrations as a function of crystal size and core composition that are anomalous in comparison to the behaviour of the other divalent cations. We interpret these observations as the result of thermally accelerated diffusion-controlled garnet growth, in circumstances that promoted rapid intergranular diffusion and thus rock-wide equilibration of Mn, Mg and Fe, but that prevented equilibration at similar scale for Ca because of its more sluggish intergranular diffusion. The anomalous behaviour of Ca is made evident in these garnets by the presence of sharp spikes in Ca concentration, which are demonstrably not a consequence of any simultaneous rock-wide event, such as a change in pressure, temperature, or some other intensive parameter. Instead, Ca concentrations probably reflect the local extent of reaction in the immediate vicinity of each porphyroblast. To the degree that such kinetic factors introduce departures from chemical equilibrium for Ca, thermobarometric estimates that involve grossular contents of pelitic garnet will be in error.     

稳定同位素分馏蒸汽压效应的计算方法

稳定同位素分馏的蒸汽压效应（vaporpressureisotopeeffects,简称VPIE）,在地球化学和天体化学上有着非常重要的研究意义。大部分情况下,由于轻重同位素体具有不同的蒸汽压,在经历挥发和蒸发过程时,含有重同位素的物种挥发得慢,轻同位素物种挥发得快,最终结果导致凝聚相富集重同位素,气相含有较多的轻同位素。在地球化学上,VPIE直接同非常重要的地学参数——同位素平衡分馏系数仅联系在一起。本文应用Bigeleisen提出的方法,直接将VPIE和约化配分函数比（RPFR）相联系,只需要通过理论计算获得两种物质的简谐振动频率,就能够得到非高压情况下该物质的VPIE。本文以水和硫镉矿（CdS）为例,详细介绍了如何计算蒸发和气化过程VPIE的方法,并指出了其在天体化学和矿床学中的一些潜在应用。