Effects of geological inhomogeneity on high Rayleigh number steady state heat and mass transfer in fluid-saturated porous media heated from below

A parametric study is carried out to investigate how geological inhomogeneity affects the pore-fluid convective flow field, the temperature distribution, and the mass concentration distribution in a fluid-saturated porous medium. The related numerical results have demonstrated that (1) the effects of both medium permeability inhomogeneity and medium thermal conductivity inhomogeneity are significant on the pore-fluid convective flow and the species concentration distribution in the porous medium; (2) the effect of medium thermal conductivity inhomogeneity is dramatic on the temperature distribution in the porous medium, but the effect of medium permeability inhomogeneity on the temperature distribution may be considerable, depending on the Rayleigh number involved in the analysis; (3) if the coupling effect between pore-fluid flow and mass transport is weak, the effect of the Lewis number is negligible on the pore-fluid convective flow and temperature distribution, hut it is significant on the species concentration distribution in the medium.

A computational study of shock speeds in high-performance shock tubes

This paper describes U2DE, a finite-volume code that numerically solves the Euler equations. The code was used to perform multi-dimensional simulations of the gradual opening of a primary diaphragm in a shock tube. From the simulations, the speed of the developing shock wave was recorded and compared with other estimates. The ability of U2DE to compute shock speed was confirmed by comparing numerical results with the analytic solution for an ideal shock tube. For high initial pressure ratios across the diaphragm, previous experiments have shown that the measured shock speed can exceed the shock speed predicted by one-dimensional models. The shock speeds computed with the present multi-dimensional simulation were higher than those estimated by previous one-dimensional models and, thus, were closer to the experimental measurements. This indicates that multi-dimensional flow effects were partly responsible for the relatively high shock speeds measured in the experiments.

A study of the stability of subcycling algorithms in structural dynamics

Algorithms for explicit integration of structural dynamics problems with multiple time steps (subcycling) are investigated. Only one such algorithm, due to Smolinski and Sleith has proved to be stable in a classical sense. A simplified version of this algorithm that retains its stability is presented. However, as with the original version, it can be shown to sacrifice accuracy to achieve stability. Another algorithm in use is shown to be only statistically stable, in that a probability of stability can be assigned if appropriate time step limits are observed. This probability improves rapidly with the number of degrees of freedom in a finite element model. The stability problems are shown to be a property of the central difference method itself, which is modified to give the subcycling algorithm. A related problem is shown to arise when a constraint equation in time is introduced into a time-continuous space-time finite element model. (C) 1998 Elsevier Science S.A.

Characterizing Greenberger-Horne-Zeilinger correlations in nondegenerate parametric oscillation via phase measurements

We present a potential realization of the Greenberger-Horne-Zeilinger all or nothing contradiction of quantum mechanics with local realism using phase measurement techniques in a simple photon number triplet. Such a triplet could be generated using nondegenerate parametric oscillation. [S0031-9007(98)07671-6].

Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses

We present finite element simulations of temperature gradient driven rock alteration and mineralization in fluid saturated porous rock masses. In particular, we explore the significance of production/annihilation terms in the mass balance equations and the dependence of the spatial patterns of rock alteration upon the ratio of the roll over time of large scale convection cells to the relaxation time of the chemical reactions. Special concepts such as the gradient reaction criterion or rock alteration index (RAI) are discussed in light of the present, more general theory. In order to validate the finite element simulation, we derive an analytical solution for the rock alteration index of a benchmark problem on a two-dimensional rectangular domain. Since the geometry and boundary conditions of the benchmark problem can be easily and exactly modelled, the analytical solution is also useful for validating other numerical methods, such as the finite difference method and the boundary element method, when they are used to dear with this kind of problem. Finally, the potential of the theory is illustrated by means of finite element studies related to coupled flow problems in materially homogeneous and inhomogeneous porous rock masses. (C) 1998 Elsevier Science S.A. All rights reserved.

Effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in deformable fluid-saturated porous media heated from below

In this paper, a solution method is presented to deal with fully coupled problems between medium deformation, pore-fluid flow and heat transfer in fluid-saturated porous media having supercritical Rayleigh numbers. To validate the present solution method, analytical solutions to a benchmark problem are derived for some special cases. After the solution method is validated, a numerical study is carried out to investigate the effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in fluid-saturated media when they are heated from below. The related numerical results have demonstrated that: (1) medium thermoelasticity has a little influence on the overall pattern of convective pore-fluid flow, but it has a considerable effect on the localization of medium deformation, pore-fluid flow, heat transfer and mineralization in a porous medium, especially when the porous medium is comprised of soft rock masses; (2) convective pore-fluid flow plays a very important role in the localization of medium deformation, heat transfer and mineralization in a porous medium. (C) 1999 Elsevier Science S.A. All rights reserved.

Modelling the large deformations in stratified media - the Cosserat continuum approach

Methods employing continuum approximation in describing the deformation of layered materials possess a clear advantage over explicit models, However, the conventional implicit models based on the theory of anisotropic continua suffers from certain difficulties associated with interface slip and internal instabilities. These difficulties can be remedied by considering the bending stiffness of the layers. This implies the introduction of moment (couple) stresses and internal rotations, which leads to a Cosserat-type theory. In the present model, the behaviour of the layered material is assumed to be linearly elastic; the interfaces are assumed to be elastic perfectly plastic. Conditions of slip or no slip at the interfaces are detected by a Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformation analysis. The model is incorporated into the finite element program AFENA and validated against analytical solutions of elementary buckling problems in layered medium. A problem associated with buckling of the roof and the floor of a rectangular excavation in jointed rock mass under high horizontal in situ stresses is considered as the main application of the theory. Copyright (C) 1999 John Wiley & Sons, Ltd.

A numerical study of pore-fluid, thermal and mass flow iu fluid-saturated porous rock basins

We present a numerical methodology for the study of convective pore-fluid, thermal and mass flow in fluid-saturated porous rock basins. lit particular, we investigate the occurrence and distribution pattern of temperature gradient driven convective pore-fluid flow and hydrocarbon transport in the Australian North West Shelf basin. The related numerical results have demonstrated that: (1) The finite element method combined with the progressive asymptotic approach procedure is a useful tool for dealing with temperature gradient driven pore-fluid flow and mass transport in fluid-saturated hydrothermal basins; (2) Convective pore-fluid flow generally becomes focused in more permeable layers, especially when the layers are thick enough to accommodate the appropriate convective cells; (3) Large dislocation of strata has a significant influence off the distribution patterns of convective pore;fluid flow, thermal flow and hydrocarbon transport in the North West Shelf basin; (4) As a direct consequence of the formation of convective pore-fluid cells, the hydrocarbon concentration is highly localized in the range bounded by two major faults in the basin.

Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe less than or equal to 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright (C) 1999 John Wiley & Sons, Ltd.

The crack tip strain field of AISI 4340 - Part I - Measurement technique

This is the first paper in a study on the influence of the environment on the crack tip strain field for AISI 4340. A stressing stage for the environmental scanning electron microscope (ESEM) was constructed which was capable of applying loads up to 60 kN to fracture-mechanics samples. The measurement of the crack tip strain field required preparation (by electron lithography or chemical etching) of a system of reference points spaced at similar to 5 mu m intervals on the sample surface, loading the sample inside an electron microscope, image processing procedures to measure the displacement at each reference point and calculation of the strain field. Two algorithms to calculate strain were evaluated. Possible sources of errors were calculation errors due to the algorithm, errors inherent in the image processing procedure and errors due to the limited precision of the displacement measurements. Estimation of the contribution of each source of error was performed. The technique allows measurement of the crack tip strain field over an area of 50 x 40 mu m with a strain precision better than +/- 0.02 at distances larger than 5 mu m from the crack tip. (C) 1999 Kluwer Academic Publishers.

Localizing the relativistic electron

A causally well-behaved solution of the localization problem for the free electron is given, with natural space-time transformation properties, in terms of Dirac's position operator x. It is shown that, although x is not an observable in the usual sense, and has no positive-energy (generalized) eigenstates, the four-vector density (rho(x, t), j(x, t)/c) is observable, and can be localized arbitrarily precisely about any point in space, at any instant of time, using only positive energy states. A suitable spin operator can be diagonalized at the same time.

Bounds on integrals of the Wigner function

The integral of the Wigner function over a subregion of the phase space of a quantum system may be less than zero or greater than one. It is shown that for systems with 1 degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over an possible states, reduces to the problem of finding the greatest and least eigenvalues of a Hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.

Visual function: How spiders find the right rock to crawl under

Animals that go on hunting expeditions face the problem of finding the way home at the end of the day. A group of hunting spiders has now been added to the list of animals that use the celestial pattern of polarized light as a compass for navigation. (C) 1999 Elsevier Science Ltd. All rights reserved.

Complexes of 1-thia-4,7,10-triazacyclododecane ([12]aneN(3)S) - Synthesis, structure and stability constants

The 12-membered macrocyclic ligand 1-thia-4,7, 10-triazacyclododecane ([12]aneN(3)S) has been synthesised, although upon crystallization from acetonitrile a product in which carbon dioxide had added to one secondary amine in the macrocyclic ring (H[12]aneN(3)SCO(2). H2O) was isolated and subsequently characterised by X-ray crystallography. The protonation constants for [12]aneN(3)S and stability constants with Zn(II), Pb(II), Cd(II) and Cu(II) have been determined either potentiometrically or spectrophotometrically in aqueous solution, and compared with those measured or reported for the ligands 1-oxa-4,7,10-triazacyclododecane ([12]aneN(3)O) and 1,4,7,10-tetraazacyclododecane ([12]aneN(4)). The magnitudes of the stability constants are consistent with trends observed previously for macrocyclic ligands as secondary amine donors are replaced with oxygen and thioether donors although the stability constant for the [Hg([12]aneN(4))](2+) complex has been estimated from an NMR experiment to be at least three orders of magnitude larger than reported previously. Zinc(II), mercury(II), lead(II), copper(II) and nickel(II) complexes of [12]aneN(3)S have been isolated and characterised by X-ray crystallography. In the case of copper(II), two complexes [Cu([12]aneN(3)S)(H2O)](ClO4)(2) and [Cu-2([12]aneN(3)S)(2)(OH)(2)](ClO4)(2) were isolated, depending on the conditions employed. Molecular mechanics calculations have been employed to investigate the relative metal ion size preferences of the [3333], asym-[2424] and sym-[2424] conformation isomers. The calculations predict that the asym-[2424] conformer is most stable for M-N bond lengths in the range 2.00-2.25 Angstrom whilst for the larger metal ions the [3333] conformer is dominant. The disorder seen in the structure of the [Zn([12]aneN(3)S)(NO3)](+) complex is also explained by the calculations. (C) 1999 Elsevier Science Ltd. All rights reserved.

Quantum and classical chaos for a single trapped ion

In this paper we investigate the quantum and classical dynamics of a single trapped ion subject to nonlinear kicks derived from a periodic sequence of Gaussian laser pulses. We show that the classical system exhibits: diffusive growth in the energy, or heating,'' while quantum mechanics suppresses this heating. This system may be realized in current single trapped-ion experiments with the addition of near-field optics to introduce tightly focused laser pulses into the trap.