The Drained Strength of Bentonite Enhanced Sand

INTRODUCTION Barriers with a low hydraulic conductivity are used as part of waste containment systems to prevent groundwater contamination by liquids from the waste. Commonly barriers are either a geomembrane (usually an HDPE sheet), a mineral layer or a combination of the two. Recently there has been increasing interest in the use of bentonite±sand mixtures as the mineral layer, in both land®ll liners and vertical cut-off walls, partly because they are less susceptible to frost damage and desiccation cracking than compacted clay (Dixon et al., 1985; Kraus et al., 1997). Currently there is uncertainty about the strength and bearing capacity of these materials. This note reports drained strength data for bentonite±sand mixtures and proposes that trends in these data are mainly the result of variations in the relative density of the sand

The strength of unsaturated bentonite-enhanced sand

A modification to Rowe’s stress-dilatancy equation is presented that extends its range of application to include unsaturated soil behaviour. The results of a programme of constant water content triaxial tests on unsaturated bentonite-enhanced sand (BES) are reported, together with those of a programme of saturated drained triaxial tests on the sand. It is shown that the variation in the rate of dilation at failure with the sand relative density is similar for the two materials. It is proposed that the packing and friction angle of the sand particles and the degree of saturation control the shear strength of unsaturated BES containing modest amounts of bentonite, and that the shear strength of the bentonite component can be ignored

Preliminary genetic analyses of important musculoskeletal conditions of thoroughbred racehorses in Hong Kong

A retrospective cohort study of important musculoskeletal conditions of Thoroughbred racehorses was conducted using health records generated over a 15 year period (n = 5062, 1296 sires). The prevalence of each condition in the study population was: fracture, 13%; osteoarthritis, 10%; suspensory ligament injury, 10%; and tendon injury, 19%. Linear and logistic sire and animal regression models were built to describe the binary occurrence of these musculoskeletal conditions, and to evaluate the significance of possible environmental risk factors. The heritability of each condition was estimated using residual maximum likelihood (REML). Bivariate mixed models were used to generate estimates of genetic correlations between each pair of conditions.<p></p> Heritability estimates of fracture, osteoarthritis, suspensory ligament and tendon injury were small to moderate (range: 0.01–0.20). Fracture was found to be positively genetically correlated with both osteoarthritis and suspensory ligament injury. These results suggest that there is a significant genetic component involved in the risk of the studied conditions. Due to positive genetic correlations, a reduction in prevalence of one of the correlated conditions may effect a reduction in risk of the other condition.<p></p&gt

Fast linear algebra is stable

In an earlier paper, we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of $n$-by-$n$ matrices can be done by any algorithm in $O(n^{\omega + \eta})$ operations for any $\eta > 0$, then it can be done stably in $O(n^{\omega + \eta})$ operations for any $\eta > 0$. Here we extend this result to show that essentially all standard linear algebra operations, including LU decomposition, QR decomposition, linear equation solving, matrix inversion, solving least squares problems, (generalized) eigenvalue problems and the singular value decomposition can also be done stably (in a normwise sense) in $O(n^{\omega + \eta})$ operations.Comment: 26 pages; final version; to appear in Numerische Mathemati

Constraint propagation in the family of ADM systems

The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on "asymptotically constrained" systems, we here present constraint propagation equations and their eigenvalues for the Arnowitt-Deser-Misner (ADM) evolution equations with additional constraint terms (adjusted terms) on the right hand side. We conjecture that the system is robust against violation of constraints if the amplification factors (eigenvalues of Fourier-component of the constraint propagation equations) are negative or pure-imaginary. We show such a system can be obtained by choosing multipliers of adjusted terms. Our discussion covers Detweiler's proposal (1987) and Frittelli's analysis (1997), and we also mention the so-called conformal-traceless ADM systems.Comment: 11 pages, RevTeX, 2 eps figure

Ultra-cold atoms in an optical cavity: two-mode laser locking to the cavity avoiding radiation pressure

The combination of ultra-cold atomic clouds with the light fields of optical cavities provides a powerful model system for the development of new types of laser cooling and for studying cooperative phenomena. These experiments critically depend on the precise tuning of an incident pump laser with respect to a cavity resonance. Here, we present a simple and reliable experimental tuning scheme based on a two-mode laser spectrometer. The scheme uses a first laser for probing higher-order transversal modes of the cavity having an intensity minimum near the cavity's optical axis, where the atoms are confined by a magnetic trap. In this way the cavity resonance is observed without exposing the atoms to unwanted radiation pressure. A second laser, which is phase-locked to the first one and tuned close to a fundamental cavity mode drives the coherent atom-field dynamics.Comment: 7 pages, 7 figure

Gravitational field around a screwed superconducting cosmic string in scalar-tensor theories

We obtain the solution that corresponds to a screwed superconducting cosmic string (SSCS) in the framework of a general scalar-tensor theory including torsion. We investigate the metric of the SSCS in Brans-Dicke theory with torsion and analyze the case without torsion. We show that in the case with torsion the space-time background presents other properties different from that in which torsion is absent. When the spin vanish, this torsion is a $\phi$-gradient and then it propagates outside of the string. We investigate the effect of torsion on the gravitational force and on the geodesics of a test-particle moving around the SSCS. The accretion of matter by wakes formation when a SSCS moves with speed $v$ is investigated. We compare our results with those obtained for cosmic strings in the framework of scalar-tensor theory.Comment: 22 pages, LaTeX, presented at the "XXII - Encontro Nacional de Fisica de Particulas e Campos", Sao Lourenco, MG, Brazi

Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations

We present a new many-parameter family of hyperbolic representations of Einstein's equations, which we obtain by a straightforward generalization of previously known systems. We solve the resulting evolution equations numerically for a Schwarzschild black hole in three spatial dimensions, and find that the stability of the simulation is strongly dependent on the form of the equations (i.e. the choice of parameters of the hyperbolic system), independent of the numerics. For an appropriate range of parameters we can evolve a single 3D black hole to $t \simeq 600 M$ -- $1300 M$, and are apparently limited by constraint-violating solutions of the evolution equations. We expect that our method should result in comparable times for evolutions of a binary black hole system.Comment: 11 pages, 2 figures, submitted to PR

Strongly Hyperbolic Extensions of the ADM Hamiltonian

The ADM Hamiltonian formulation of general relativity with prescribed lapse and shift is a weakly hyperbolic system of partial differential equations. In general weakly hyperbolic systems are not mathematically well posed. For well posedness, the theory should be reformulated so that the complete system, evolution equations plus gauge conditions, is (at least) strongly hyperbolic. Traditionally, reformulation has been carried out at the level of equations of motion. This typically destroys the variational and Hamiltonian structures of the theory. Here I show that one can extend the ADM formalism to (i) incorporate the gauge conditions as dynamical equations and (ii) affect the hyperbolicity of the complete system, all while maintaining a Hamiltonian description. The extended ADM formulation is used to obtain a strongly hyperbolic Hamiltonian description of Einstein's theory that is generally covariant under spatial diffeomorphisms and time reparametrizations, and has physical characteristics. The extended Hamiltonian formulation with 1+log slicing and gamma--driver shift conditions is weakly hyperbolic.Comment: This version contains minor corrections and clarifications. The format has been changed to conform with IOP styl

Maximally incompressible neutron star matter

Relativistic kinetic theory, based on the Grad method of moments as developed by Israel and Stewart, is used to model viscous and thermal dissipation in neutron star matter and determine an upper limit on the maximum mass of neutron stars. In the context of kinetic theory, the equation of state must satisfy a set of constraints in order for the equilibrium states of the fluid to be thermodynamically stable and for perturbations from equilibrium to propagate causally via hyperbolic equations. Application of these constraints to neutron star matter restricts the stiffness of the most incompressible equation of state compatible with causality to be softer than the maximally incompressible equation of state that results from requiring the adiabatic sound speed to not exceed the speed of light. Using three equations of state based on experimental nucleon-nucleon scattering data and properties of light nuclei up to twice normal nuclear energy density, and the kinetic theory maximally incompressible equation of state at higher density, an upper limit on the maximum mass of neutron stars averaging 2.64 solar masses is derived.Comment: 8 pages, 2 figure