Boundary element method predictions of the influence of the electrolyte on the galvanic corrosion of AZ91D coupled to steel

This research investigated the galvanic corrosion of the magnesium alloy AZ91D coupled to steel. The galvanic current distribution was measured in 5% NaCl solution, corrosive water and an auto coolant. The experimental measurements were compared with predictions from a Boundary Element Method (BEM) model. The boundary condition, required as an input into the BEM model, needs to be a polarization curve that accurately reflects the corrosion process. Provided that the polarization curve does reflect steady state, the BEM model is expected to be able to reflect steady state galvanic corrosion.

Quantum dynamics of three coupled atomic Bose-Einstein condensates

The simplest model of three coupled Bose-Einstein condensates is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean-field approximation. This semiclassical analysis, using system symmetries, shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points, and our analysis shows that the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, and undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays a dynamical transition. The quantum case has collapse and revival sequences superimposed on the semiclassical dynamics, reflecting the underlying discreteness of the spectrum. Nonzero circular current states are also demonstrated as one of the higher-dimensional effects displayed in this system.

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

An open-boundary integrable model of three coupled XY spin chains

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.

A simplified, sequential, phosphorus fractionation method

Hedley er al. (1982) developed what has become the most widely used land modified), phosphorus (P) fractionation technique. It consists of sequential extraction of increasingly less phytoavailable P pools. Extracts are centrifuged at up to 25000 g (RCF) and filtered to 0.45 mu m to ensure that soil is not lost between extractions. In attempting to transfer this method to laboratories with limited facilities, it was considered that access to high-speed centrifuges, and the cost of frequent filtration may prevent adoption of this P fractionation technique. The modified method presented here was developed to simplify methodology, reduce cost, and therefore increase accessibility of P fractionation technology. It provides quantitative recovery of soil between extractions, using low speed centrifugation without filtration. This is achieved by increasing the ionic strength of dilute extracts, through the addition of NaCl, to flocculate clay particles. Addition of NaCl does not change the amount of P extracted. Flocculation with low speed centrifugation produced extracts comparable with those having undergone filtration (0.025 mu m). A malachite green colorimetric method was adopted for inorganic P determination, as this simple manual method provides high sensitivity with negligible interference from other anions. This approach can also be used for total P following digestion, alternatively non-discriminatory methods, such as inductively coupled plasma atomic emission spectroscopy, may be employed.

Hybrid modelling of coupled pore fluid-solid deformation problems

A hybrid formulation for coupled pore fluid-solid deformation problems is proposed. The scheme is a hybrid in the sense that we use a vertex centered finite volume formulation for the analysis of the pore fluid and a particle method for the solid in our model. The pore fluid formally occupies the same space as the solid particles. The size of the particles is not necessarily equal to the physical size of materials. A finite volume mesh for the pore fluid flow is generated by Delaunay triangulation. Each triangle possesses an initial porosity. Changes of the porosity are specified by the translations of the mass centers of particles. Net pore pressure gradients are applied to the particle centers and are considered in the particle momentum balance. The potential of our model is illustrated by means of a simulation of coupled fracture and fluid flow developed in porous rock under biaxial compression condition.

Computer simulations of coupled problems in geological and geochemical systems

The finite element method is used to simulate coupled problems, which describe the related physical and chemical processes of ore body formation and mineralization, in geological and geochemical systems. The main purpose of this paper is to illustrate some simulation results for different types of modelling problems in pore-fluid saturated rock masses. The aims of the simulation results presented in this paper are: (1) getting a better understanding of the processes and mechanisms of ore body formation and mineralization in the upper crust of the Earth; (2) demonstrating the usefulness and applicability of the finite element method in dealing with a wide range of coupled problems in geological and geochemical systems; (3) qualitatively establishing a set of showcase problems, against which any numerical method and computer package can be reasonably validated. (C) 2002 Published by Elsevier Science B.V.

Integrable open boundary conditions for the Bariev model of three coupled X Y spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

Analysis of acousto-ultrasonic characteristics for contact-type transducers coupled to composite laminated plates

The acousto-ultrasonic (AU) input-output characteristics for contact-type transmitting and receiving transducers coupled to composite laminated plates are considered in this paper. Combining a multiple integral transform method, an ordinary discrete layer theory for the laminates and some simplifying assumptions for the electro-mechanical transduction behaviour of the transducers, an analytical solution is developed which can deal with all the wave processes involved in the AU measurement system, i.e, wave generation, wave propagation and wave reception. The spectral response of the normal contact pressure sensed by the receiving transducer due to an arbitrary input pulse excited by the transmitting transducer is obtained. To validate the new analytical-numerical spectral technique in the low-frequency regime, the results are compared with Mindlin plate theory solutions. Based on the analytical results, numerical calculations are carried out to investigate the influence of various external parameters such as frequency content of the input pulse, transmitter/receiver spacing and transducer aperture on the output of the measurement system. The results show that the presented analytical-numerical procedure is an effective tool for understanding the input-output characteristics of the AU technique for laminated plates. (C) 2001 Elsevier Science Ltd. All rights reserved.

Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach

We obtain the finite-temperature unconditional master equation of the density matrix for two coupled quantum dots (CQD's) when one dot is subjected to a measurement of its electron occupation number using a point contact (PC). To determine how the CQD system state depends on the actual current through the PC device, we use the so-called quantum trajectory method to derive the zero-temperature conditional master equation. We first treat the electron tunneling through the PC barrier as a classical stochastic point process (a quantum-jump model). Then we show explicitly that our results can be extended to the quantum-diffusive limit when the average electron tunneling rate is very large compared to the extra change of the tunneling rate due to the presence of the electron in the dot closer to the PC. We find that in both quantum-jump and quantum-diffusive cases, the conditional dynamics of the CQD system can be described by the stochastic Schrodinger equations for its conditioned state vector if and only if the information carried away from the CQD system by the PC reservoirs can be recovered by the perfect detection of the measurements.

Crack detection in hollow section structures through coupled response measurements

Detection of a circumferential crack in a hollow section beam is investigated using coupled response measurements. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. This matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. The suitability of the mode coupling methodology is first demonstrated analytically. Laboratory test results are then presented for circular hollow section beams with artificially generated cracks of varying severity. It is shown that this method has the potential as a damage detection tool for mechanical structures. (C) 2002 Elsevier Science Ltd. All rights reserved.

Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

Distortional buckling of I-beams by finite element method

Distortional buckling, unlike the usual lateral-torsional buckling in which the cross-section remains rigid in its own plane, involves distortion of web in the cross-section. This type of buckling typically occurs in beams with slender web and stocky flanges. Most of the published studies assume the web to deform with a cubic shape function. As this assumption may limit the accuracy of the results, a fifth order polynomial is chosen here for the web displacements. The general line-type finite element model used here has two nodes and a maximum of twelve degrees of freedom per node. The model not only can predict the correct coupled mode but also is capable of handling the local buckling of the web.

Simulation of galvanic corrosion of magnesium coupled to a steel fastener in NaCl solution

The galvanic corrosion of magnesium alloy AZ91D coupled to a steel fastener was studied using a boundary element method (BEM) model and experimental measurements. The BEM model used the measured polarization curves as boundary conditions. The experimental program involved measuring the total corrosion rate as a function of distance from the interface of the magnesium in the form of a sheet containing a mild steel circular insert (5 to 30 mm in diameter). The measured total corrosion rate was interpreted as due to galvanic corrosion plus self corrosion. For a typical case, the self corrosion was estimated typically to be similar to 230 mm/y for an area surrounding the interface and to a distance of about I cm from the interface. Scanning Kelvin Probe Force Microscopy (SKPFM) revealed microgalvanic cells with potential differences of approximately 100 mV across the AZ91D surface. These microgalvanic cells may influence the relative contributions of galvanic and self corrosion to the total corrosion of AZ91D.

Influence of geometry on galvanic corrosion of AZ91D coupled to steel

The influence of geometric factors on the galvanic current density distribution for AZ91D coupled to steel was investigated using experimental measurements and a BEM model. The geometric factors were area ratio of anode/cathode, insulation distance between anode and cathode, depth of solution film covering the galvanic couple and the manner of interaction caused by two independent interacting galvanic couples. The galvanic current density distribution calculated from the BEM model was in good agreement with the experimental measurements. The galvanic current density distribution caused by the interaction of two independent galvanic couples can be reasonably predicted as the linear addition of the galvanic current density caused by each individual galvanic couple. (c) 2005 Elsevier Ltd. All rights reserved.