Boundary Element Method (BEM) Analysis for Galvanic Corrosion of Hot Dip Galvanized Steel Immersed in Seawater

A numerical analysis of galvanic corrosion of hot-dip galvanized steel immersed in seawater was presented. The analysis was based on the boundary element methods (BEMs) coupled with Newton-Raphson iterative technique to treat the nonlinear boundary conditions, which were determined by the experimental polarization curves. Results showed that galvanic current density concentrates on the boundary of steel substrate and zinc coating, and the sacrificial protection of zinc coating to steel substrate results in overprotection of steel cathode. Not only oxygen reduction but also hydrogen reduction could occur as cathode reactions, which probably led up to the adsorption and absorption of hydrogen atoms. Flat galvanized steel tensile sample shows a brittle behavior similar to hydrogen embrittlement according to the SSRT (show strain rate test) in seawater.

Winkler springs (p-y curves) for liquefied soil from element tests.

In practice, piles are most often modelled as "Beams on Non-Linear Winkler Foundation" (also known as “p-y spring” approach) where the soil is idealised as p-y springs. These p-y springs are obtained through semi-empirical approach using element test results of the soil. For liquefied soil, a reduction factor (often termed as p-multiplier approach) is applied on a standard p-y curve for the non-liquefied condition to obtain the p-y curve liquefied soil condition. This paper presents a methodology to obtain p-y curves for liquefied soil based on element testing of liquefied soil considering physically plausible mechanisms. Validation of the proposed p-y curves is carried out through the back analysis of physical model tests.

Applications of finite element computer modelling and thermal infrared remote sensing to the study of geothermal anomalies

Buried heat sources can be investigated by examining thermal infrared images and comparing these with the results of theoretical models which predict the thermal anomaly a given heat source may generate. Key factors influencing surface temperature include the geometry and temperature of the heat source, the surface meteorological environment, and the thermal conductivity and anisotropy of the rock. In general, a geothermal heat flux of greater than 2% of solar insolation is required to produce a detectable thermal anomaly in a thermal infrared image. A heat source of, for example, 2-300K greater than the average surface temperature must be a t depth shallower than 50m for the detection of the anomaly in a thermal infrared image, for typical terrestrial conditions. Atmospheric factors are of critical importance. While the mean atmospheric temperature has little significance, the convection is a dominant factor, and can act to swamp the thermal signature entirely. Given a steady state heat source that produces a detectable thermal anomaly, it is possible to loosely constrain the physical properties of the heat source and surrounding rock, using the surface thermal anomaly as a basis. The success of this technique is highly dependent on the degree to which the physical properties of the host rock are known. Important parameters include the surface thermal properties and thermal conductivity of the rock. Modelling of transient thermal situations was carried out, to assess the effect of time dependant thermal fluxes. One-dimensional finite element models can be readily and accurately applied to the investigation of diurnal heat flow, as with thermal inertia models. Diurnal thermal models of environments on Earth, the Moon and Mars were carried out using finite elements and found to be consistent with published measurements. The heat flow from an injection of hot lava into a near surface lava tube was considered. While this approach was useful for study, and long term monitoring in inhospitable areas, it was found to have little hazard warning utility, as the time taken for the thermal energy to propagate to the surface in dry rock (several months) in very long. The resolution of the thermal infrared imaging system is an important factor. Presently available satellite based systems such as Landsat (resolution of 120m) are inadequate for detailed study of geothermal anomalies. Airborne systems, such as TIMS (variable resolution of 3-6m) are much more useful for discriminating small buried heat sources. Planned improvements in the resolution of satellite based systems will broaden the potential for application of the techniques developed in this thesis. It is important to note, however, that adequate spatial resolution is a necessary but not sufficient condition for successful application of these techniques.

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations

This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.

A binding site for the cyclic adenosine 3',5'-monophosphate-response element-binding protein as a regulatory element in the grp78 promoter.

The 78-kDa glucose-regulated protein (GRP78) is ubiquitously expressed in many cell types. Its promoter contains multiple protein-binding sites and functional elements. In this study we examined a high affinity protein-binding site spanning bp -198 to -180 of the rat grp78 promoter, using nuclear extracts from both B-lymphoid and HeLa cells. This region contains a sequence TGACGTGA which, with the exception of one base, is identical to the cAMP-response element (CRE). Site-directed mutagenesis reveals that this sequence functions as a major basal level regulatory element in hamster fibroblast cells and is also necessary to maintain high promoter activity under stress-induced conditions. By gel mobility shift analysis, we detect two specific protein complexes. The major specific complex I, while immunologically distinct from the 42-kDa CRE-binding protein (CREB), binds most strongly to the grp site, but also exhibits affinity for the CRE consensus sequence. As such, complex I may consist of other members of the CREB/activating transcription factor protein family. The minor specific complex II consists of CREB or a protein antigenically related to it. A nonspecific complex III consists of the Ku autoantigen, an abundant 70- to 80-kDa protein complex in HeLa nuclear extracts. By cotransfection experiments, we demonstrate that in F9 teratocarcinoma cells, the grp78 promoter can be transactivated by the phosphorylated CREB or when the CREB-transfected cells are treated with the calcium ionophore A23187. The differential regulation of the grp78 gene by cAMP in specific cell types and tissues is discussed.

An extension of Purcell's vector method with applications to panel element equations

The classical Purcell's vector method, for the construction of solutions to dense systems of linear equations is extended to a flexible orthogonalisation procedure. Some properties are revealed of the orthogonalisation procedure in relation to the classical Gauss-Jordan elimination with or without pivoting. Additional properties that are not shared by the classical Gauss-Jordan elimination are exploited. Further properties related to distributed computing are discussed with applications to panel element equations in subsonic compressible aerodynamics. Using an orthogonalisation procedure within panel methods enables a functional decomposition of the sequential panel methods and leads to a two-level parallelism.