Steel Engraved print featuring a portrait of William H. Seward

An oval shaped portrait of William H. Seward. The print is ornately decorated with numerous fleurs-de-lis. published by Virtue & Yorston (British, ca. 1859?-1890s?)https://scholarsjunction.msstate.edu/fvw-prints/1910/thumbnail.jp

Mixed formulations for the convection-diffusion equation

This thesis explores the numerical stability of the stationary Convection-Diffusion-Reaction (CDR) equation in mixed form, where the second-order equation is expressed as two first-order equations using a second variable relating to a derivative of the primary variable. This first-order system uses either a total or diffusive flux formulation. Westart by numerically testing the unstabilised Douglas and Roberts classical discretisation of the mixed CDR equation using Raviart-Thomas elements. The results indicate that,as expected, for both total and diffusive flux, the stability of the formulation degrades dramatically as diffusion decreases.Next, we investigate stabilised formulations that are designed to improve the ability of the discrete problem to cope with problems containing layers. We test the Masud and Kwack method that uses Lagrangian elements but whose analysis has not been developed.We then significantly modify the formulation to allow us to prove existence of a solution and facilitate the analysis. Our new method, which uses total flux, is then tested for convergence with standard tests and found to converge satisfactorily over a range of values of diffusion.Another family of first-order methods called First-Order System of Least-Squares (FOSLS/LSFEM) is also investigated in relation to solving the CDR equation. These symmetric,elliptic methods do not require stabilisation but also do not cope well with sharp layers and small diffusion. Modifications have been proposed and this study includes aversion of Chen et al. which uses diffusive flux, imposing boundary conditions weakly in a weighted formulation.We test our new method against all the aforementioned methods, but we find that other methods do not cope well with layers in standard tests. Our method compares favourably with the standard Streamline-Upwind-Petrov-Galerkin method (SUPG/SDFEM), but overall is not a significant improvement. With further fine-tuning, our method could improve but it has more computational overhead than SUPG.This thesis explores the numerical stability of the stationary Convection-Diffusion-Reaction (CDR) equation in mixed form, where the second-order equation is expressed as two first-order equations using a second variable relating to a derivative of the primary variable. This first-order system uses either a total or diffusive flux formulation. Westart by numerically testing the unstabilised Douglas and Roberts classical discretisation of the mixed CDR equation using Raviart-Thomas elements. The results indicate that,as expected, for both total and diffusive flux, the stability of the formulation degrades dramatically as diffusion decreases.Next, we investigate stabilised formulations that are designed to improve the ability of the discrete problem to cope with problems containing layers. We test the Masud and Kwack method that uses Lagrangian elements but whose analysis has not been developed.We then significantly modify the formulation to allow us to prove existence of a solution and facilitate the analysis. Our new method, which uses total flux, is then tested for convergence with standard tests and found to converge satisfactorily over a range of values of diffusion.Another family of first-order methods called First-Order System of Least-Squares (FOSLS/LSFEM) is also investigated in relation to solving the CDR equation. These symmetric,elliptic methods do not require stabilisation but also do not cope well with sharp layers and small diffusion. Modifications have been proposed and this study includes aversion of Chen et al. which uses diffusive flux, imposing boundary conditions weakly in a weighted formulation.We test our new method against all the aforementioned methods, but we find that other methods do not cope well with layers in standard tests. Our method compares favourably with the standard Streamline-Upwind-Petrov-Galerkin method (SUPG/SDFEM), but overall is not a significant improvement. With further fine-tuning, our method could improve but it has more computational overhead than SUPG

Geology of the south half of the Meramec Spring Quadrangle, Missouri

This report is a continuation of the work initiated by Mueller in his mapping of the north half of the Meramec Spring Quadrangle. The completion of this work provides not only a geologic map of the whole quadrangle but also completes the mapping of the geology of a strip of quadrangles extending from Rolla to the Mississippi River. In addition to being a step closer to the goal of complete geologic coverage for the state, this work will be of value to those concerned with the prediction of depths of wells drilled in search for water, which in view of the drought of the past year may become increasingly important in the near future. The study is confined to the geology and associated features of this region. Additional data have been included where the author believes it to be of interest or to add to the general value of the report --Introduction, page 1

Some fluoride ion-initiated reactions of fluoroethylenes

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Corneal grafting: what eye care workers need to know

This article provides guidance to eye care workers who want to know who should be referred for a corneal graft and what complications they may need to manage after patients have had their operation

Clinical auditing to improve patient outcomes

Clinical audit is about measuring the quality of care we provide against relevant standards. If we are failing to meet these standards, the audit should help us understand the factors that are causing us to fail, so that we can set priorities and make improvements