In the experiment E683 at Fermi National Accelerator Lab (FNAL) in Batavia, Illinois, a modular, high-energy sampling calorimeter was the basis of the detector system. In order to monitor each of the 528 modules of the calorimeter, an embedded LED was flashed directly into each of the 528 PMT tubes (which normally pick up the light from the sampling modules of the calorimeter) and their responses were recorded. The purpose of this investigation was to observe, study, and possibly make corrections for any fluctuations in the PMT response to the LED signals. Also, as a check, the PMT data was analyzed to see if any LED fluctuations were correlated with any fluctuations in the calorimeter module data coming from particles produced when targets were exposed to accelerator beam particles. These studies were done using a VAXstation model 4000/60, and the database and graphics components (called 'N-tuples' and `PAW' respectively) of a High Energy Physics math package called 'CERNLIB'. By putting the analyzed data into n-tuple files, many different modelings of the same data could be checked more efficiently. The study found that the LED system was useful for detecting and correcting for signal degradation due to calamp failure and these corrections were put in the E683 analysis package. It was also found that long term LED response signal fluctuations were not completely explained, but that there was no correlation with beam induced calorimeter response signal fluctuations. / Department of Physics and Astronomy

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In this thesis, we study the complex sine-Gordon model on a half line. The model in the bulk is an integrable (l+1) dimensional field theory which is U(1) gauge invariant and comprises a generalisation of the sine-Gordon theory. It accepts soliton and breather solutions. By introducing suitably selected boundary conditions we may consider the model on a half line. Through such conditions the model can be shown to remain integrable and various aspects of the boundary theory can be examined. The first chapter serves as a brief introduction to some basic concepts of integrability and soliton solutions. As an example of an integrable system with soliton solutions, the sine-Gordon model is presented both in the bulk and on a half line. These results will serve as a useful guide for the model at hand. The introduction finishes with a brief overview of the two methods that will be used on the fourth chapter in order to obtain the quantum spectrum of the boundary complex sine-Gordon model. In the second chapter the model is properly introduced along with a brief literature review. Different realisations of the model and their connexions are discussed. The vacuum of the theory is investigated. Soliton solutions are given and a discussion on the existence of breathers follows. Finally the collapse of breather solutions to single solitons is demonstrated and the chapter concludes with a different approach to the breather problem. In the third chapter, we construct the lowest conserved currents and through them we find suitable boundary conditions that allow for their conservation in the presence of a boundary. The boundary term is added to the Lagrangian and the vacuum is reexamined in the half line case. The reflection process of solitons from the boundary is studied and the time-delay is calculated. Finally we address the existence of boundary-bound states. In the fourth chapter we study the quantum complex sine-Gordon model. We begin with a brief overview of the theory in the bulk where the semi-classical spectrum and an exact S'-matrix are presented. Following that we use the stationary phase method to derive the semi-classical spectrum of boundary bound states. The bootstrap method is used as an alternative approach to obtain the same spectrum. The results are discussed and compared. The final chapter consists of a general discussion on open questions and problems of the model, and some proposals for further research.

Unitary models in two dimensions are classes of low dimensional theories which provide us with a convenient theoretical laboratory for studying various aspects of the theory of elementary particles. In this thesis, purely bosonic U(N) sigma models with the Wess-Zuraino-Witten (WZW) term in two-dimensional Euclidean space and the supersymmetric (Susy) U(N) σ models with and without this term are discussed. Particular attention is paid to the classical solutions of the equations of motion of these models. Due to the integrabihty of these models, we can associate with them a Lax-pair formalism. We observe that solutions of the Lax-pair equations of the U(N) a model provide us with solutions of the U(N) a model with the WZW-term. This is also the case for solutions of the Susy U(N) a model with the WZW-term which can be constructed from solutions of the Lax-pair equations of the Susy U(N) σ model. We present also some explicit solutions of the Susy U(N) a model without the WZW-term. Many properties of the constructed solutions for both the purely bosonic and Susy models are explored. In particular, we calculate the values of the action for some solutions and study the stability properties of these solutions and find that all the constructed solutions of these models correspond to the saddle points of the action. Finally we consider the hnearized fermion equations in the fixed background of a bosonic field. Special attention is paid to the case when the background field is given by a solution of the U(N) σ model with and/or without the WZW-term. Some classes of solutions of this problem are presented and their properties are discussed. We observe that a class of these solutions is related to the components of the energy-momentum tensor of the purely bosonic σ model and prove that some of these solutions are traceless.

Low dimensional models are generally regarded to be a convenient theoretical laboratory for studying various aspects of elementary particle theory. In this thesis, the extended solutions of one particular class of such models, namely the ₵p(^n-1) non-linear a-models in 2 dimensions, are discussed. Special attention is paid to the shape of these extended structures and their dependence on the parameters of the solutions. Time dependence is introduced into the models, and properties of the moving objects in these (2 + l)-dimensional theories are explored. In particular, the Hopf terms of the theories are investigated, and their relation to the spin of the extended solutions is discussed. Also the classical dynamics of these moving objects, and their explanation in terms of the geodesic motions on certain Hermitian and Kāhler manifolds is considered. Finally the embedding of the (₵p(^n-1)) solutions into the 2-dimensional U(n) chiral models is studied, paying particular attention to the stability of these embedded solutions in the larger group space, and to the number of independent negative modes of the fluctuation operator around these solutions.

A systematic study of the microstructures of particulate material from the Tamar Estuary using a BET nitrogen adsorption technique has been carried out. The results showed that suspended material had a higher BET surface area (approximately 20m²/g ) than the associated sediments (approximately 13m²/g) . Also the BET surface areas (8-20m²/g) of suspended material collected during axial transects (S = 0-30°/oo) of the Tamar Estuary indicated relatively higher BET surface areas in the turbidity maximum zone as compared to material from up or down estuary. The BET surface areas were inversely related to the carbon content of the particles and although the role of Fe and Mn coatings was examined no definitive relationship to BET surface area was evident. Analysis of nitrogen adsorption-desorption hysteresis loops indicated the pores to be of the parallel plate or slit type in the size range <2-50 nm. The shape and dimensions of these pores would accomodate the penetration of metal ions, like Zn and Cu, into the pore spaces in the particle matrix. A method was designed to enable the analysis of natural Zn and Cu concentrations in small volumes extracted from a reactor on a timescale suitable for kinetic analysis. Dissolved Cu and Zn adsorption-desorption experiments were carried out under controlled conditions using Tamar suspended solids as the adsorbents. The uptake and release profiles were interpreted in terms of a two stage reaction mechanism which involved both surface adsorption and solid state diffusion into the pores. Rate constants were derived from a kinetic analysis to enable evaluation of the chemical timescales of the sorption reactions. When compared to field data of Zn distributions in the Tamar Estuary the time constants allowed a reasoned explanation of the observations. They also pointed to a strong coupling between the physical and chemical timescales within estuaries. This work has indicated an association between trace metal sorption reaction rates and estuarine particle microstructure. These rate constants are of value in the refinement of hydrodynamic models and this study has implications for the availability of trace metals for biological or chemical remobilisation.

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We compute the σ(α3/8) virtual QCD corrections for the process e+e- →qqg arising from the interference of the two-loop and tree amplitudes and from the self-interference of the one-loop amplitude. The results are presented in the form of both matrix elements and helicity amplitudes. The calculation of the matrix elements is performed by the direct evaluation of the Feynman diagrams and corresponding loop integrals. The helicity amplitudes are derived in a scheme-independent way from the coefficients appearing in the general expression for the tensorial structure of this process. The tensor coefficients are then extracted from the Feynman diagrams by means of projectors. The one- and two-loop integrals appearing in the amplitudes are reduced to a small set of known master integrals by means of integration-by-parts identities. This reduction has been automated by construction of an algorithm based on that proposed by Laporta. The infrared pole structure of both the matrix elements and helicity amplitudes is shown to agree with the predictions made by the infrared factorisation formula of Catani. The analytic results for the finite terms, regularised in conventional dimensional regularisation and renormalised in the MS scheme, are presented, expressed in terms of one- and two-dimensional harmonic polylogarithms.

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