An innovative research study was established at IGER, North Wyke, Devon, to investigate preferential flow through a poorly structured relatively impermeable soil. Macropore channels were added by a mole plough in order to investigate soil water pathways and chemical transport in a soil in which preferential flow was guaranteed. The investigation focused on water and solute movement through specific flowpaths, namely macropores and mesopores, and the interaction between mobile and immobile zones within the soil. Two large soil blocks (1 m2 by 0.85 m) of the Hallsworth series were removed from the field and placed on sand tables so that a suction could be induced at the base of the soil block. The edge was sealed using paraffin wax. Eight tensiometers and suction cup lysimeters were installed in each block together with fifteen pairs of time-domain reflectometry wave guides. A regular spacing pattern was employed so that spatial variations could be easily identified. Samples were collected from suction cup lysimeters every 4 hours. Soil water status was observed from the TDR probes daily and from tensiometers every 10 minutes. Five tracer experiments were conducted; three involved the miscible displacement of chloride at concentrations of 100 and 250 mg I"' and two used nitrate (500 mg l ') and chloride (2500 mg 1') applied as a pulse. Tracer and irrigation water was applied through a misting system at an irrigation rate of 2.76 mm h-1. Three techniques were used to examine soil structure in the macropore and mesopore pore size range to investigate potential flowpaths in more detail. The profile tracing method (PTM). binary transect method (BTM) and resinated core section method (RCSM) provided useful quantitative structural information. Soil water status averaged over a large sampling volume (TDR, 1540000 mm3) was considered to be stable through time. Detailed observations of soil water suction using tensiometers showed that soil water conditions remained unsaturated, at approximately 10 to 20 cm H2O, and varied by 3 cm H2O throughout the experiment. Suction varied depending on the location of each tensiometer with respect to position within or between aggregates. Results based on Poiseuille's law and suction data showed that the flowpaths were predominantly mesopores. This result was supported by breakthrough curve analysis for the bulk of the soil although macropore flow was observed towards the mole drain. Flow rates observed from tracer movement varied throughout the soil regardless of depth. Chloride moved quickly towards the mole drain and the arrival of tracer was recorded within 4 hours. Time to breakthrough monitored at the suction cups varied from 4 to 76 hours. When the concentration gradient between applied solute and antecedent solute was large, reduced time to attain peak concentration was noted. As the concentration gradient reduced, speed of rise to peak concentration increased. An advection-dispersion model (CLEARY) fitted change in observed solute concentration through time at the suction cup lysimeters well. The study concluded that although water moved rapidly through the soil, the tortuous nature and increased contact with soil particles encountered as water moved through the mesopores resulted in water with matrix flow solute characteristics.

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This thesis describes a technical advance in the treatment of massive fermion two-loop calculations in QED and QCD, which allows us to reduce complicated on-shell Feynman integrals tö-a-large number-of simpië integrals, and one particularly complicated, but evaluable, one. The method extends the work of Chetyrkin and Tkachov to massive integrals, and is applicable to on-shell mass and wavefunction renormalisation. After an extensive review of the relevant areas of renormalisation, and of the rôle of quark masses in current algebra, we go on to use the extended technique to extract the fermion mass and wavefunction renormalisation constants to O(?²_s), and to relate the running and pole masses to the bare mass and to each other. We find that the ratio of the running to the pole mass may be rather smaller than might be expected, which allows us to claim a perturbative source for a larger proportion of the strange quark constituent mass than has been usual before. In passing, we extract a number of two-loop renormalisation group coefficients, and find ourselves to be in agreement with other calculations. We also find that the on-shell fermion wavefunction renormalisation constant is quite unexpectedly gauge invariant to two loops, and that it is relatively simply related to the mass renormalisation constant. We suggest that this is the result of such intricate calculations that there must be a field-theoretic explanation waiting to be uncovered. We relate our results to the effective theory of a static quark.

Since the advent of Quantum Field Theory (QFT) in the late 1940's, perturbation theory has become one of the most developed and successful means of extracting phenomenologically useful information from a QFT. In the ever- increasing enthusiasm for new phenomenological predictions, the mechanics of perturbation theory itself have often taken a back seat. It is in this light that this thesis aims to investigate some of the more fundamental properties of perturbation theory. The benefits of resumming perturbative series are highlighted by the explicit calculation of the three-jet rate in e+e- annihilation, resummed to all orders in leading and next-to-leading large logarithms. It is found that the result can be expressed simply in terms of exponentials and error functions. In general it is found that perturbative expansions in QED and QCD diverge at large orders. The nature of these divergences has been explored and found to come from two sources. The first are instanton singularities, which correspond to the combinatoric factors involved in counting Feynman diagrams at large orders. The second are renormalon singularities, which are closely linked to non-perturbative effects through the operator product expansion (OPE).By using Borel transform techniques, the singularity structure in the Borel plane for the QCD vacuum polarization is studied in detail. The renormalon singularity structure is as expected from OPE considerations. These results and existing exact large-A^/ results for the QCD Adler D-function and Deep Inelastic Scattering sum rules are used to resum to all orders the portion of the QCD perturbative coefficients which is leading in b, the first coefficient of the QCD beta-function. This part is expected asymptotically to dominate the coefficients in a large-Nj expansion. Resummed results are also obtained for the e+e- R-ratio and the r-lepton decay ratio. The renormalization scheme dependence of these resummed results is discussed in some detail.

Aspects of the Affine Superalgebra sl(2|l) at Fractional Level Ph.D. Thesis by Gavin Balfour Johnstone, April 2001 In this thesis we study the affine superalgebra sl(2|l; C) at fractional levels of the form k = l/u-l,uєN\{l}. It is for these levels that admissible representations exist, which transform into each other under modular transformations. In the second chapter we review background material on conformal field theory, particularly the Wess-Zumino-Witten model and the connection with modular transformations. The superalgebra sl(2|l;C) is introduced, as is its affine version. The next chapter studies the modular transformation properties of sl(2|l;C) characters. We derive formulae for these transformations for all levels of the form K = 1/u-1,uєN\{1}. We also investigate some modular invariant combinations of characters and find two series of modular invariants, analogous to the A- and D-series of the classification of sl{2) modular invariants. In chapter 4 we turn to the study of fusion rules. We concentrate on the case k = -1/2. By considering the decoupling of singular vectors, we are able to find consistent fusion rules for this particular level. These fusion rules correspond to a modular invariant found in chapter 3. This study suggests that one may consistently define a conformal field theory based on sl(2|l;C) at fractional level.

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Thesis (Ph. D.)--University of Hawaii at Manoa, 1994. / Includes bibliographical references (leaves 185-186). / Microfiche. / xviii, 186 leaves, bound ill. 29 cm