The dominant electroweak two-loop corrections to the precision observables M(_w) and sin(^2) θ off are calculated in the MSSM. They are obtained by evaluating the two loop Yukawa contributions of ϭ (aas) and ϭ (at2), ϭ (a2ab), ϭ (a2b), to the quantity Ap. A review of the one-loop Standard Model calculation is given in the large Top-Yukawa coupling limit. The 0{aļ), 0{atab), 0{al) result, involving the contributions from Standard Model fermions, sfermions, Higgs bosons and higgsinos, is derived in the gauge- less limit for arbitrary values of the lightest CP-even Higgs boson mass. A thorough discussion of the parameter relations enforced by super symmetry is given. Two different renormalisation schemes are applied. Compared to the previously known result for the quark-loop contribution we find a shift of up to +8 MeV in Mw and —4 X 10—5 in sin2 ^eff- Detailed numerical estimates of the remaining uncertainties of Mw and sin2 もff from unknown higher-order contributions are obtained for different values of the supersymmetric mass scale. The calculations are preceded by a review of EWPO and super symmetry. The electroweak precision variable Ap is defined. We renormalise using both dimensional regularisation and dimensional reduction.

We present results of our studies of various scattering properties of topological and non-topological solitons on obstructions in the form of holes and barriers in (1+1) and (2+1) dimensions. These obstructions, barriers and holes, are inserted into the potential of the theory via the coupling parameter, ${\it ie}$ $\tilde\lambda$, that is effective only in a certain region of space. When $\tilde\lambda>1$ the obstruction is a barrier and when $0<\tilde\lambda<1$ the obstruction is a hole. Our results are based on numerical simulations and analytical considerations for a variety of models. First, we discuss the scattering properties of two models involving a $\varphi^{4}$ potential. In the first model the potential parameter is included in the potential and in the second model the potential parameter is included in the metric. Second, we study various scattering properties of topological solitons in two classes of models, which are the generalisations of the Sine-Gordon model and which have recently been proposed by Bazeia et al. These two classes of models depend on a positive real non-zero parameter $n$ but in this paper we consider the models only for its integer values as when $n=2$ (for the first class) and $n=1$ (for the second class), the model reduce to the Sine-Gordon one. We take the soliton solutions of these models (generalisations of the `kink' solution of the Sine-Gordon model) and consider their scattering on potential holes and barriers. We present our results for $n=1,...6$. We find that, like in the Sine-Gordon models, the scattering on the barrier is very elastic while the scattering on the hole is inelastic and can, at times, lead to a reflection. We discuss the dependence of our results on $n$ and find that the critical velocity for the transmission through the hole is lowest for $n=3$. Next, we discuss various scattering properties of non-topological solitons, Q-balls, on potential obstructions in $\left(1+1\right)$ and $\left(2+1\right)$ dimensions. The dynamics of Q-balls on such obstructions in $\left(1+1\right)$ dimensions is shown to be very similar to that of topological solitons provided that the Q-balls are stable. In $\left(2+1\right)$ dimensions, numerical simulations have shown some differences from the dynamics of topological solitons. We discuss these differences in some detail. Next, we approach the dynamics of various soliton-obstruction systems from analytical perspective and compare the analytical results with the ones observed in numerical simulations. Finally, we show that a realisation of spectral flow as a coordinate transformation for asymptotically four-dimensional solutions can be extended to the non-supersymmetric case. We apply this transformation to smooth geometries describing microstates of the D1-D5-KK monopole system in type IIB supergravity compactified on a six-torus, and obtain solutions with an additional momentum charge. We study the supersymmetric and near-core limits of this construction.

It has been known that the CSW rules correctly reproduce all tree-level scattering amplitudes for perturbative non-abelian gauge theory but fail to explain some of the loop order results. In this thesis we generalise the lagrangian derivation of the rules and account for the missing amplitudes in dimensional regularisation scheme. We analyse generically when the equivalence between MHV rules lagrangian and Yang-Mills lagrangian theory is violated and hence the CSW rules do not apply. We find a type of generalised measure-preserving transformations which when applied to the Yang-Mills lagrangian also produce vertices that have same the helicity structure as the CSW rules. Among these transformations we find in 4-dimensions the canonical transformation generates the MHV vertices that are described by the Parke-Taylor formula. Finally we generalise the canonical transformation on supersymmetric theories. In light-cone gauge the physical components of the N=1 SYM lagrangian are closed under a subgroup of the SUSY transformations. We find the N=1 super Yang-Mills lagrangian can be rewritten in terms of chiral and anti-chiral superfields. In both N=1 and N=4 theories we perform a fermionic integral transformation on superfields analogous to Fourier transform which takes functions from coordinate space into momentum space. The on-shell SUSY generators we derive from the integral transformation agree with the prescription commonly used in the supersymmetry BCFW recursion formula. We apply the canonical transformation on both supersymmetric theories and compute the generic n-point MHV super-vertex. The N=4 MHV super-vertices are shown to agree with Nair's formula which was originally derived from WZW model.

In this thesis, we discuss the observational consequences of extra dimensions on cosmological phenomena. We begin with an overview of extra dimensions, from the initial ideas of Kaluza and Klein to the more recent concept of braneworld models and in particular review the cosmological aspects of the DGP braneworld model, which can produce late time acceleration. We then go on to consider the asymmetric brane model, comparing its cosmology to the standard concordance and DGP models and showing how the asymmetric model can be considered a one-parameter extension of the DGP model over a range of relevant physical scales. Using type Ia supernovae data and the cosmic microwave background shift parameter, the effect of this new parameter on the expansion history of the universe is considered. We then turn our attention to cosmic string loops, which emit bursts of gravitational radiation, produced by cusps and kinks on the loops. We investigate the kinematic effect extra dimensions will have on these gravitational wave bursts and find that the effects of the additional dimensions are more pronounced for cusps than for kinks: cusps are rounded off and their probability of formation is reduced, however, the probability of kink formation is unchanged. Finally, we recompute the gravitational wave bursts taking the various factors into account and look at the implications of this recalculation for the LIGO and LISA gravitational wave detectors, find that both signals, and in particular the cusp signal, have a potentially significant damping, and consider the implications for the detection of extra dimensions.

The research presented in this thesis is concerned with soliton interactions and bound states. We consider a on-topological soliton in (1 + 1) dimensions and topological models in (2 + 1) and (3 + 1) dimensions. In chapter 2 we consider Qballs, which are non-topological solitons, in (1 + 1) dimensions. Here we note the semi-integrable behaviour of small-charge Qballs. This leads us to propose a possible mechanism to explain the two distinct oscillatory modes of a Qball breather. In chapter 3 we are interested in the (2+1)-dimensional baby-skyrme model, which is a lower-dimensional analogue of the Skyrme theory. We discover new chain-like bound-state minimum-energy solutions. We then analyse whether these solutions are the minimum-energy solutions on a cylinder, and then finally on the torus. In chapter 4 we discuss a new (2 + 1)-dimensional model containing a baby skyrmion coupled to a vector meson. This is an analogue of the (3 + 1)-dimensional Skyrme theory containing a vector meson. We use this lower-dimensional analogue to numerically justify the use of a rational map ansatz in the analysis of the (3 + 1)-dimensional skyrmion. Also we analytically prove why the baby-skyrme model, and the model containing a baby skyrmion stabilised by a vector meson, have very similar solutions. Chapter 5 discusses Hopf solitons. Instead of being lumps, Hopf solitons actually resemble loops of string. Their charge is related to the string's knotting and twisting. In this chapter we include an extra mass term in the Skyrme-Faddeev theory; this gives solitons which are exponentially localised. We then explore the infinite-coupling case, which gives compact Hopons. This chapter is part of an ongoing investigation. All of the original research results presented are my own results.

Understanding vertical heat transfer and through flow in porous media such as geothermal reservoirs is of great interest. In a geothermal system, a denser layer of liquid water may overlie a less dense layer of water vapour. Vertical and horizontal thermal diffusion stabilises such configurations, but the buoyancy contrast can cause instability. In this study, the mechanisms contributing to the stability and instability of such systems are analysed using a separate-phase model with a sharp interface be- tween liquid and vapour. The governing equations representing incompressibility, Darcy’s law and energy conservation for each phase are linearised about suitable base states and the stability of these states is investigated. We have considered two different thermal boundary conditions, both with and without a vertical through- flow. In the first case, the boundaries above and below the layer of interest are assumed to be isothermal. We found that due to the competition between thermal and hydrostatic effects, the liquid–vapour interface may have multiple positions. A two-dimensional linear stability analysis of these basic states shows that the Rayleigh–Taylor mechanism is the dominant contributor to instability, but that there are circumstances under which the basic state may be stable, especially when the front is close to one of the boundaries. In the second case, a constant heat flux is imposed at the liquid boundary and a fixed temperature at the vapour boundary. We have shown that competition between the effects of cooling and the viscosity difference between the fluid phases causes multiple liquid-vapour front positions, whether or not gravity is considered. The stability analysis has shown that along with the Rayleigh-Taylor (buoyancy- driven) mechanism, a Saffman-Taylor viscous fingering mechanism can also play an important rule in the transition to instability.

No description available.

Linking number, writhe and twist are three important measures of a curve's geometry. They have been well studied and their de nitions extended to open curves situated between two horizontal planes [1]. However, many applications of these tools involve geometries that have a curved nature to them [2]. For example, the magnetic coronal-loops in the Sun's atmosphere share a spherical boundary (the photosphere). We reformulate these ideas in a spherical geometry, and then explore the oddities of this curved space to show that our new concept is consistent with its older, at counterpart. The second part of this project concerns a series of datasets from plasma experiments at Basic Plasma Science Facility, UCLA, Los Angeles. These experiments involve the creation of ux ropes inside a large (18m) plasma machine. A strong background magnetic eld is applied which ensures that eld lines travel from one end of the cylindrical device to the other. Due to mutual J B forces, the ux ropes twist and tangle about each other. We study three separate datasets: the rst one involving two ux ropes; the second, three ux ropes; the nal two ux ropes. The last experiment is perhaps the most exciting as the plasma velocity has been recorded. This extra data allows us to employ two di erent non-equivalent concepts of magnetic helicity. First, we use the surface ux formulation that makes various ideal assumptions, discarding several terms in Ohm's law. This is compared to helicity calculated by use of winding numbers { a construction without these ideal assumptions. By examining the di erence of these two results, it is shown that we may arrive at a measure of the resistivity present in the system. The plasma investigations described above rely on being able to seed magnetic eld lines across the length of the machine. This is not a simple process. The dataset itself is spatially non-uniform which makes numerical integration to obtain eld lines di cult. Even before integration is considered, a method to interpolate on our data grid of magnetic ux density is needed. This requires further careful considerations. Any interpolator must ensure that the data remains divergence-free; this requirement imposes conditions on the continuity of the derivatives. We have written a code to perform tricubic spline interpolation, and demonstrate that by using a particular method for xing the coe cients, this level of continuity can be achieved.

Recently there has been much interact in the group theoretical investigation of inherent dynamical symmetries of exactly solvable systems such as the non-relativistic Kepler problem, rigid rotator and the isotropic harmonic oscillator. One reason for such a study is that the structure of closely related problems in hadron physics may be studied, namely the use of higher symmetry of interaction® in order to classify the spectrum of the system by the corresponding non-invariance dynamical groups.

No description available.