We consider a Riemannian manifold M with no focal points such that the universal cover contains a geodesic which does not bound a flat totally geodesically embedded half plane. It is shown that (i) If the non-wandering set of the geodesic flow is the whole of SM , then the closed orbits are dense in SM . (ii) If M is compact then the geodesic flow is ergodic and Bernoulli with respect to the Liouville measure on SM.

This thesis is composed of three independent chapters and an appendix. Each chapter has its own introduction, references and notation. In chapter One a new proof of a theorem of Ruelle about real Perron-Frobenius type operators is given. t This theorem is then extended to complex Perron-Frobenius type operators in analogy with Wielandt's theorem for matrices. Finally two questions raised by Ruelle and Bowen concerning analyticity properties of seta functions for flows are answered. In Chapter Two we improve a result of Ruello on the domain of analyticity of the zeta function for an Axiom A flow. The method used requires results on complex Perron-Frobenius operators derived in the first chapter. These results are reproduced with alternative proofs. Finally, asymptotic estimates for numbers of closed orbits are deduced by analogy with the prime number theorem. This extends a result of Margulis. In the first section of Chapter Three we give a relationship between periodic points and certain equilibrium states for subshifto of finite type. We next study geodesic flows on surfaces of constant negative curvature. We compare the zeta functions of a geodesic flow and a certain suspension flow. These results are then used to recover asymptotic estimates by Margulis and Bowen on the distribution of closed geodesics. Finally new results are given in two special cases. The Appendix is an outline of Bowen's symbolic dynamics for Axiom A flows. This material is purely expository.

The subject matter of this thesis lies within the confines of the mathematical study of finite deformation solid mechanics. The pertinent equations of the field of study are first surveyed. Following this an ad-hoc solution method is developed and used to solve a variety of plane strain problems. The method is compared and contrasted with that of JOHN. A complex variable formulation is developed for finite deformation plane strain problems. Out of this formulation a general solution method for a significant class of materials results. This method is developed and applied to a variety of problems. For one problem the solution is developed to the stage where the deformation field may be plotted. The solution method is compared with that of MUSKHELISHVILI. At all points in the thesis material limitations in the form of inequalities are highlighted where appropriate.

This thesis addresses two similar problems that combine the theory of Coulomb drag with the emerging field of graphene physics. First, the theory of Coulomb drag between two graphene mono-layers is extended to include finite temperature. It is found that the effect is strongly enhanced at intermediate temperatures by coupled plasmon modes. This behaviour is similar to that seen between two dimensional electron gasses. In the second, we investigate the finite temperature polarisability of a graphene bilayer and apply this to the problem of Coulomb drag in a bilayer system. We find that enhancement due to coupled plasmon nodes is suppressed, and dependence of the position and width of the plasmon peak on carrier density and interlayer separation is enhanced.

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This thesis develops a general procedure for the calculation of longitudinal magnetoconductivities in the high field quantum regime, assuming a transport equation of Boltzmann form. Earlier work has been extended, both in the treatment of the scattering problem, and in the generality of the solution to the Boltzmann equation. Potential scattering in a magnetic field is treated via a quasi one-dimensional Schrodinger equation, giving a simple physical picture of the scattering process. The 0 function scatterer is briefly mentioned, while scattering by a cylindrical square well is treated in detail. Green's Function methods for the solution of the scattering equations are developed, and general features of the theory, in particular resonant bound states, are noted. Transport theory is developed from the Kubo formula by resolvent methods, to derive the Boltzmann equation with transition rates given either by the Born approximation or the t-matrix element. A general solution of the Boltzmann equation valid for elastic scattering is derived, involving multiple 'relaxation times' obtained by the inversion of a relaxation matrix. Time dependent relaxation is also treated and shown to involve multiple decay constants related to, but not identical with, the above 'relaxation times'. Regimes in which simple or approximate inversions of the relaxation matrix apply are investigated, in particular ihe quantum limit and isotropic scattering. The above theory is applied to an analysis of the electron-holedroplet (EHD) magnetoresonance of germanium. The practicability of the relaxation matrix method is shown, and accurate analytical approximations to the solution obtained. The experimentally observed features are explained by the analysis, which shows how accurate estimates of the droplet radius· may be obtained from the data. Further resonances are predicted which, if observed, will reinforce these estimates. Certain features of the analysis also suggest that the strength of EHO's as scattering potentials is less than has been previously assumed.

I examine some logical and epistemological problems arising in quantum theory. Two historical episodes are considered in detail: Planck's adoption of the quantum hypothesis and Heisenberg's discovery of matrix mechanics. The former episode is, I argue, more compa tLbLe with logical empiricist views of scientific progress than it is with more recent and currently influential philosophies. My examination of the latter concerns the influences - epistemological as well as.sci~ntific- which may have affected the manner in which Heisenberg chose to present. his discoveries; these considerations a~low me to rebut ... the suggestion that Heisenberg's practice was incompatible with his professed views and to counter the claim that this episode provided unwarranted support to formalistic ideas concerning scientific explanation. The connexions between Bohr's principle of complementarity and logical empiricist views concerning language change in science are explored, and I argue that the transition from classical to quantum mechanics· can be seen as involving a shift in the meanings of "position" and "momentum" so that these terms obtain unambiguous empirical meanings from the viewpoint of quantum· theory. Discussing the relevance of quantum mechanics to logic I contend that, although classical logic may be retained, empirical considerations may make it advisable to adopt a non-classical logic for quantum theory. An analysis of Bell' s inequality.:is a prelude to some speculations concerning the interpretation of quantum theory. I examine the possibility of interpreting the formalism as descriptive not of an external world but of the expectati.ons of subjects. The final chapter explores the relevance of physics to questions concerning human freedom. Classical physics, I argue, did not have the devastating implications for personal autonomy that it was often assumed to have; quantum physics does not explain . human freedom but, under certain assumptions, it does show how it is possible.

La actual situación energética estimula el uso de las tecnologías de cogeneración y trigeneración como posibles soluciones para alcanzar el ahorro de energía primaria deseado. Estas tecnologías pueden ser una alternativa atractiva a los sistemas convencionales para el suministro energético en edificios. En esta tesis se identifican y modelan diferentes configuraciones de trigeneración avanzadas que potencialmente pueden ofrecer una mayor eficiencia energética en comparación con los sistemas convencionales para aplicaciones en edificios.