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Increasingly, tunnels are being planned in weak rock beneath urban areas in Australia and worldwide. Designers of these projects are required to predict the tunnel induced settlement so that an assessment of the possible effects on buildings and services above can be made. However, the existing methods for making such predictions require either a database of similar projects, or a knowledge of suitable parameters for use in numerical models. Numerical models of tunnelling are sensitive to model inputs. Some of these model inputs are irrelevant to the actual physical problem. The thesis discusses two key issues in solving elastoplastic tunnel problems, one being the inertial effects in finite difference methods, and the other being the mesh discretisation error. The causes and possible remedies for these is discussed, and an a priori predictive technique for discretisation error is developed. The method of choice for selecting parameters in numerical models is to use the backanalysis of a suitable pilot activity. However, traditional backanalysis methods suffer from non-uniqueness. The results of a backanalysis is not a single combination of parameters, but a zone in parameter space within which the fit to the observations is acceptable. The shape of this zone in parameter space is affected by the degree of correlation of the parameters, and by the non-linear nature of the problem. The technique of predictive analysis solves the problem of non-uniqueness in parameter estimation by backanalysis by choosing the point in parameter space which gives the most adverse prediction for the future construction, yet which maintains a reasonable fit to the pilot activity. The thesis uses three reference projects in Australia to show the techniques of backanalysis and predictive analysis. Cross sections of the Brisbane Rail Tunnels are backanalysed, and the resulting range in parameter space is discussed. For prediction of settlement in the New Southern Railway tunnel in Sydney, and the South East Transit project in Brisbane, the weak rock pressuremeter is proposed as a suitable and inexpensive pilot activity for the future tunnel construction. The results of the predictive analysis show that the method works. Therefore an improved method of predicting tunnel induced settlement in shallow tunnels is proposed, using the combination of numerical modelling, the weak rock pressuremeter and predictive analysis.

Inspired by the success of the ring-polymer molecular dynamics (RPMD) method, we derive a transition-state-theory version (RPTST) with a dividing surface which is, in general, conical in ring-polymer space. It is explained why this conical form is a good approximation to the optimal dividing surface and therefore why centroid-based quantum transition-state theories are inaccurate for asymmetric barriers at low temperatures. The geometry of the ring-polymer transition state is found to describe a finite-difference approximation to the semi-classical instanton trajectory (a classical periodic orbit of length βħ on the inverted potential). Based on this, a new practical method for locating multidimensional instantons is proposed, by computing saddle points on the ring-polymer surface, and a derivation for the reaction rate constant based on the "ImF" premise using the ring-polymer formalism is shown to be far simpler than in previous instanton approaches based on functional determinants. The resulting expression is based only on the ring-polymer potential at the transition-state and its Hessian, and is applied to evaluate the rate in a number of polyatomic systems. We show that a free-energy version of the ImF instanton theory is related to RPTST and thereby provide an explanation for why RPMD produces accurate results for thermal reaction rates in the deep-tunnelling regime and demonstrate how it can be made more efficient and systematically improved. From this, we also explain why RPMD is seen to underestimate the rates of symmetric reactions and overestimate the rates of asymmetric reactions. We also present a ring-polymer instanton derivation of a theory for calculating tunnelling splittings leading to another new practical method, which owing to its simple form, is easily extended to determine the entire tunnelling-splitting pattern of molecular clusters with two or more degenerate wells. This method is applied to the water dimer, trimer, and octamer, and shown to be in good overall agreement with experiment and to provide a deeper understanding of the tunnelling pathways.

In this thesis, four different numerical techniques are implemented for the purpose of simulating resonant tunnelling diodes (RTDs). The chosen methods were: piecewise constant transfer matrix (TMM-C), piecewise linear transfer matrix (TMM-L), quantum transmitting boundary method (QTBM), and the Crank-Nicolson method (CN). The numerical methods converged compared with the known analytic simulation for plane waves tunnelling through a single barrier. To better represent the semiconductor-based RTDs, the effective mass approximation was adopted with accompanying modifications to the Hamiltonian operators to ensure the continuity of the wave function and its derivative. Using the Tsu-Esaki formula, the current density was calculated as a function of bias voltage for two different RTD devices. The numerically obtained current density was of the same order of magnitude as referenced experimental values but differed significantly enough to require better models if engineering applications are decided. The models in this thesis were able to display resonant tunnelling and a negative differential resistance (NDR), giving them plausible educational value.

The discovery of high-temperature superconductivity in 1986 in copper-oxide materials have opened up new avenues to investigate new families of quantum materials that were previously not known. Understanding the mechanism of superconductivity in high-T[sub]c superconductors has been an important research theme in condensed matter physics, as it is believed to be essential to realize the next generation engineered materials that become superconducting at room temperature. Discovered in 2006, iron based superconductors are a new addition to the family of high-T[sub]c superconductors, these materials exhibit several interesting properties and show some vivid similarities with cuprates and other families of high-temperature superconductors. In this thesis, I will present the spin-polarized scanning tunneling microscopy (SPSTM) study carried out on the parent compound of iron chalcogenide high temperature superconductor Fe[sub](1+y)Te to investigate the bi-collinear antiferromagnetic order. Magnetic tips in this work are prepared using a novel preparation technique by picking up excess iron atoms and clusters of FeTe from the surface of the sample. Next, I will present the SP-STM results obtained in the spin glass phase of Fe[sub](1+y)SeₓTe₁₋ₓ visualizing the interplay between the short ranged bi-directional bi-collinear antiferromagnetic order and superconductivity at the atomic scale. In this thesis, I will also present the scanning tunneling microscopy and spectroscopy (STM/STS) study of the native and engineered defect bound states in the iron-pnictide superconductor LiFeAs. This study addresses the pairing symmetry of the superconducting order parameter and understanding of dip-hump features seen in STM spectra outside the superconducting gap in iron pnictide superconductor LiFeAs.

Multidimensional quantum tunnelling is an important tool that is used in many areas of physics and chemistry. Sub-barrier fusion reactions of heavy-ions are governed by quantum tunnelling. However, the complexity of the structures of heavy-ions does not allow us to use simple one-dimensional tunnelling equations to and the tunnelling probabilities. Instead of this one should consider all the degrees of freedom which affect the phenomenon and accordingly the intrinsic structure or the deformation of the nuclei must be taken into account in the modelling of heavy-ion fusion. These extra degrees of freedom result in a coupling potential term in the Schrodinger equation of the fusing system. In this thesis 16O + 238 U system is considered. Only the rotational deformation of Uranium is assumed and the coupling potential term is calculated for this system by using two diffrent potential types, namely the Woods-Saxon potential and the double folding potential. Using this term in the Schrodinger equation fusion probability and theoretical cross section are calculated. A discussion that addresses then necessity of multidimensional formulation is given. Besides this point the effects of the choice of the potential type are shown.

The study of cuprate high-temperature superconductors has undergone a recent resurgence due to the discovery of charge order in several families of cuprate materials. While its existence is now well established, little is known about its microscopic origins or its relationship to high-temperature superconductivity and the pseudogap. The aim of the research presented in this thesis is to address these questions. In this thesis I will report on the use of spectroscopic-imaging scanning tunnelling microscopy (SI-STM) to visualise the short-ranged charge density wave (CDW) in Bi₂Sr₂CaCu₂O₈₊ₓ and NaxCa₂₋ₓCuO₂Cl₂. Building on previous measurements of the intra unit-cell electronic structure of cuprates, I introduce sub-lattice segregated SISTM to individually address the atomic sub-lattices in the CuO₂ plane with spatial phase sensitivity. Using this technique I establish that the CDW in Bi₂Sr₂CaCu₂O₈+x and NaxCa₂₋ₓCuO₂Cl₂ has a previously unobserved d-symmetry form factor, where a breaking of rotational symmetry within the unit cell is modulated periodically in space. Towards identifying a mechanism of CDW formation, I establish that the amplitude of CDW modulations in the electronic structure are maximal at the pseudogap energy-scale and that these modulations exhibit a spatial phase difference of π between filled and empty states. Together with the doping evolution of the CDW wave-vector this highlights the role of the low-energy electronic structure of the pseudogap regime in CDW formation. To elucidate the relationship between the CDW and the superconducting condensate I will introduce nanometer resolution scanned Josephson tunnelling microscopy (SJTM). In this approach the Cooper pair (Josephson) tunnelling current between a Bi₂Sr₂CaCu₂O₈₊ₓ sample and a scan-able Bi₂Sr₂CaCu₂O₈₊ₓ nano-flake STM tip is used to directly visualise the superconducting condensate. I will report the observation of a periodic modulation in the Cooper pair condensate at the same wave-vector as the CDW, the first direct detection of a periodically modulating condensate in any superconductor.

Säkerhet är ständigt en primär fråga vid byggnation, detta innefattar även drivning av tunnlar. För att förhindra ras eller utglidning av block undersöks och klassificeras därför berget. Tunneln som undersöks i denna studie kostar ungefär 7000 kr/timme att driva. Därför finns det mycket pengar att spara på effektivisering av arbetsmoment, däribland kartering. I denna uppsats jämförs därför tre olika karteringsmetoder såsom konventionell kartering, fotogrammetri och laserskanning. De olika metodernas Q- och RMR-index jämförs sedan med hänsyn till de olika ingående parametrarna i klassificeringssystemen.    Syftet med studien är att studera om de nya karteringsmetoderna har några ekonomiska och/eller säkerhetsmässiga fördelar, samt även eventuella fördelar vad gäller lagring av bergets kvalitet och egenskaper i digitalt format. Därutöver även att studera om de nya teknikerna kan ersätta den konventionella karteringsmetoden helt eller till viss del.     Laserskanning och fotogrammetri kan inte helt ersätta dagens konventionella kartering. Detta på grund av att alla parametrar för klassificeringssystemen inte kan observeras/tolkas i de framställda digitala modellerna, utan måste göras på plats. Dock kan de digitala metoderna kombineras med den konventionella och därmed är en fullständig kartering och klassificering möjlig. Däremot finns andra fördelar med de digitala metoderna såsom digitala lagringsmöjligheter, detaljrika lättolkade modeller och att de är tidseffektiva över längre sträckor. / Safety is always a primary concern during construction, even during tunnel construction. To prevent rock fall or sliding of blocks the rock has to be examined and classified. The tunnel examined in this report costs about 7000 SEK/hour to construct. Therefore, a lot of money can be saved by streamlining the work process, including mapping of geological structures. In this paper three mapping methods are compared, such as traditional geological mapping, photogrammetry and laser scanning. The Q and RMR index from the three different methods are then compared with respect to the various parameters included in the classification systems.    The purpose of this study is to find out whether the new mapping methods have any financial and/or safety benefits, as well as any potential benefits in terms of storage in digital format of information about the rock quality and features, or not. The purpose is also to examine if the new technologies could replace the traditional mapping method fully or partially.     Laser scanning and photogrammetry cannot completely replace today’s conventional mapping. This is because some of the parameters are not possible to be observed and interpreted in the produced digital models, but must be done in situ. However, there are other benefits of the digital methods such as digital storage capabilities, detailed, easily interpretable models and that it takes less time to map large areas or long distances.

This thesis addresses the tunnelling of charge carriers in different materials. First looking at the simplest case of electron tunnelling in metals at zero, then finite temperature, the current is obtained using the Fermi-Dirac golden rule and then the conductance is obtained. This is extended to take into account the spatial dependence of one of the metals being a tip since experimentally this is done by scanning tunnelling microscopy where a tip traces over the surface of a sample. The next step is to look at tunnelling between a metal and a semiconductor, again the current is found. Semiconductors can be doped and the effect this has on tunnelling is examined. Next superconductors are introduced. The purpose of my research has been to look at the tunnelling spectra of high-temperature superconducting cuprates for both extrinsic (metal-superconductor) and intrinsic (superconductor-superconductor) tunnelling. The main features seen experimentally with cuprate tunnelling are identified and then a theory capable of explaining these features is discussed. The theory is compared to experimental results and we find good agreement.

Earth pressure balance (EPB) tunnelling machines are commonly used for the construction of tunnels in soft soils. These machines use the excavated soil in a pressurised head chamber to apply a support pressure to the tunnel face during excavation. How well an unstable face is supported in an EPB machine depends on effectively transferring a constant pressure from the support medium to the surface of the face. If the support pressure is not constant, but instead changes, the varying pressure inevitably leads to collapse of the face or heave on the surface ground. A machine may be designed to work in “Ideal ground” conditions. However, natural soils rarely have these properties, and conditioning of the soil is usually necessary to change its properties to suit the machine. Effective soil conditioning significantly improves the machine performance and control of the soil flow through the screw conveyor. However, for soil conditioning as commonly used in practice, the effects of different conditioning treatments on soil properties and the machine performance are not clearly understood, and problems with EPB machine operations related to the soil properties are often encountered. This thesis presents experimental investigations of direct shear box tests on conditioned sands, compressibility tests on conditioned sands and a model EPB screw conveyor operating with sandy soils. Index tests were performed to investigate effects of foam and polymer conditioning treatments on the plastic fluidity of different Leighton Buzzard (L.B.) sands and Thanet sand. The index tests allowed assessment of conditioning treatments for sandy soils, and optimum ranges of treatments for Leighton Buzzard sand and Thanet sand are suggested. In the series of shear box tests, performed on conditioned Thanet sand and conditioned L.B. sands, one of the most important findings was that the pore water pressure controls the strength of the sand foam mixtures. An increase in foam injection ratio (FIR) might produce an increase of pore water pressure and a decrease of shear stress. In the series of compressibility tests, performed on conditioned Thanet sand and conditioned L.B. fine sand, one of the most important findings was that increasing FIR does not increase maximum gas expelled. The FIR and the initial relative density of the specimen have to be related to the capability of the specimen to retain the gas and establish a coexistence between grains of soil, water and gas bubbles. Finally, from the series of model (1:10 scale), screw conveyor tests, performed on conditioned Thanet sand, conditioned L.B. fine sand and conditioned Garside sand, it can be concluded that the Oxford screw conveyor model can be used as a trial machine to study the effects of different operating conditions on conditioned sand specimens similar to those used on site. This can allow choice of conditioning methods to improve the performance of an EPB machine at a given site.