This dissertation's goal is concerned with the development and numerical study of a continuum model, that describes a variety of interface growth phenomena such as fluid displacement in porous media, crystal growth and flux-lines in type-II superconductors. The continuum model is the Quenched-Edwards-Wilkinson (QEW), which is well established in the literature and we restrict ourselves in providing a brief 'derivation' in terms of symmetry considerations. A crucial part of the model is the quenched random medium where the interface moves. The 'adequate' generation of the random background is a crucial ingredient of the simulations and we use a method first employed in fluid mechanics, but never before used in this field. Massive parallel simulations of the resulting system allowed us to verify the presence of a well defined depinning transition between a pinned and moving interface. This is characterized by the presence of a spatial system size (above a certain system size) independent threshold force. The transition appears to fit well the conjecture that the ensemble and time averaged centre of mass velocity, <I>v<SUB>cm</SUB></I>, scales with the applied external driving force, <I>F</I>, according to <I>v<SUB>cm</SUB></I> ~<I> </I>(<I>(F)/(F)<SUB>c</SUB>-1</I>)<I><SUP>θ</SUP></I><SUP> </SUP>where <I>F<SUB>c</SUB> </I>is the threshold force and <I>θ </I>the velocity critical exponent. The velocity exponent is expected to be a 'universal' quantity independent of model parameters. Based on our work we estimate <I>θ </I>= 0.61 ± 0.06.

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No description available.

The work of this thesis focuses on stochastic methods for the simulation of superconducting charge qubits, also known as Cooper pair boxes, which are promising candidates for large scale quantum information processing. To aid non-physicists, a brief outline of the structure of quantum mechanics is provided using the· Dirac formalism. Using the so called 'Backreaction effect', we consider if any information can be obtained regarding the qubit behaviour, through detecting the changes observed in the frequency spectrum of the coupled biasing circuitry, modelled as a dissipative oscillator circuit. The process of modelling dissipative quantum systems is described, however an alternative approach called 'quantum trajectories' is used rather than the traditional Calderia-Leggett model, as the time evolution of a single 'trajectory' represents the evolution of an individual system coupled to a noisy environment. Through the noise generated by an excited qubit, the energy level structure of the qubit can be probed with a microwave drive field, by observing the noise power within the biasing circuit. We consider a biasing circuit of unusually high resonant frequency which can drive the qubit, this creates frequency splitting features that would not normally be observed. Weak measurement is also examined as this is closely related to the stochastic 'quantum trajectories', where the measurement is recorded by the observer rather than lost to an environment. Weakly measuring a qubit does not completely collapse it and therefore 'quantum feedback' may be employed to alter the qubit controls favourably. In particular we consider the problem of purifying a weakly measured system rapidly; given a qubit in the completely mixed state what is the best feedback to become confident in the actual qubit state quickly. There are two optimal feedback protocols proposed by Jacobs [1] and by Wiseman and Ralph [2] for purifying qubits that have ideal controls. However, we adapt these protocols for the charge qubit, whose finite Hamiltonian resources and non-zero ax tunnelling term means the Bloch vector can not be easily held in the optimal location.

The scope of the thesis is the development and application of a model for the analysis of a quench in a large size, force-flow cooled superconducting magnet, i.e. the calculation of the thermal, hydraulic and electrical processes following the local transition of the superconducting material to the normal conducting state. The general problem is presented in Part A, with particular reference to the large size magnets designed for application in fusion experiments of the next generation. The presentation is as general as possible, so that the range of applicability is wide, and it indicates the intrinsically three-dimensional nature of the quench propagation in force-flow cooled magnets of the size considered here. The numerical methods which are necessary for the solution of the quench propagation are reviewed in Part B. A convective-diffusivemodel problem is used to analyze the performance of some of the most popular finite elements algorithms for steady state and transient solution. Amplification factors and phase lag of these algorithms are compared in order to make an optimal choice. A first approach to the solution of the quench propagation, based on a one dimensional model of the superconducting cable, is used in part C to build the basis of the general three dimensional analysis code and to test and validate the numerical against analytical solutions and experimental measurements. Finally, in part D, a fully three dimensional model for the quench propagation is proposed. The model is capable of dealing with arbitrary winding geometries, a wide spectrum of time variable boundary conditions for the flow of the coolant, time changing coil current and magnetic field distribution in the winding pack. At the moment this is the most complete analysis code for superconducting magnetic systems in normal and off-normal quenches (i.e. safety related transients). The 3-D model is tested against experimental results showing good agreement. The substantial work performed to simplify and extend the state equations and transport properties of the helium and of the solid materials used at cryogenic temperatures are reported in Appendices A and B respectively. Appendix C deals with the solution of the current in a general circuit configuration and with the calculation of the magnetic field in a coil of arbitrary shape. Finally, Appendix D presents an example of application to a large force-flow cooled magnet, the NET (Next European Torus) Model Coil, designed as a proof of principle for the NET magnet system.

In low field MRl (<0.5T), the signal-to-noise ratio (SNR) is predominantly degraded by thermal noise of the imaging coil when the sample loading is minimized. This means surface coils made of high temperature superconductors (HTS) should have an SNR significantly higher than their room-temperature copper equivalents due to the reduction in resistivities. While this hypothesis has been reportedly validated, the actual efficacy of HTS coils is still debatable as the benchmark setups in the prior art had an unfavorably large coil-to-sample separation which diminished the SNR yield. This thesis is intended to perform a quantitative validation on the said hypothesis against a novel benchmark setup where the equivalent room-temperature copper coil was placed directly next to the sample to achieve the best SNR sensitivity. The HTS coil used was an YBCO surface coil having a l0-tum, 70mm-circular spiral layout. For sufficient thermal insulation, there was a 10mm gap between the YBCO coil and the sample while the sample separation for the copper coil was merely I mm. By studying the simulated B1 sensitivity profile of the designated layout, the sample loss and intrinsic resistance of both coils were calculated to allow a theoretical evaluation on the research hypothesis. Each coil was then fabricated and configured with an inductively-coupled matching circuit. The quality factors (Q) of the coils in different loading conditions were measured to allow an empirical estimation on the SNR advantage of the YBCO coil. Both coils were then tested on a saline phantom in a 0.17T MRI system where in-vivo hand images were also acquired. The results showed that the YBCO coil had an SNR gain of 2.0 over the proposed benchmark setup. Such a finding is a valuable addition to the prior art as the efficacy of HTS coils for low field MRl was conclusively proven.

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No description available.

Time-dependent Ginzburg-Land au equations are used to model 2D and 3D systems containing both superconductors and normal metals, in which both T(_c) and normal-state resistivity are spatially dependent. The equations are solved numerically using an efficient semi-implicit Crank-Nicolson algorithm. The algorithm, is used to model flux entry and exit in homogenous superconductors with metallic coatings of different resistivities. For an abrupt boundary there is a minimum field of initial vortex entry occurring at a kappa-dependent finite ratio of the normal-state resistivities of the superconductor and the normal metal. Highly reversible magnetization characteristics are achieved using a diffusive layer several coherence lengths wide between the superconductor and the normal metal. This work provides the first TD GL simulation in both 2D and 3D of current flow in polycrystalline superconductors, and provides some important new results both qualitative and quantitative. Using a magnetization method we obtain Jc for both 2D and 3D systems, and obtain the correct field and kappa dependences in 3D, given by F = 3.6 x 10-4 B}l (T) (1- b)2. The pre-factor is different (about 3 to 5 times smaller) from that observed in technological superconductors, but evidence is provided showing that this prefactor depends on the details of 1կ effects at the edges of superconducting grains. In 2D, the analytic flux shear calculation developed by Pruymboom in his thin-film work gives good agreement with our computational results.Visualization of Iぜ and dissipation (including movies in the 2D case) shows that in both 2D and 3D, Jc is determined by flux shear along grain boundaries. In 3D the moving fluxons are confined to the grain boundaries, and cut through stationary fluxons which pass through the grains and are almost completely straight.

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