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1	Physical properties of graphene nano-devices Hills, Romilly D. Y. January 2015 (has links) In this doctoral thesis the two dimensional material graphene has been studied in depth with particular respect to Zener tunnelling devices. From the hexagonal structure the Hamiltonian at a Dirac point was derived with the option of including an energy gap. This Hamiltonian was then used to obtain the tunnelling properties of various graphene nano-devices; the devices studied include Zener tunnelling potential barriers such as single and double graphene potential steps. A form of the Landauer formalism was obtained for graphene devices. Combined with the scattering properties of potential barriers the current and conductance was found for a wide range of graphene nano-devices. These results were then compared to recently obtained experimental results for graphene nano-ribbons, showing many similarities between nano-ribbons and infinite sheet graphene. The methods studied were then applied to materials which have been shown to possess three dimensional Dirac cones known as topological insulators. In the case of Cd3As2 the Dirac cone is asymmetrical with respect to the z-direction, the effect of this asymmetry has been discussed with comparison to the symmetrical case. 620.1
2	Numerical Simulation of Soliton Tunneling Tiberg, Matilda, Estensen, Elias, Seger, Amanda January 2020 (has links) This project studied two different ways of imposing boundary conditions weakly with the finite difference summation-by-parts (SBP) operators. These operators were combined with the boundary handling methods of simultaneous-approximation-terms (SAT) and the Projection to impose homogeneous Neumann and Dirichlet boundary conditions. The convergence rate of both methods was analyzed for different boundary conditions for the one-dimensional (1D) Schrödinger equation, without potential, which resulted in both methods performing similarly. A multi-block discretization was then implemented and different combinations of SBP-SAT and SBP-Projection were applied to impose inner boundary conditions of continuity between the blocks. A convergence study of the different methods of imposing the inner BC:s was conducted for the 1D Schrödinger equation without potential. The resulting convergence was the same for all methods and it was concluded that they performed similarly. Methods involving SBP-Projection had the slight advantage of faster computation time. Finally, the 1D Gross-Pitaevskii equation (GPE) and the 1D Schrödinger equation were analyzed with a step potential. The waves propagating towards the potential barrier were in both cases partially transmitted and partially reflected. The waves simulated with the Schrödinger equation dispersed, while the solitons simulated with the GPE kept their shape due to the equations reinforcing non-linear term. The bright soliton was partly transmitted and partly reflected. The dark soliton was either totally reflected or totally transmitted. soliton GPE gross pitaevskii Schrödinger step potential summation by parts SBP-SAT Simultaneous approximation term SAT Projection SBP-Projection finite differences boundary treatment interface treatment Computational Mathematics Beräkningsmatematik
3	Mathematical modelling of primary alkaline batteries Johansen, Jonathan Frederick January 2007 (has links) Three mathematical models, two of primary alkaline battery cathode discharge, and one of primary alkaline battery discharge, are developed, presented, solved and investigated in this thesis. The primary aim of this work is to improve our understanding of the complex, interrelated and nonlinear processes that occur within primary alkaline batteries during discharge. We use perturbation techniques and Laplace transforms to analyse and simplify an existing model of primary alkaline battery cathode under galvanostatic discharge. The process highlights key phenomena, and removes those phenomena that have very little effect on discharge from the model. We find that electrolyte variation within Electrolytic Manganese Dioxide (EMD) particles is negligible, but proton diffusion within EMD crystals is important. The simplification process results in a significant reduction in the number of model equations, and greatly decreases the computational overhead of the numerical simulation software. In addition, the model results based on this simplified framework compare well with available experimental data. The second model of the primary alkaline battery cathode discharge simulates step potential electrochemical spectroscopy discharges, and is used to improve our understanding of the multi-reaction nature of the reduction of EMD. We find that a single-reaction framework is able to simulate multi-reaction behaviour through the use of a nonlinear ion-ion interaction term. The third model simulates the full primary alkaline battery system, and accounts for the precipitation of zinc oxide within the separator (and other regions), and subsequent internal short circuit through this phase. It was found that an internal short circuit is created at the beginning of discharge, and this self-discharge may be exacerbated by discharging the cell intermittently. We find that using a thicker separator paper is a very effective way of minimising self-discharge behaviour. The equations describing the three models are solved numerically in MATLABR, using three pieces of numerical simulation software. They provide a flexible and powerful set of primary alkaline battery discharge prediction tools, that leverage the simplified model framework, allowing them to be easily run on a desktop PC. advection anode asymptotic analysis BET surface area binary electrolyte boundary condition Butler-Volmer equation cathode closed circuit voltage concentration polarisation control volume current path discretisation diffusion electrochemical reaction electrode electrolytic manganese dioxide EMD crystals EMD particles exchange current density geometric surface area initial condition linearisation macrohomogeneous porous electrode theory mathematical model Nernst equation ohmic losses open circuit voltage ordinary differential equation overpotential partial differential equation perturbation techniques potassium hydroxide potassium zincate precipitation reaction primary battery separator paper simulation ternary electrolyte theoretical capacity utilisation zinc zinc oxide

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