DSpace Collection:
https://dspace.lboro.ac.uk/2134/91
2015-11-27T19:06:01ZTransition in the decay rates of stationary distributions of Lévy motion in an energy landscape
https://dspace.lboro.ac.uk/2134/18655
Title: Transition in the decay rates of stationary distributions of Lévy motion in an energy landscape
Authors: Kaleta, Kamil; Lorinczi, Jozsef
Abstract: The time evolution of random variables with Levy statistics has the ability to develop jumps displaying very different behaviours from continuously fluctuating cases. Such patterns appear in an ever broadening range of sources including random lasers, non-Gaussian kinetics or foraging strategies. The penalizing or reinforcing effect of the environment, however, has been little explored so far. We report a new phenomenon which manifests as a qualitative transition in the spatial decay behaviour of the stationary measure of a jump process under an external potential, occurring on a combined change in the characteristics of the process and the lowest eigenvalue resulting from the effect of the potential. This also provides insight in the fundamental question of what is the mechanism of the spatial decay of a ground state.
Description: This revised pre-print was submitted to arXiv on 1st September 2015.2015-01-01T00:00:00ZModelling CdTe thin film growth over realistic time scales
https://dspace.lboro.ac.uk/2134/18000
Title: Modelling CdTe thin film growth over realistic time scales
Authors: Yu, Miao
Abstract: Cadmium Telluride (CdTe) is an excellent material for low-cost, high efficiency thin-film solar cells and holds the record for watts/cost performance. The laboratory record efficiency of CdTe solar cells lags significantly behind the theoretical maximum for the material. This discrepancy is often attributed to defects such as grain boundaries and dislocations. Thus it is important to do research on how these defects are formed during the growth process.
Atomistic simulations, such as Molecular Dynamics (MD) and on-the-fly Kinetic Monte Carlo (OTF-KMC), are widely used in partnership with experiments in addressing problems in materials science. In this work we use computer simulation to predict the growth of the sputter deposited CdTe thin film.
At the first stage, MD studies of small cluster energetic impacts were carried out by repeatedly depositing CdxTey (x, y = 0, 1) clusters onto different CdTe surfaces with different energies at random positions. The impacts were simulated on Cd- and Te-terminated (100) surfaces and Cd- and Te-terminated (111) surfaces with typical industrial energies varies from 1 to 40 eV at a temperature of 350 K. More than 1,000 simulations have been preformed for each of these cases so as to sample the possible deposition positions and to collect sufficient statistics. The behaviour of deposited clusters under different conditions are studies.
To simulate the process of thin film growth is the next stage in this work. We use different techniques to simulate the growth process on different surfaces. OTF-KMC simulations are performed to simulate the thin film growth process on the (111) CdTe surfaces. Starting with several ad-atoms deposited on the surfaces, in each step, the OTF-KMC method searches for all possible atomic movements (transitions) and randomly selects a transition or deposition to execute based on their corresponding rates. The thin film grows with more and more clusters to be deposited onto the surface with numerous ad-atom diffusions.
The growth process on the dimerised Te-terminated (100) surface is very interesting. Knowledge of how the Te dimers on the surface split during the growth is gained in the simulations. MD is used to simulate the growth process with an accelerated deposition rate. Several simulations with different deposition energies are performed to see the differences of dissociation of the surface Te dimers. Post-annealing at different temperatures are applied after the growth simulations to find the optimal annealing temperature.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2015-01-01T00:00:00ZJordan-Kronecker invariants of finite-dimensional Lie algebras
https://dspace.lboro.ac.uk/2134/17892
Title: Jordan-Kronecker invariants of finite-dimensional Lie algebras
Authors: Bolsinov, Alexey V.; Zhang, Pumei
Abstract: For any finite-dimensional Lie algebra we introduce the notion of Jordan-Kronecker invariants, study their properties and discuss examples. These invariants naturally appear in the framework of the bi-Hamiltonian approach to integrable systems on Lie algebras and are closely related to Mischenko-Fomenko's argument shift method.2012-01-01T00:00:00ZNonlinear free surface flows past a semi-infinite flat plate in water of finite depth
https://dspace.lboro.ac.uk/2134/2969
Title: Nonlinear free surface flows past a semi-infinite flat plate in water of finite depth
Authors: Maleewong, M.; Grimshaw, Roger H.J.
Abstract: We consider the steady free surface two-dimensional flow past a semi-infinite flat plate in
water of a constant finite depth. The fluid is assumed to be inviscid, incompressible and
the flow is irrotational; surface tension at the free surface is neglected. Our concern is with
the periodic waves generated downstream of the plate edge. These can be characterized
by a depth-based Froude number, F, and the depth d (draft) of the depressed plate.
For small d and subcritical flows, we may use the linearized problem, combined with
conservation of momentum, to obtain some analytical results. These linear results are
valid when F is not close to 0 or 1. As F approaches 1, we use a weakly nonlinear longwave
analysis, and in particular show that the results can be extended to supercritical
flows. For larger d nonlinear effects need to be taken account, and so we solve the fully
nonlinear problem numerically using a boundary integral equation method. Here the
predicted wavelength from the linear and weakly nonlinear results is used to set the
mean depth condition for the nonlinear problem. The results by these three approaches
are in good agreement when d is relatively small. For larger d our numerical results are
compared with known results for the highest wave.We also find some wave-free solutions,
which when compared with the weakly nonlinear results are essentially just one-half of
a solitary wave solution.
Description: This is a pre-print.2007-01-01T00:00:00Z