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Title: Propagation of fronts with gradient and curvature dependent velocities
Author: Al-Barwani, Hamdi
ISNI:       0000 0001 3405 200X
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 1996
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The thesis considers and examines methods of surface propagation, where the normal velocity of the surface depends on the local curvature and the gradient of the surface. Such fronts occur in many different physical situations from the growth of crystals to the spreading of flames. A number of different methods are considered to find solutions to these physical problems. First the motion is modelled by partial differential equations and numerical methods are developed for solving these equations. The numerical methods involve characteristic, finite differences and transformation of the equations. Stability of the solutions is also briefly considered. Secondly the fronts are modelled by using a cellular approach which subdivides space into regions of small cells. The fronts are assumed to propagate through the region according to stochastic rules. Monte-Carlo simulations are carried out using this approach. Results of the simulations are carried out in two-dimensions and three-dimensions for a number of interesting physical examples.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Monte-Carlo simulations; Surface propagation