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Title: Numerical simulations of interface kinetics
Author: Demetriou, D. A.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2000
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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, vcm, scales with the applied external driving force, F, according to vcm ~ ((F)/(F)c-1)θ where Fc is the threshold force and θ the velocity critical exponent. The velocity exponent is expected to be a 'universal' quantity independent of model parameters. Based on our work we estimate θ = 0.61 ± 0.06.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available