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Full-Text Articles in Physical Sciences and Mathematics
Fluid-Dynamic Models Of Geophysical Waves, Alan Compelli
Fluid-Dynamic Models Of Geophysical Waves, Alan Compelli
Doctoral
Geophysical waves are waves that are found naturally in the Earth's atmosphere and oceans. Internal waves, that is waves that act as an interface between uids of dierent density, are examples of geophysical waves. A uid system with a at bottom, at surface and internal wave is initially considered. The system has a depth-dependent current which mimics a typical ocean set-up and, as it is based on the surface of the rotating Earth, incorporates Coriolis forces. Using well established uid dynamic techniques, the total energy is calculated and used to determine the dynamics of the system using a procedure called …
Integrable Systems As Fluid Models With Physical Applications, Tony Lyons
Integrable Systems As Fluid Models With Physical Applications, Tony Lyons
Doctoral
In this thesis we begin with the development and analysis of hydrodynamical models as they arise in the theory of water waves and in the modelling of blood flow within arteries. Initially we derive three models of hydrodynamical relevance, namely the KdV equation, the two component Camassa-Holm equation and the Kaup-Boussinesq equation. We develop a model of blood flowing within an artery with elastic walls, and from the principles of Newtonian mechanics we derive the two-component Burger's equation as our first integrable model. We investigate the analytic properties of the system briefly, with the aim of demonstrating the phenomenon of …
Covariant Relativistic Quantum Mechanics Analysis Of A Linearly Accelerated Scalar Particle, Karol Mcdonald
Covariant Relativistic Quantum Mechanics Analysis Of A Linearly Accelerated Scalar Particle, Karol Mcdonald
Doctoral
A covariant formalism of Relativistic Quantum Mechanics is demonstrated, through it's de- velopment and application. The Relativistic Case is shown to follow a similar structure to the established Non-Relativistic formalism. Reasons for preferring the new covariant formalism over the established method are presented. Solutions to the case of a scalar particle in a one-dimensional field are presented. The Relativistic Energy Eigenfunction is derived. Results are generated from initial Gaussian states via a Green's Function method. A Green's Function for the system is derived and applied. The solution to the Quantum System is shown to follow a scaled version of the …