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Stationary Solutions For The 1+1 Nonlinear Schrodinger Equation Modeling Repulsive Bose-Einstein Condensates In Small Potentials, Kristina Mallory, Robert A. Van Gorder
Stationary Solutions For The 1+1 Nonlinear Schrodinger Equation Modeling Repulsive Bose-Einstein Condensates In Small Potentials, Kristina Mallory, Robert A. Van Gorder
Faculty Bibliography 2010s
Stationary solutions for the 1 + 1 cubic nonlinear Schrodinger equation modeling repulsive Bose-Einstein condensates (BEC) in a small potential are obtained through a form of nonlinear perturbation. In particular, for sufficiently small potentials, we determine the perturbation theory of stationary solutions, by use of an expansion in Jacobi elliptic functions. This idea was explored before in order to obtain exact solutions [Bronski, Carr, Deconinck, and Kutz, Phys. Rev. Lett. 86, 1402 (2001)], where the potential itself was fixed to be a Jacobi elliptic function, thereby reducing the nonlinear ODE into an algebraic equation, (which could be easily solved). However, …
Scaling Laws And Accurate Small-Amplitude Stationary Solution For The Motion Of A Planar Vortex Filament In The Cartesian Form Of The Local Induction Approximation, Robert A. Van Gorder
Scaling Laws And Accurate Small-Amplitude Stationary Solution For The Motion Of A Planar Vortex Filament In The Cartesian Form Of The Local Induction Approximation, Robert A. Van Gorder
Faculty Bibliography 2010s
We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrodinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and …
Sludge Formation In The Activated Sludge Process: Mathematical Analysis, Asma O. M Alharbi, Mark I. Nelson, Annette L. Worthy, Harvinder S. Sidhu
Sludge Formation In The Activated Sludge Process: Mathematical Analysis, Asma O. M Alharbi, Mark I. Nelson, Annette L. Worthy, Harvinder S. Sidhu
Faculty of Engineering and Information Sciences - Papers: Part A
One drawback associated with the activated sludge process is the production of 'sludge'. The expense for treating excess sludge can account for 50-60% of the running costs of a plant. Traditional methods for disposing of excess sludge, which include incineration, the use of landfill sites and dumping at sea are becoming increasingly regulated worldwide due to concerns about the presence of potentially toxic elements in it. Furthermore, a combination of the limited amount of land available for landfill, particularly in urban areas, with stringent legislation has seen the economic costs of using landfill sites increasing sharply. Thus there is a …
Applying Mathematical Model To Simplify The Procession Of Pipeline Route Selection, Jianli Liu, Shuqing Yang, Joseph Wiltshire
Applying Mathematical Model To Simplify The Procession Of Pipeline Route Selection, Jianli Liu, Shuqing Yang, Joseph Wiltshire
Faculty of Engineering and Information Sciences - Papers: Part A
Now there are many pipelines to deliver liquid-like water diversions in the world. Optimal route for pipeline transportation is a major concern for engineers, economists, and decision makers. Pipeline route selection is governed by many factors such as the shortest distance between supply and demand points, constructability, affordability, environmental impacts, and approachability. There are many methods developed for the pipeline route selection like Gestalt method, land suitability mapping techniques, geographic information systems (GIS), imaging technologies for pipeline mapping with the use of airborne lidar, etc. But these methods, though robust in translating physical constraints into feasible alternatives for route location, …
A Mathematical Function To Represent S-Shaped Relationships For Geotechnical Applications, Martin D. Liu, K J. Xu, Suksun Horpibulsuk
A Mathematical Function To Represent S-Shaped Relationships For Geotechnical Applications, Martin D. Liu, K J. Xu, Suksun Horpibulsuk
Faculty of Engineering and Information Sciences - Papers: Part A
In this paper a new mathematical function is proposed for describing the S-shape relationship in both normal x and y scale and the semi-logarithmic x and y scale. Basic features of the proposed function have been demonstrated. The proposed function has then been used to simulate the S-shape relationship for seven categories of engineering phenomena. It is seen that the proposed mathematical function has a great potential for representing various S-shape relationships and provides a powerful tool for characterising properties of materials or response of systems; it is thus useful for further numerical analysis.