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A Mathematical Model For The Biological Treatment Of Industrial Wastewater In A Reactor Cascade, Rubayyi Turki Alqahtani, Mark I. Nelson, Annette L. Worthy
A Mathematical Model For The Biological Treatment Of Industrial Wastewater In A Reactor Cascade, Rubayyi Turki Alqahtani, Mark I. Nelson, Annette L. Worthy
Associate Professor Annette Worthy
Many industrial processes, particularly in the food industry, produce slurries or wastewaters containing high concentrations of biodegradable organic materials. Before these contaminated wastewaters can be discharged the concentration of the biodegradable organic pollutant must be reduced. One way to do this is to pass the wastewater through a bioreactor containing biomass which grows through consumption of the pollutant. Anaerobic conditions are often favoured for the processing of waste materials with high levels of biodegradable organic pollutants as these can be removed with low investment and operational costs. We investigate the steady state effluent concentration leaving a cascade of two reactors. …
A Mathematical Model For The Biological Treatment Of Industrial Wastewaters In A Cascade Of Four Reactors, Annette L. Worthy, Mark I. Nelson, Rubayyi Turki Alqahtani
A Mathematical Model For The Biological Treatment Of Industrial Wastewaters In A Cascade Of Four Reactors, Annette L. Worthy, Mark I. Nelson, Rubayyi Turki Alqahtani
Associate Professor Annette Worthy
Many industrial processes, particularly in the food industry, produce slurriesor wastewaters containing high concentrations of biodegradable organicmaterials. Before these contaminated wastewaters can be dischargedthe concentration of these pollutants must be reduced. A method which has beenextensively employed to remove biodegradable organic matter is biologicaltreatment. In this process the wastewater (or slurry) is passed through abioreactor containing biomass which grows through consumption of thepollutants.The industrial treatment of wastewaters typically employs a reactor cascade.In a reactor cascade of n reactors the effluent stream from the ith reactor inthe cascade acts as the feed stream for the (i+1)th reactor, i.e. the nextreactor. The …
Mathematical Modelling In Nanotechnology, Ngamta Thamwattana, James M. Hill
Mathematical Modelling In Nanotechnology, Ngamta Thamwattana, James M. Hill
Dr Ngamta Thamwattana
The interaction of nano particles with conventional materials dramatically changes all the physical parameters, which usually characterize the bulk material. The nano particles constitute highly reactive isolated sites to the extent that it leads to a change in the electronic structure of the nano composite, and accordingly all the physical properties, such as thermal, mechanical and electrical properties become different from those of the bulk material. To successfully exploit nano composites as components and devices, this fundamental shift of physical properties must be properly understood and accurately modelled. While experimentation is crucial, a theoretical understanding is also necessary and with …
Unifying Model Of Driven Polymer Translocation, T. Ikonen, A. Bhattacharya, T. Ala-Nissila, W. Sung
Unifying Model Of Driven Polymer Translocation, T. Ikonen, A. Bhattacharya, T. Ala-Nissila, W. Sung
Faculty Bibliography 2010s
We present a Brownian dynamics model of driven polymer translocation, in which nonequilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the effective friction, we develop a finite chain length TP formalism, based on the idea suggested by Sakaue [Phys. Rev. E 76, 021803 (2007)]. We validate the model by numerical comparisons with high-accuracy molecular dynamics simulations, showing excellent agreement in a wide range of parameters. Our results show that the dynamics of driven translocation is dominated by the nonequilibrium TP along the cis side subchain. Furthermore, by …
Spectral Analysis Of Certain Schrodinger Operators, Mourad E.H. Ismail, Erik Koelink
Spectral Analysis Of Certain Schrodinger Operators, Mourad E.H. Ismail, Erik Koelink
Faculty Bibliography 2010s
The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynomials with explicit three term recurrence relations where nothing is known about their explicit representations or orthogonality measures. Each model we analyze is a discrete quantum mechanical model in the sense of Odake and Sasaki [J. Phys. A: Math. Theor. 44 (2011), 353001, 47 pages].
Orthogonal Basic Hypergeometric Laurent Polynomials, Mourad E.H. Ismail
Orthogonal Basic Hypergeometric Laurent Polynomials, Mourad E.H. Ismail
Faculty Bibliography 2010s
The Askey-Wilson polynomials are orthogonal polynomials in x = cos theta, which are given as a terminating (4)phi(3) basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in z = e(i theta), which are given as a sum of two terminating (4)phi(3)'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single (4)phi(3)'s which are Laurent polynomials in z are given, which imply the non-symmetric Askey-Wilson biorthogonality. These results include discrete orthogonality relations. They can be considered as a classical analytic study of the results for non-symmetric Askey-Wilson polynomials which were previously obtained by affine Hecke …
Unstaggered-Staggered Solitons In Two-Component Discrete Nonlinear Schrodinger Lattices, Boris A. Malomed, D. J. Kaup, Robert A. Van Gorder
Unstaggered-Staggered Solitons In Two-Component Discrete Nonlinear Schrodinger Lattices, Boris A. Malomed, D. J. Kaup, Robert A. Van Gorder
Faculty Bibliography 2010s
We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schrodinger equations with the attractive self-phase-modulation nonlinearity, coupled by the repulsive cross-phase-modulation interaction. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. The results are obtained in an analytical form, using the variational and Thomas-Fermi approximations (VA and TFA), and the generalized Vakhitov-Kolokolov (VK) criterion for the evaluation of the stability. The analytical predictions are verified against numerical results. Almost all the symbiotic solitons are predicted by the VA quite …
Exact Solution For The Self-Induced Motion Of A Vortex Filament In The Arc-Length Representation Of The Local Induction Approximation, Robert A. Van Gorder
Exact Solution For The Self-Induced Motion Of A Vortex Filament In The Arc-Length Representation Of The Local Induction Approximation, Robert A. Van Gorder
Faculty Bibliography 2010s
We review two formulations of the fully nonlinear local induction equation approximating the self-induced motion of the vortex filament (in the local induction approximation), corresponding to the Cartesian and arc-length coordinate systems. The arc-length representation put forth by Umeki [Theor. Comput. Fluid Dyn. 24, 383 (2010)] results in a type of 1 + 1 derivative nonlinear Schrodinger (NLS) equation describing the motion of such a vortex filament. We obtain exact stationary solutions to this derivative NLS equation; such exact solutions are a rarity. These solutions are periodic in space and we determine the nonlinear dependence of the period on the …