Dr Maureen Edwardshttps://works.bepress.com/medwards/Recent works by Dr Maureen Edwardsen-usCopyright (c) 2021 All rights reserved.Sun, 01 Jan 2012 08:00:00 +00003600The effect of incomplete mixing upon quadratic autocatalysishttps://works.bepress.com/medwards/5/We analyse a model for a continuously stirred tank reactor with imperfect mixing in which the reactor is represented by two well mixed compartments with material transfer between them. These reactors represent `highly agitated' and `less agitated' regions. The chemical model used is a quadratic autocatalytic scheme with linear decay of the autocatalyst. We investigate how the reactor performance depends upon the degree of mixing in the reactor and the size of the less agitated region. Surprisingly, the performance of the reactor with sufficiently small values of mixing is inferior to that with no mixing between the compartments.Ahmed Hussein Msmali et al.Sun, 01 Jan 2012 08:00:00 +0000https://works.bepress.com/medwards/5/No Subject AreaModelling pattern formation in plantshttps://works.bepress.com/medwards/1/Performing simulations with simple models is a key activity in the recovery of information about the mechanisms which underlie the observed dynamics of biological processes, such as the posi- tioning of the hairs (trichomes) on the leaves of plants. The discovery of a robust representative model is a highly non-trivial process. Without appropriate constraints to regularize the choice of a model, the non-uniqueness of possibilities is vast. As acknowledged by Young (1983) in his modelling of pea leaf development, the degree of non-uniqueness can be reduced by constraining the model to reproduce the patterns observed in mutants as well as on the wild type. Recently, Pereverzyev Jr. and Anderssen (2008) have proposed an explorative combinatorial algebraic ansatz for modelling the genetic signaling, com- munication and switching controlling the growth of a plant leaf along with the positioning of the hairs (trichomes) on Arabidopsis leaves. The surface of the leaf is modelled as an array of hexagonal cells and the fate of a cell (hair or non-hair) as it grows out from the meristem is determined by a hexagonal recursion anzatz. The application of this simple recursion allows the normal arrangement of trichomes to be generated, while subtle variations of parameters in the model capture mutant forms. In the earlier work, only the sets of model parameters that lead to symmetric patterns were considered. In this paper, nonsymmetric patterns, which can be obtained using the proposed modelling framework, are investigated. Also, the possibility to capture the patterns with the clumps of trichomes is studied. The leaves of some known mutants show the clumping effects, and reproducing these effects with the existing modeling approaches is problematic. The appropriate modification of the hexagonal algebraic model that gives rise to the clumping patterns is proposed. The overall goal is an investigation of how modelling and simulation can be utilized to study the genetics of geometry. Here, the geometry of the positioning of trichomes on plant (Arabidopsis) leaves is the model system that is used to formalize and implement ideas. As in much modelling of complex processes, it is necessary to have appropriate "link concepts" that are the stepping stone of the multi-step model that connects the observational data to the information to be recovered. In particular, the role of the link concepts is to identify a logical sequence of steps that connects the observational characterization of the process with the mathematical model that defines how that characterization is related to some assumed internal structure of the process. In the current situation the link concept is the "geometry of the cellular structure where the growth occurs". It is at that location that "the genetics controls the mechanism which in turn orchestrates the cellular growth".Sat, 01 Jan 2011 08:00:00 +0000https://works.bepress.com/medwards/1/No Subject AreaLie group symmetry analysis of transport in porous media with variable transmissivityhttps://works.bepress.com/medwards/2/We determine the Lie group symmetries of the coupled partial differential equations governing a novel problem for the transient flow of a fluid containing a solidifiable gel, through a hydraulically isotropic porous medium. Assuming that the permeability ($K^*$) of the porous medium is a function of the gel concentration ($c^*$), we determine a number of exact solutions corresponding to the cases where the concentration-dependent permeability is either arbitrary or has a power law variation or is a constant. Each case admits a number of distinct Lie symmetries and the solutions corresponding to the optimal systems are determined. Some typical concentration and pressure profiles are illustrated and a specific moving boundary problem is solved and the concentration and pressure profiles are displayed.Tue, 01 Jan 2008 08:00:00 +0000https://works.bepress.com/medwards/2/No Subject AreaGroup invariant solutions for two dimensional solute transport under realistic water flowshttps://works.bepress.com/medwards/3/Sun, 01 Jan 2006 08:00:00 +0000https://works.bepress.com/medwards/3/No Subject AreaSymmetry Solutions for Transient Solute Transport in Unsaturated Soils with Realistic Water Profilehttps://works.bepress.com/medwards/6/Maureen P Edwards et al.Sat, 01 Jan 2005 08:00:00 +0000https://works.bepress.com/medwards/6/No Subject AreaExact solutions of nonlinear diffusion-convection equationshttps://works.bepress.com/medwards/4/We consider the class of nonlinear diffusion-convection equations which contain arbitrary functions of the dependent variable. We perform a thorough symmetry analysis of the general equation in one, two and three spatial dimensions. We identify all special forms of the two arbitrary functions which admit special symmetry properties and for these cases, attempt to reduce the governing equation to an differential equation. We show that reduction of the governing equation an ordinary differential equation is possible in many cases. We seek solutions the reduced equations and hence are able to construct time-dependent similarity solutions to the governing equation.
We extend a previously derived method for reducing a power law case of our governing equation through our knowledge of the symmetries of the class of equations. As a result, we construct an infinite family of time-dependent solutions satisfying nonsingular initial conditions for special cases of the governing equation in both and three dimensions.
Finally, we develop an inverse method by exploiting a linearisable form of our governing equation in one spatial dimension. The method is used to derive two solutions with distinct variable flux boundary conditions for an unsaturated soil.Wed, 01 Jan 1997 08:00:00 +0000https://works.bepress.com/medwards/4/No Subject Area