Research Letters in the Information and Mathematical Sciences
Permanent URI for this collectionhttps://mro.massey.ac.nz/handle/10179/4332
Research Letters welcomes papers from staff and graduate students at Massey University in the areas of: Computer Science, Information Science, Mathematics, Statistics and the Physical and Engineering Sciences. Research letters is a preprint series that accepts articles of completed research work, technical reports, or preliminary results from ongoing research. After editing, articles are published online and can be referenced, or handed out at conferences.
Copyright remains with the authors and the articles can be used as preprints to academic journal publications or handed out at conferences.
Editors Dr Elena Calude Dr Napoleon Reyes The guidelines for writing a manuscript can be accessed here.
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Item A comparison of some numerical methods for the advection-diffusion equation(Massey University, 2006) Thongmoon, M.; McKibbin, R.This paper describes a comparison of some numerical methods for solving the advection-diffusion (AD) equation which may be used to describe transport of a pollutant. The one-dimensional advection-diffusion equation is solved by using cubic splines (the natural cubic spline and a ”special” AD cubic spline) to estimate first and second derivatives, and also by solving the same problem using two standard finite difference schemes (the FTCS and Crank-Nicolson methods). Two examples are used for comparison; the numerical results are compared with analytical solutions. It is found that, for the examples studied, the finite difference methods give better point-wise solutions than the spline methods.Item Source release-rate estimation of atmospheric pollution from a non-steady point source - Part 2: Source at an unknown location(Massey University, 2003) Kathirgamanathan, P.; McKibbin, R.; McLachlan, R.I.This paper presents an inverse modelling procedure to estimate the location and release rate of atmospheric pollution. The input to this model requires measured pollution concentration at a minimum of three observation sites on the ground and meteorological conditions such as wind speed and cloud cover. The inverse model is formulated as a least squares minimisation problem coupled with the solution of an advection-diffusion equation for a non-steady point source model. Since the minimisation problem has a combination of linear and non-linear parameters the problem is solved in two steps. Non-linear parameters are found by constructing an iterative procedure using an optimisation routine such as MATLAB’s lsqnonlin and at each iteration, the linear subproblem is solved to estimate the linear parameters. Finding the linear parameters is an ill-posed problem and consequently its solution is extremely sensitive to errors in the data. Tikhonov regularisation, which stabilises the process of the solution, is used to overcome the ill posedness of the problem and the regularisation parameter is estimated using the properties of the non-linear L-curve, linear L-curve and generalised cross validation. Finally, the accuracy of the model is examined by imposing normally-distributed relative noise into concentration data generated by the forward model.Item Source release-rate estimation of atmospheric pollution from a non-steady point source - Part I: Source at a known location(Massey University, 2003) Kathirgamanathan, P.; McKibbin, R.; McLachlan, R.I.The goal is to build up an inverse model capable of finding the release history of atmospheric pollution by using measured gas concentration data at just one location on the ground and identify the factors which affects the accuracy of the model predictions. The problem involves a non-steady point source of pollution at a known location in the atmosphere. This problem of finding the release rate is an ill-posed inverse problem and its solution is extremely sensitive to errors in the measurement data. Special regularisation methods, which stabilise the process of the solution, must be used to solve the problem. The method described in this paper is based on linear least-squares regression and Tikhonov regularisation, coupled with the solution of an advection-diffusion equation for a non-steady point source. The accuracy of the method is examined by imposing normally-distributed relative noise into the concentration data generated by the forward model as well as some real experimental data.Item Solution of the Young-Laplace equation for three particles(Massey University, 2003) Rynhart, P.R.; McLachlan, R.; Jones, J.R.; McKibbin, R.This paper presents the solution to the liquid bridge profile formed between three equally sized spherical primary particles. The particles are equally separated, with sphere centres located on the vertices of an equilateral triangle. Equations for the problem are derived and solved numerically for given constant mean curvature H0, contact angle , and inter-particle separation distance S. The binding force between particles is calculated and plotted as a function of liquid bridge volume for a particular example. Agreement with experiment is provided.Item Agglomerate properties(Massey University, 2003) Rynhart, P.R.; Jones, J.R.; McKibbin, R.Modelling of wet granulation requires the rate of agglomerate coalescence to be estimated. Coalescence is dependent on the frequency of collisions that occur, and the fraction of collisions which result in coalescence. The collision rate is a function of granulator kinetics and powder properties, while the coalescence success rate is dependent on factors including the Stokes number and particle geometry. This work investigates an aspect of the geometry by examining the distribution of liquid on the surface of agglomerates in the capillary state. Agglomerates are created by adding particles, one at a time, about a central tetrahedral arrangement of four primary particles. For a given agglomerate, the wetted fraction of surface area, defined as the wetness, is evaluated using an approximate fluid surface. Packing density and binder saturation parameters are incorporated into the model. Given a number of primary particles and the volume of binder in a particle, the agglomerate wetness is able to be estimated using computational geometry.Item Source term estimation of pollution from an instantaneous point source(Massey University, 2002) Kathirgamanathan, P.; McKibbin, R.; McLachlan, R.I.The goal is to develop an inverse model capable of simultaneously estimating the parameters appearing in an air pollution model for an instantaneous point source, by using measured gas concentration data. The approach taken was to develop the inverse model as a non-linear least squares estimation problem in which the source term is estimated using measurements of pollution concentration on the ground. The statistical basis of the least squares inverse model allows quantification of the uncertainty of the parameter estimates, which in turn allows estimation of the uncertainty of the simulation model predictions.