In the following:
Various applied mathematics undergraduate skills are demonstrated via an adaptation of Crank's axisymmetric spherical diffusion model. By the introduction of a one-parameter Heaviside initial condition, the pharmaceutically problematic initial mass flux is attenuated. Quantities germane to the pharmaceutical industry are examined and the model is tested with data derived from industry journals. A binomial algorithm for the acceleration of alternating sequences is demonstrated. The model is accompanied by a MAPLE worksheet for further student exploration
C.S. Ormerod and M. Nelson, Controlled release drug delivery via polymeric microspheres: a neat application of the spherical diffusion equation. International Journal of Mathematical Education in Science and Technology, 48(8): 1268-1281. http://dx.doi.org/10.1080/0020739X.2017.1324116. 2017.
This study investigated the fate of trace organic contaminants (TrOCs) in an oxic-settling-anoxic (OSA) process consisting of a sequencing batch reactor (SBR) with external aerobic/anoxic and anoxic reactors. OSA did not negatively affect TrOC removal of the SBR. Generally, low TrOC removal was observed under anoxic and low substrate conditions, implicating the role of co-metabolism in TrOC biodegradation. Several TrOCs that were recalcitrant in the SBR (e.g., benzotriazole) were biodegraded in the external aerobic/anoxic reactor. Some hydrophobic TrOCs (e.g., triclosan) were desorbed in the anoxic reactor possibly due to loss of sorption sites through volatile solids destruction. In OSA, the sludge was discharged from the aerobic/anoxic reactor which contained lower concentration of TrOCs (e.g., triclosan and triclocarban) than that of the control aerobic digester, suggesting that OSA can also help to reduce TrOC concentration in residual biosolids.
G.U. Semblante, H.I. Hai, J. McDonald, S.J. Khan, M. Nelson, D-J. Lee, W.E. Price, and L.D. Nghiem. Fate of trace organic contaminants in oxic-settling-anoxic (OSA) process applied for biosolids reduction during wastewater treatment. Bioresource Technology, 240: 181--191, 2017. http://dx.doi.org/10.1016/j.biortech.2017.02.053.
We provide a qualitative analysis of a system of nonlinear differential equations that model the spread of alcoholism through a population. Alcoholism is viewed as an infectious disease and the model treats it within a sir framework. The model exhibits two generic types of steady-state diagram. The first of these is qualitatively the same as the steady-state diagram in the standard sir model. The second exhibits a backwards transcritical bifurcation. As a consequence of this, there is a region of bistability in which a population of problem drinkers can be sustained, even when the reproduction number is less than one. We obtain a succinct formula for this scenario when the transition between these two cases occurs.
M.I. Nelson, P. Hagedoornu, and A.L. Worthy. The demon drink. ANZIAM Journal, 59(2): 135--154, 2017. http://dx.doi.org/10.1017/S1446181117000347.
Alcohol based biofuels, such as bio-butanol, have considerable potential to reduce the demand for petrochemical fuels. However, one of the main obstacles to the commercial development of biological based production processes of biofuels is end-product toxicity to the biocatalyst. We investigate the effect of end-product toxicity upon the steady-state production of a biofuel produced through the growth of microorganisms in a continuous flow bioreactor. The novelty of the model formulation is that the product is assumed to be toxic to the biomass. The increase in the per-capita decay rate due to the presence of the product is assumed to be proportional to the the concentration of the product. The steady-state solutions for the model are obtained, and their stability determined as a function of the residence time. These solutions are used to investigate how the maximum yield and the reactor productivity depend upon system parameters. Unlike systems which do not exhibit toxicity there is a value of the feed concentration which maximises the product yield. The maximum reactor productivity is shown to be a sharply decreasing function of both the feed concentration and the toxicity parameter. In conclusion, alternative reactor configurations are required to reduce the effects of highly toxic products.
M.I. Nelson, H.S. Sidhu, R.O. Weber, and G.N. Mercer. A dynamical systems model of the limiting oxygen index test. Submitted 1999.