Mathematical contributions to the theory of evolution

Mode of access: Internet.

Mapping Whidbey Island and Possession Sound landslide susceptibility using an additive linear model

Senior thesis written for Oceanography 445

Modelling of froth transportation in industrial flotation cells: Part I. Development of froth transportation models for attached particles

Modelling of froth transportation, as part of modelling of froth recovery, provides a scale-up procedure for flotation cell design. It can also assist in improving control of flotation operation. Mathematical models of froth velocity on the surface and froth residence time distribution in a cylindrical tank flotation cell are proposed, based on mass balance principle of the air entering the froth. The models take into account factors such as cell size, concentrate launder configuration, use of a froth crowder, cell operating conditions including froth height and air rate, and bubble bursting on the surface. (C) 2004 Elsevier Ltd. All rights reserved.

Prediction of the growth of wear-type rail corrugation

The growth behaviour of the vibrational wear phenomenon known as rail corrugation is investigated analytically and numerically using mathematical models. A simplified feedback model for wear-type rail corrugation that includes a wheel pass time delay is developed with an aim to analytically distil the most critical interaction occurring between the wheel/rail structural dynamics, rolling contact mechanics and rail wear. To this end, a stability analysis on the complete system is performed to determine the growth of wear-type rail corrugations over multiple wheelset passages. This analysis indicates that although the dynamical behaviour of the system is stable for each wheel passage, over multiple wheelset passages, the growth of wear-type corrugations is shown to be the result of instability due to feedback interaction between the three primary components of the model. The corrugations are shown analytically to grow for all realistic railway parameters. From this analysis an analytical expression for the exponential growth rate of corrugations in terms of known parameters is developed. This convenient expression is used to perform a sensitivity analysis to identify critical parameters that most affect corrugation growth. The analytical predictions are shown to compare well with results from a benchmarked time-domain finite element model. (C) 2004 Elsevier B.V. All rights reserved.

A genetic estimation algorithm for parameters of stochastic ordinary differential equations

A generic method for the estimation of parameters for Stochastic Ordinary Differential Equations (SODEs) is introduced and developed. This algorithm, called the GePERs method, utilises a genetic optimisation algorithm to minimise a stochastic objective function based on the Kolmogorov-Smirnov statistic. Numerical simulations are utilised to form the KS statistic. Further, the examination of some of the factors that improve the precision of the estimates is conducted. This method is used to estimate parameters of diffusion equations and jump-diffusion equations. It is also applied to the problem of model selection for the Queensland electricity market. (C) 2003 Elsevier B.V. All rights reserved.

Marriage breakdown in Australia - The social correlates of separation and divorce

Marriage breakdown through separation and divorce is a pervasive feature of Australian society. But little research investigates the social factors associated with marital breakdown in Australia. This study builds on and extends Australian research by using survival analysis models to examine patterns of association among temporal, life-course, attitudinal and economic factors associated with marital breakdown. Using data from the Household Income and Labour Dynamics in Australia (HILDA) survey, we find marital breakdown in Australia is socially patterned in similar ways to other Western countries. But our findings point to several directions for future research into marriage breakdown in Australia, and we identify certain unique features of Australian marriage breakdown that warrant a more detailed investigation, such as the relationship between ethnic origin and the risk of marital breakdown.

Using the canonical modelling approach to simplify the simulation of function in functional-structural plant models

Functional-structural plant models that include detailed mechanistic representation of underlying physiological processes can be expensive to construct and the resulting models can also be extremely complicated. On the other hand, purely empirical models are not able to simulate plant adaptability and response to different conditions. In this paper, we present an intermediate approach to modelling plant function that can simulate plant response without requiring detailed knowledge of underlying physiology. Plant function is modelled using a 'canonical' modelling approach, which uses compartment models with flux functions of a standard mathematical form, while plant structure is modelled using L-systems. Two modelling examples are used to demonstrate that canonical modelling can be used in conjunction with L-systems to create functional-structural plant models where function is represented either in an accurate and descriptive way, or in a more mechanistic and explanatory way. We conclude that canonical modelling provides a useful, flexible and relatively simple approach to modelling plant function at an intermediate level of abstraction.

A simple lifestyle score predicts survival in healthy elderly men

Background. Although improvements in life expectancy have been attributed in part to the adoption or a more prudent lifestyle, few studies have examined the association of lifestyle with survival, using several lifestyle factors simultaneously, in a healthy elderly population. Methods. We investigated the association of health related behaviors with mortality in 7989 men aged 65 to 83 years participating in a population-based trial in Perth, Western Australia, by calculating a lifestyle score as a simple tally of flow many or eight prudent behaviors each individual followed. Results. Invitations to screening produced a corrected response of 70.5%. Out of a possible score of 8.46% of men had a score of less than 5. Within 5 years, a total of 703 men (9%) had died from any cause. The hazard ratio in men with a low lifestyle score was 1.3 [95% confidence interval (CI): 1.1-1.5] compared with men with a score of 5 or more. Conclusions. Lifestyle remains an important predictor of mortality even in old age. Survival in older men without a history of cardiovascular disease can potentially be enhanced by promoting a healthy lifestyle. © 2004 Elsevier Inc, All rights reserved.

Analysis of trigonometric implicit Runge-Kutta methods

Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge-Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. (c) 2006 Elsevier B.V. All rights reserved.