Role of rainfall and catchment characteristics on urban stormwater quality

Urbanisation significantly changes the characteristics of a catchment as natural areas are transformed to impervious surfaces such as roads, roofs and parking lots. The increased fraction of impervious surfaces leads to changes to the stormwater runoff characteristics, whilst a variety of anthropogenic activities common to urban areas generate a range of pollutants such as nutrients, solids and organic matter. These pollutants accumulate on catchment surfaces and are removed and trans- ported by stormwater runoff and thereby contribute pollutant loads to receiving waters. In summary, urbanisation influences the stormwater characteristics of a catchment, including hydrology and water quality. Due to the growing recognition that stormwater pollution is a significant environmental problem, the implementation of mitigation strategies to improve the quality of stormwater runoff is becoming increasingly common in urban areas. A scientifically robust stormwater quality treatment strategy is an essential requirement for effective urban stormwater management. The efficient design of treatment systems is closely dependent on the state of knowledge in relation to the primary factors influencing stormwater quality. In this regard, stormwater modelling outcomes provide designers with important guidance and datasets which significantly underpin the design of effective stormwater treatment systems. Therefore, the accuracy of modelling approaches and the reliability modelling outcomes are of particular concern. This book discusses the inherent complexity and key characteristics in the areas of urban hydrology and stormwater quality, based on the influence exerted by a range of rainfall and catchment characteristics. A comprehensive field sampling and testing programme in relation to pollutant build-up, an urban catchment monitoring programme in relation to stormwater quality and the outcomes from advanced statistical analyses provided the platform for the knowledge creation. Two case studies and two real-world applications are discussed to illustrate the translation of the knowledge created to practical use in relation to the role of rainfall and catchment characteristics on urban stormwater quality. An innovative rainfall classification based on stormwater quality was developed to support the effective and scientifically robust design of stormwater treatment systems. Underpinned by the rainfall classification methodology, a reliable approach for design rainfall selection is proposed in order to optimise stormwater treatment based on both, stormwater quality and quantity. This is a paradigm shift from the common approach where stormwater treatment systems are designed based solely on stormwater quantity data. Additionally, how pollutant build-up and stormwater runoff quality vary with a range of catchment characteristics was also investigated. Based on the study out- comes, it can be concluded that the use of only a limited number of catchment parameters such as land use and impervious surface percentage, as it is the case in current modelling approaches, could result in appreciable error in water quality estimation. Influential factors which should be incorporated into modelling in relation to catchment characteristics, should also include urban form and impervious surface area distribution. The knowledge created through the research investigations discussed in this monograph is expected to make a significant contribution to engineering practice such as hydrologic and stormwater quality modelling, stormwater treatment design and urban planning, as the study outcomes provide practical approaches and recommendations for urban stormwater quality enhancement. Furthermore, this monograph also demonstrates how fundamental knowledge of stormwater quality processes can be translated to provide guidance on engineering practice, the comprehensive application of multivariate data analyses techniques and a paradigm on integrative use of computer models and mathematical models to derive practical outcomes.

Modelling intermittent microwave convective drying (IMCD) of food materials

This thesis develops comprehensive mathematical models for an advanced drying technology Intermittent Microwave Convective Drying (IMCD). The models provide an improved physical understanding of the heat and mass transport during the drying process, which will help to improve the quality of dried food and energy efficiency of the process, as well as will increase the ability of automation and optimization. The final model in this thesis represents the most comprehensive fundamental multiphase model for IMCD that considers 3D electromagnetics coupled with multiphase porous media transport processes. The 3D electromagnetics considers Maxwell's equation and multiphase transport model considers three different phases: solid matrix, liquid water and gas consisting water vapour and air. The multiphase transport includes pressure-driven flow, capillary diffusion, binary diffusion, and evaporation. The models developed in this thesis were validated with extensive experimental investigations.

Linking business goals to process models in semantic business process modeling

Broad knowledge is required when a business process is modeled by a business analyst. We argue that existing Business Process Management methodologies do not consider business goals at the appropriate level. In this paper we present an approach to integrate business goals and business process models. We design a Business Goal Ontology for modeling business goals. Furthermore, we devise a modeling pattern for linking the goals to process models and show how the ontology can be used in query answering. In this way, we integrate the intentional perspective into our business process ontology framework, enriching the process description and enabling new types of business process analysis. © 2008 IEEE.

Mathematical modelling of the impaction and spreading of spray droplets on leaves

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.

Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0

Effects of environmental variation on ecological and evolutionary dynamics

Environmental variation is a fact of life for all the species on earth: for any population of any particular species, the local environmental conditions are liable to vary in both time and space. In today's world, anthropogenic activity is causing habitat loss and fragmentation for many species, which may profoundly alter the characteristics of environmental variation in remaining habitat. Previous research indicates that, as habitat is lost, the spatial configuration of remaining habitat will increasingly affect the dynamics by which populations are governed. Through the use of mathematical models, this thesis asks how environmental variation interacts with species properties to influence population dynamics, local adaptation, and dispersal evolution. More specifically, we couple continuous-time continuous-space stochastic population dynamic models to landscape models. We manipulate environmental variation via parameters such as mean patch size, patch density, and patch longevity. Among other findings, we show that a mixture of high and low quality habitat is commonly better for a population than uniformly mediocre habitat. This conclusion is justified by purely ecological arguments, yet the positive effects of landscape heterogeneity may be enhanced further by local adaptation, and by the evolution of short-ranged dispersal. The predicted evolutionary responses to environmental variation are complex, however, since they involve numerous conflicting factors. We discuss why the species that have high levels of local adaptation within their ranges may not be the same species that benefit from local adaptation during range expansion. We show how habitat loss can lead to either increased or decreased selection for dispersal depending on the type of habitat and the manner in which it is lost. To study the models, we develop a recent analytical method, Perturbation expansion, to enable the incorporation of environmental variation. Within this context, we use two methods to address evolutionary dynamics: Adaptive dynamics, which assumes mutations occur infrequently so that the ecological and evolutionary timescales can be separated, and via Genotype distributions, which assume mutations are more frequent. The two approaches generally lead to similar predictions yet, exceptionally, we show how the evolutionary response of dispersal behaviour to habitat turnover may qualitatively depend on the mutation rate.

Build-up of toxic metals on the impervious surfaces of a commercial seaport

In the context of increasing threats to the sensitive marine ecosystem by toxic metals, this study investigated the metal build-up on impervious surfaces specific to commercial seaports. The knowledge generated in this study will contribute to managing toxic metal pollution of the marine ecosystem. The study found that inter-modal operations and main access roadway had the highest loads followed by container storage and vehicle marshalling sites, while the quay line and short term storage areas had the lowest. Additionally, it was found that Cr, Al, Pb, Cu and Zn were predominantly attached to solids, while significant amount of Cu, Pb and Zn were found as nutrient complexes. As such, treatment options based on solids retention can be effective for some metal species, while ineffective for other species. Furthermore, Cu and Zn are more likely to become bioavailable in seawater due to their strong association with nutrients. Mathematical models to replicate the metal build-up process were also developed using experimental design approach and partial least square regression. The models for Cr and Pb were found to be reliable, while those for Al, Zn and Cu were relatively less reliable, but could be employed for preliminary investigations.

A quantum stochastic Lie-Trotter product formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

Models of Dispersal and Diversification

Ecology and evolutionary biology is the study of life on this planet. One of the many methods applied to answering the great diversity of questions regarding the lives and characteristics of individual organisms, is the utilization of mathematical models. Such models are used in a wide variety of ways. Some help us to reason, functioning as aids to, or substitutes for, our own fallible logic, thus making argumentation and thinking clearer. Models which help our reasoning can lead to conceptual clarification; by expressing ideas in algebraic terms, the relationship between different concepts become clearer. Other mathematical models are used to better understand yet more complicated models, or to develop mathematical tools for their analysis. Though helping us to reason and being used as tools in the craftmanship of science, many models do not tell us much about the real biological phenomena we are, at least initially, interested in. The main reason for this is that any mathematical model is a simplification of the real world, reducing the complexity and variety of interactions and idiosynchracies of individual organisms. What such models can tell us, however, both is and has been very valuable throughout the history of ecology and evolution. Minimally, a model simplifying the complex world can tell us that in principle, the patterns produced in a model could also be produced in the real world. We can never know how different a simplified mathematical representation is from the real world, but the similarity models do strive for, gives us confidence that their results could apply. This thesis deals with a variety of different models, used for different purposes. One model deals with how one can measure and analyse invasions; the expanding phase of invasive species. Earlier analyses claims to have shown that such invasions can be a regulated phenomena, that higher invasion speeds at a given point in time will lead to a reduction in speed. Two simple mathematical models show that analysis on this particular measure of invasion speed need not be evidence of regulation. In the context of dispersal evolution, two models acting as proof-of-principle are presented. Parent-offspring conflict emerges when there are different evolutionary optima for adaptive behavior for parents and offspring. We show that the evolution of dispersal distances can entail such a conflict, and that under parental control of dispersal (as, for example, in higher plants) wider dispersal kernels are optimal. We also show that dispersal homeostasis can be optimal; in a setting where dispersal decisions (to leave or stay in a natal patch) are made, strategies that divide their seeds or eggs into fractions that disperse or not, as opposed to randomized for each seed, can prevail. We also present a model of the evolution of bet-hedging strategies; evolutionary adaptations that occur despite their fitness, on average, being lower than a competing strategy. Such strategies can win in the long run because they have a reduced variance in fitness coupled with a reduction in mean fitness, and fitness is of a multiplicative nature across generations, and therefore sensitive to variability. This model is used for conceptual clarification; by developing a population genetical model with uncertain fitness and expressing genotypic variance in fitness as a product between individual level variance and correlations between individuals of a genotype. We arrive at expressions that intuitively reflect two of the main categorizations of bet-hedging strategies; conservative vs diversifying and within- vs between-generation bet hedging. In addition, this model shows that these divisions in fact are false dichotomies.

Non-conservatively loaded stochastic columns

A new finite element method is developed to analyse non-conservative structures with more than one parameter behaving in a stochastic manner. As a generalization, this paper treats the subsequent non-self-adjoint random eigenvalue problem that arises when the material property values of the non-conservative structural system have stochastic fluctuations resulting from manufacturing and measurement errors. The free vibration problems of stochastic Beck's column and stochastic Leipholz column whose Young's modulus and mass density are distributed stochastically are considered. The stochastic finite element method that is developed, is implemented to arrive at a random non-self-adjoint algebraic eigenvalue problem. The stochastic characteristics of eigensolutions are derived in terms of the stochastic material property variations. Numerical examples are given. It is demonstrated that, through this formulation, the finite element discretization need not be dependent on the characteristics of stochastic processes of the fluctuations in material property value.

Mathematical modelling of neurons and neural networks

The basic concepts and techniques involved in the development and analysis of mathematical models for individual neurons and networks of neurons are reviewed. Some of the interesting results obtained from recent work in this field are described. The current status of research in this field in India is discussed

Relative performances of textural models in estimating soil moisture characteristic

The soil moisture characteristic (SMC) forms an important input to mathematical models of water and solute transport in the unsaturated-soil zone. Owing to their simplicity and ease of use, texture-based regression models are commonly used to estimate the SMC from basic soil properties. In this study, the performances of six such regression models were evaluated on three soils. Moisture characteristics generated by the regression models were statistically compared with the characteristics developed independently from laboratory and in-situ retention data of the soil profiles. Results of the statistical performance evaluation, while providing useful information on the errors involved in estimating the SMC, also highlighted the importance of the nature of the data set underlying the regression models. Among the models evaluated, the one possessing an underlying data set of in-situ measurements was found to be the best estimator of the in-situ SMC for all the soils. Considerable errors arose when a textural model based on laboratory data was used to estimate the field retention characteristics of unsaturated soils.

Advances in the Mathematical Modelling of Hepatitis C Virus Dynamics

Mathematical models have provided key insights into the pathogenesis of hepatitis C virus (HCV) in vivo, suggested predominant mechanism(s) of drug action, explained confounding patterns of viral load changes in HCV infected patients undergoing therapy, and presented a framework for therapy optimization. In this article, I present an overview of the major advances in the mathematical modeling of HCV dynamics.

First passage distributions for long memory processes

We study the distribution of first passage time for Levy type anomalous diffusion. A fractional Fokker-Planck equation framework is introduced.For the zero drift case, using fractional calculus an explicit analytic solution for the first passage time density function in terms of Fox or H-functions is given. The asymptotic behaviour of the density function is discussed. For the nonzero drift case, we obtain an expression for the Laplace transform of the first passage time density function, from which the mean first passage time and variance are derived.