Exact series solutions of reactive transport models with general initial conditions

Exact solutions of partial differential equation models describing the transport and decay of single and coupled multispecies problems can provide insight into the fate and transport of solutes in saturated aquifers. Most previous analytical solutions are based on integral transform techniques, meaning that the initial condition is restricted in the sense that the choice of initial condition has an important impact on whether or not the inverse transform can be calculated exactly. In this work we describe and implement a technique that produces exact solutions for single and multispecies reactive transport problems with more general, smooth initial conditions. We achieve this by using a different method to invert a Laplace transform which produces a power series solution. To demonstrate the utility of this technique, we apply it to two example problems with initial conditions that cannot be solved exactly using traditional transform techniques.

Mathematical modelling of fumigant transport in stored grain

Computational fluid dynamics, analytical solutions, and mathematical modelling approaches are used to gain insights into the distribution of fumigant gas within farm-scale, grain storage silos. Both fan-forced and tablet fumigation are considered in this work, which develops new models for use by researchers, primary producers and silo manufacturers to assist in the eradication grain storage pests.

Bayesian models for spatio-temporal assessment of disease

This thesis has contributed to the advancement of knowledge in disease modelling by addressing interesting and crucial issues relevant to modelling health data over space and time. The research has led to the increased understanding of spatial scales, temporal scales, and spatial smoothing for modelling diseases, in terms of their methodology and applications. This research is of particular significance to researchers seeking to employ statistical modelling techniques over space and time in various disciplines. A broad class of statistical models are employed to assess what impact of spatial and temporal scales have on simulated and real data.

An investigation of the impact of various geographical scales for the specification of spatial dependence

Ecological studies are based on characteristics of groups of individuals, which are common in various disciplines including epidemiology. It is of great interest for epidemiologists to study the geographical variation of a disease by accounting for the positive spatial dependence between neighbouring areas. However, the choice of scale of the spatial correlation requires much attention. In view of a lack of studies in this area, this study aims to investigate the impact of differing definitions of geographical scales using a multilevel model. We propose a new approach -- the grid-based partitions and compare it with the popular census region approach. Unexplained geographical variation is accounted for via area-specific unstructured random effects and spatially structured random effects specified as an intrinsic conditional autoregressive process. Using grid-based modelling of random effects in contrast to the census region approach, we illustrate conditions where improvements are observed in the estimation of the linear predictor, random effects, parameters, and the identification of the distribution of residual risk and the aggregate risk in a study region. The study has found that grid-based modelling is a valuable approach for spatially sparse data while the SLA-based and grid-based approaches perform equally well for spatially dense data.

Bayesian hierarchical models for analysing spatial point-based data at a grid level: A comparison of approaches

Spatial data are now prevalent in a wide range of fields including environmental and health science. This has led to the development of a range of approaches for analysing patterns in these data. In this paper, we compare several Bayesian hierarchical models for analysing point-based data based on the discretization of the study region, resulting in grid-based spatial data. The approaches considered include two parametric models and a semiparametric model. We highlight the methodology and computation for each approach. Two simulation studies are undertaken to compare the performance of these models for various structures of simulated point-based data which resemble environmental data. A case study of a real dataset is also conducted to demonstrate a practical application of the modelling approaches. Goodness-of-fit statistics are computed to compare estimates of the intensity functions. The deviance information criterion is also considered as an alternative model evaluation criterion. The results suggest that the adaptive Gaussian Markov random field model performs well for highly sparse point-based data where there are large variations or clustering across the space; whereas the discretized log Gaussian Cox process produces good fit in dense and clustered point-based data. One should generally consider the nature and structure of the point-based data in order to choose the appropriate method in modelling a discretized spatial point-based data.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Nutritional support in chronic obstructive Pulmonary Disease (COPD) a randomised trial

Rationale Nutritional support is effective in managing malnutrition in COPD (Collins et al., 2012) leading to functional improvements (Collins et al., 2013). However, comparative trials of first line interventions are lacking. This randomised trial compared the effectiveness of individualised dietary advice by a dietitian (DA) versus oral nutritional supplements (ONS). Methods A target sample of 200 stable COPD outpatients at risk of malnutrition (‘MUST’; medium + high risk) were randomised to either a 12-week intervention of ONS (ONS: ~400 kcal/d, ~40 g/d protein) or DA with supportive written advice. The primary outcome was quality of life (QoL) measured using St George’s Respiratory Questionnaire with secondary outcomes including handgrip strength, body weight and nutritional intake. Both the change from baseline and the differences between groups was analysed using SPSS version 20. Results 84 outpatients were recruited (ONS: 41 vs. DA: 43), 72 completed the intervention (ONS: 33 vs. DA: 39). Mean BMI was 18.2 SD 1.6 kg/m2, age 72.6 SD 10 years, FEV1% predicted 36 SD 15% (severe COPD). In comparison to the DA group, the ONS group experienced significantly greater improvements in protein intakes above baseline values at both week 6 (+21.0 SEM 4.3 g/d vs. +0.52 SEM 4.3 g/d; p < 0.001) and week 12 (+19.0 SEM 5.0 g/d vs. +1.0 SEM 3.6 g/d; p = 0.033;ANOVA). QoL and secondary outcomes remained stable at 12 weeks in both groups with slight improvements in the ONS group but no differences between groups. Conclusion In outpatients at risk of malnutrition with severe COPD, nutritional support involving either ONS or DA appears to maintain in tritional status, functional capacity and QoL. However, larger trials, and earlier, multi-modal nutritional interventions for an extended duration should be explored.

New insights from IODP Expedition 340 offshore Montserrat: First drilling of large volcanic island landslides

Montserrat now provides one of the most complete datasets for understanding the character and tempo of hazardous events at volcanic islands. Much of the erupted material ends up offshore, and this offshore record may be easier to date due to intervening hemiplegic sediments between event beds. The offshore dataset includes the first scientific drilling of volcanic island landslides during IODP Expedition 340, together with an unusually comprehensive set of shallow sediment cores and 2-D and 3-D seismic surveys. Most recently in 2013, Remotely Operated Vehicle (ROV) dives mapped and sampled the surface of the main landslide deposits. This contribution aims to provide an overview of key insights from ongoing work on IODP Expedition 340 Sites offshore Montserrat.Key objectives are to understand the composition (and hence source), emplacement mechanism (and hence tsunami generation) of major landslides, together with their frequency and timing relative to volcanic eruption cycles. The most recent major collapse event is Deposit 1, which involved ~1.8 km cubed of material and produced a blocky deposit at ~12-14ka. Deposit 1 appears to have involved not only the volcanic edifice, but also a substantial component of a fringing bioclastic shelf, and material locally incorporated from the underlying seafloor. This information allows us to test how first-order landslide morphology (e.g. blocky or elongate lobes) is related to first-order landslide composition. Preliminary analysis suggests that Deposit 1 occurred shortly before a second major landslide on the SW of the island (Deposit 5). It may have initiated English's Crater, but was not associated with a major change in magma composition. An associated turbidite-stack suggests it was emplaced in multiple stages, separated by at least a few hours and thus reducing the tsunami magnitude. The ROV dives show that mega-blocks in detail comprise smaller-scale breccias, which can travel significant distances without complete disintegration. Landslide Deposit 2 was emplaced at ~130ka, and is more voluminous (~8.4km cubed). It had a much more profound influence on the magmatic system, as it was linked to a major explosive mafic eruption and formation of a new volcanic centre (South Soufriere Hills) on the island. Site U1395 confirms a hypothesis based on the site survey seismic data that Deposit 2 includes a substantial component of pre-existing seafloor sediment. However, surprisingly, this pre-existing seafloor sediment in the lower part of Deposit 2 at Site U1395 is completely undeformed and flat lying, suggesting that Site U1395 penetrated a flat lying block. Work to date material from the upper part of U1396, U1395 and U1394 will also be summarised. This work is establishing a chronostratigraphy of major events over the last 1 Ma, with particularly detailed constraints during the last ~250ka. This is helping us to understand whether major landslides are related to cycles of volcanic eruptions.

The subordinated processes controlled by a family of subordinators and corresponding Fokker-Planck type equations

In this work, we consider subordinated processes controlled by a family of subordinators which consist of a power function of a time variable and a negative power function of an α-stable random variable. The effect of parameters in the subordinators on the subordinated process is discussed. By suitable variable substitutions and the Laplace transform technique, the corresponding fractional Fokker–Planck-type equations are derived. We also compute their mean square displacements in a free force field. By choosing suitable ranges of parameters, the resulting subordinated processes may be subdiffusive, normal diffusive or superdiffusive

Methods for constructing uncertainty intervals for queries of Bayesian nets

In this paper the issue of finding uncertainty intervals for queries in a Bayesian Network is reconsidered. The investigation focuses on Bayesian Nets with discrete nodes and finite populations. An earlier asymptotic approach is compared with a simulation-based approach, together with further alternatives, one based on a single sample of the Bayesian Net of a particular finite population size, and another which uses expected population sizes together with exact probabilities. We conclude that a query of a Bayesian Net should be expressed as a probability embedded in an uncertainty interval. Based on an investigation of two Bayesian Net structures, the preferred method is the simulation method. However, both the single sample method and the expected sample size methods may be useful and are simpler to compute. Any method at all is more useful than none, when assessing a Bayesian Net under development, or when drawing conclusions from an ‘expert’ system.

A directed continuous time random walk model with jump length depending on waiting time

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x,t) of finding the walker at position at time is completely determined by the Laplace transform of the probability density function φ(t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.

Has the Three-Gorges Dam made the Poyang Lake wetlands wetter and drier?

The Three-Georges Dam holds many records in the history of engineering. While the dam has produced benefits in terms of flood control, hydropower generation and increased navigation capacity of the Yangtze River, serious questions have been raised concerning its impact on both upstream and downstream ecosystems. It has been suggested that the dam operation intensifies the extremes of wet and dry conditions in the downstream Poyang Lake, and affects adversely important local wetlands. A floodgate has been proposed to maintain the lake water level by controlling the flow between the Poyang Lake and Yangtze River. Using extensive hydrological data and generalized linear statistical models, we demonstrated that the dam operation induces major changes in the downstream river discharge near the dam, including an average "water loss". The analysis also revealed considerable effects on the Poyang Lake water level, particularly a reduced level over the dry period from late summer to autumn. However, the dam impact needs to be further assessed based on long-term monitoring of the lake ecosystem, covering a wide range of parameters related to hydrological and hydraulic characteristics of the lake, water quality, geomorphological characteristics, aquatic biota and their habitat, wetland vegetation and associated fauna.

Scheme of squares: Part I. Systems formalism for potentiostatic studies

The so-called “Scheme of Squares”, displaying an interconnectivity of heterogeneous electron transfer and homogeneous (e.g., proton transfer) reactions, is analysed. Explicit expressions for the various partial currents under potentiostatic conditions are given. The formalism is applicable to several electrode geometries and models (e.g., semi-infinite linear diffusion, rotating disk electrodes, spherical or cylindrical systems) and the analysis is exact. The steady-state (t→∞) expressions for the current are directly given in terms of constant matrices whereas the transients are obtained as Laplace transforms that need to be inverted by approximation of numerical methods. The methodology employs a systems approach which replaces a system of partial differential equations (governing the concentrations of the several electroactive species) by an equivalent set of difference equations obeyed by the various partial currents.

The conservation status of the world’s reptiles

Effective and targeted conservation action requires detailed information about species, their distribution, systematics and ecology as well as the distribution of threat processes which affect them. Knowledge of reptilian diversity remains surprisingly disparate, and innovative means of gaining rapid insight into the status of reptiles are needed in order to highlight urgent conservation cases and inform environmental policy with appropriate biodiversity information in a timely manner. We present the first ever global analysis of extinction risk in reptiles, based on a random representative sample of 1500 species (16% of all currently known species). To our knowledge, our results provide the first analysis of the global conservation status and distribution patterns of reptiles and the threats affecting them, highlighting conservation priorities and knowledge gaps which need to be addressed urgently to ensure the continued survival of the world’s reptiles. Nearly one in five reptilian species are threatened with extinction, with another one in five species classed as Data Deficient. The proportion of threatened reptile species is highest in freshwater environments, tropical regions and on oceanic islands, while data deficiency was highest in tropical areas, such as Central Africa and Southeast Asia, and among fossorial reptiles. Our results emphasise the need for research attention to be focussed on tropical areas which are experiencing the most dramatic rates of habitat loss, on fossorial reptiles for which there is a chronic lack of data, and on certain taxa such as snakes for which extinction risk may currently be underestimated due to lack of population information. Conservation actions specifically need to mitigate the effects of human-induced habitat loss and harvesting, which are the predominant threats to reptiles.

Two-dimensional heat conduction with phase change in a semi-infinite mould

Analytical solution of a 2-dimensional problem of solidification of a superheated liquid in a semi-infinite mould has been studied in this paper. On the boundary, the prescribed temperature is such that the solidification starts simultaneously at all points of the boundary. Results are also given for the 2-dimensional ablation problem. The solution of the heat conduction equation has been obtained in terms of multiple Laplace integrals involving suitable unknown fictitious initial temperatures. These fictitious initial temperatures have interesting physical interpretations. By choosing suitable series expansions for fictitious initial temperatures and moving interface boundary, the unknown quantities can be determined. Solidification thickness has been calculated for short time and effect of parameters on the solidification thickness has been shown with the help of graphs.