Intrinsic kinetics of titania photocatalysis : simplified models for their investigation

Even though titanium dioxide photocatalysis has been promoted as a leading green technology for water purification, many issues have hindered its application on a large commercial scale. For the materials scientist the main issues have centred the synthesis of more efficient materials and the investigation of degradation mechanisms; whereas for the engineers the main issues have been the development of appropriate models and the evaluation of intrinsic kinetics parameters that allow the scale up or re-design of efficient large-scale photocatalytic reactors. In order to obtain intrinsic kinetics parameters the reaction must be analysed and modelled considering the influence of the radiation field, pollutant concentrations and fluid dynamics. In this way, the obtained kinetic parameters are independent of the reactor size and configuration and can be subsequently used for scale-up purposes or for the development of entirely new reactor designs. This work investigates the intrinsic kinetics of phenol degradation over titania film due to the practicality of a fixed film configuration over a slurry. A flat plate reactor was designed in order to be able to control reaction parameters that include the UV irradiance, flow rates, pollutant concentration and temperature. Particular attention was paid to the investigation of the radiation field over the reactive surface and to the issue of mass transfer limited reactions. The ability of different emission models to describe the radiation field was investigated and compared to actinometric measurements. The RAD-LSI model was found to give the best predictions over the conditions tested. Mass transfer issues often limit fixed film reactors. The influence of this phenomenon was investigated with specifically planned sets of benzoic acid experiments and with the adoption of the stagnant film model. The phenol mass transfer coefficient in the system was calculated to be km,phenol=8.5815x10-7Re0.65(ms-1). The data obtained from a wide range of experimental conditions, together with an appropriate model of the system, has enabled determination of intrinsic kinetic parameters. The experiments were performed in four different irradiation levels (70.7, 57.9, 37.1 and 20.4 W m-2) and combined with three different initial phenol concentrations (20, 40 and 80 ppm) to give a wide range of final pollutant conversions (from 22% to 85%). The simple model adopted was able to fit the wide range of conditions with only four kinetic parameters; two reaction rate constants (one for phenol and one for the family of intermediates) and their corresponding adsorption constants. The intrinsic kinetic parameters values were defined as kph = 0.5226 mmol m-1 s-1 W-1, kI = 0.120 mmol m-1 s-1 W-1, Kph = 8.5 x 10-4 m3 mmol-1 and KI = 2.2 x 10-3 m3 mmol-1. The flat plate reactor allowed the investigation of the reaction under two different light configurations; liquid and substrate side illumination. The latter of particular interest for real world applications where light absorption due to turbidity and pollutants contained in the water stream to be treated could represent a significant issue. The two light configurations allowed the investigation of the effects of film thickness and the determination of the catalyst optimal thickness. The experimental investigation confirmed the predictions of a porous medium model developed to investigate the influence of diffusion, advection and photocatalytic phenomena inside the porous titania film, with the optimal thickness value individuated at 5 ìm. The model used the intrinsic kinetic parameters obtained from the flat plate reactor to predict the influence of thickness and transport phenomena on the final observed phenol conversion without using any correction factor; the excellent match between predictions and experimental results provided further proof of the quality of the parameters obtained with the proposed method.

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

An investigation on the accuracy of regional ocean models through field trials

Recent efforts in mission planning for underwater vehicles have utilised predictive models to aid in navigation, optimal path planning and drive opportunistic sampling. Although these models provide information at a unprecedented resolutions and have proven to increase accuracy and effectiveness in multiple campaigns, most are deterministic in nature. Thus, predictions cannot be incorporated into probabilistic planning frameworks, nor do they provide any metric on the variance or confidence of the output variables. In this paper, we provide an initial investigation into determining the confidence of ocean model predictions based on the results of multiple field deployments of two autonomous underwater vehicles. For multiple missions conducted over a two-month period in 2011, we compare actual vehicle executions to simulations of the same missions through the Regional Ocean Modeling System in an ocean region off the coast of southern California. This comparison provides a qualitative analysis of the current velocity predictions for areas within the selected deployment region. Ultimately, we present a spatial heat-map of the correlation between the ocean model predictions and the actual mission executions. Knowing where the model provides unreliable predictions can be incorporated into planners to increase the utility and application of the deterministic estimations.

Towards Bayesian experimental design for nonlinear models that require a large number of sampling times

The use of Bayesian methodologies for solving optimal experimental design problems has increased. Many of these methods have been found to be computationally intensive for design problems that require a large number of design points. A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented. The approach involves the use of lower dimensional parameterisations that consist of a few design variables, which generate multiple design points. Using this approach, one simply has to search over a few design variables, rather than searching over a large number of optimal design points, thus providing substantial computational savings. The methodologies are demonstrated on four applications, including the selection of sampling times for pharmacokinetic and heat transfer studies, and involve nonlinear models. Several Bayesian design criteria are also compared and contrasted, as well as several different lower dimensional parameterisation schemes for generating the many design points.

Coordinated probabilistic optimal decision-making model for multi-area ATC with risk control

In the decision-making of multi-area ATC (Available Transfer Capacity) in electricity market environment, the existing resources of transmission network should be optimally dispatched and coordinately employed on the premise that the secure system operation is maintained and risk associated is controllable. The non-sequential Monte Carlo simulation is used to determine the ATC probability density distribution of specified areas under the influence of several uncertainty factors, based on which, a coordinated probabilistic optimal decision-making model with the maximal risk benefit as its objective is developed for multi-area ATC. The NSGA-II is applied to calculate the ATC of each area, which considers the risk cost caused by relevant uncertainty factors and the synchronous coordination among areas. The essential characteristics of the developed model and the employed algorithm are illustrated by the example of IEEE 118-bus test system. Simulative result shows that, the risk of multi-area ATC decision-making is influenced by the uncertainties in power system operation and the relative importance degrees of different areas.

Damping structure selection in nonlinear ship manoeuvring models

This paper presents the application of a statistical method for model structure selection of lift-drag and viscous damping components in ship manoeuvring models. The damping model is posed as a family of linear stochastic models, which is postulated based on previous work in the literature. Then a nested test of hypothesis problem is considered. The testing reduces to a recursive comparison of two competing models, for which optimal tests in the Neyman sense exist. The method yields a preferred model structure and its initial parameter estimates. Alternatively, the method can give a reduced set of likely models. Using simulated data we study how the selection method performs when there is both uncorrelated and correlated noise in the measurements. The first case is related to instrumentation noise, whereas the second case is related to spurious wave-induced motion often present during sea trials. We then consider the model structure selection of a modern high-speed trimaran ferry from full scale trial data.

Comparing different approach and avoidance models of learning and personality in the prediction of work, university, and leadership outcomes

Jackson (2005) developed a hybrid model of personality and learning, known as the learning styles profiler (LSP) which was designed to span biological, socio-cognitive, and experiential research foci of personality and learning research. The hybrid model argues that functional and dysfunctional learning outcomes can be best understood in terms of how cognitions and experiences control, discipline, and re-express the biologically based scale of sensation-seeking. In two studies with part-time workers undertaking tertiary education (N equals 137 and 58), established models of approach and avoidance from each of the three different research foci were compared with Jackson's hybrid model in their predictiveness of leadership, work, and university outcomes using self-report and supervisor ratings. Results showed that the hybrid model was generally optimal and, as hypothesized, that goal orientation was a mediator of sensation-seeking on outcomes (work performance, university performance, leader behaviours, and counterproductive work behaviour). Our studies suggest that the hybrid model has considerable promise as a predictor of work and educational outcomes as well as dysfunctional outcomes.

Simulation-based fully Bayesian experimental design for mixed effects models

In this paper, we present fully Bayesian experimental designs for nonlinear mixed effects models, in which we develop simulation-based optimal design methods to search over both continuous and discrete design spaces. Although Bayesian inference has commonly been performed on nonlinear mixed effects models, there is a lack of research into performing Bayesian optimal design for nonlinear mixed effects models that require searches to be performed over several design variables. This is likely due to the fact that it is much more computationally intensive to perform optimal experimental design for nonlinear mixed effects models than it is to perform inference in the Bayesian framework. In this paper, the design problem is to determine the optimal number of subjects and samples per subject, as well as the (near) optimal urine sampling times for a population pharmacokinetic study in horses, so that the population pharmacokinetic parameters can be precisely estimated, subject to cost constraints. The optimal sampling strategies, in terms of the number of subjects and the number of samples per subject, were found to be substantially different between the examples considered in this work, which highlights the fact that the designs are rather problem-dependent and require optimisation using the methods presented in this paper.

A comparison of three models for mine water management

Water management is vital for mine sites both for production and sustainability related issues. Effective water management is a complex task since the role of water on mine sites is multifaceted. Computers models are tools that represent mine site water interaction and can be used by mine sites to inform or evaluate their water management strategies. There exist several types of models that can be used to represent mine site water interactions. This paper presents three such models: an operational model, an aggregated systems model and a generic systems model. For each model the paper provides a description and example followed by an analysis of its advantages and disadvantages. The paper hypotheses that since no model is optimal for all situations, each model should be applied in situations where it is most appropriate based upon the scale of water interactions being investigated, either unit (operation), inter-site (aggregated systems) or intra-site (generic systems).

Compressed sensing using hidden Markov models with application to vision based aircraft tracking

This paper investigates compressed sensing using hidden Markov models (HMMs) and hence provides an extension of recent single frame, bounded error sparse decoding problems into a class of sparse estimation problems containing both temporal evolution and stochastic aspects. This paper presents two optimal estimators for compressed HMMs. The impact of measurement compression on HMM filtering performance is experimentally examined in the context of an important image based aircraft target tracking application. Surprisingly, tracking of dim small-sized targets (as small as 5-10 pixels, with local detectability/SNR as low as − 1.05 dB) was only mildly impacted by compressed sensing down to 15% of original image size.

An evaluation of crowd counting methods, features and regression models

Existing crowd counting algorithms rely on holistic, local or histogram based features to capture crowd properties. Regression is then employed to estimate the crowd size. Insufficient testing across multiple datasets has made it difficult to compare and contrast different methodologies. This paper presents an evaluation across multiple datasets to compare holistic, local and histogram based methods, and to compare various image features and regression models. A K-fold cross validation protocol is followed to evaluate the performance across five public datasets: UCSD, PETS 2009, Fudan, Mall and Grand Central datasets. Image features are categorised into five types: size, shape, edges, keypoints and textures. The regression models evaluated are: Gaussian process regression (GPR), linear regression, K nearest neighbours (KNN) and neural networks (NN). The results demonstrate that local features outperform equivalent holistic and histogram based features; optimal performance is observed using all image features except for textures; and that GPR outperforms linear, KNN and NN regression

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.

Accounting for management costs in sensitivity analyses of matrix population models

Traditional sensitivity and elasticity analyses of matrix population models have been used to inform management decisions, but they ignore the economic costs of manipulating vital rates. For example, the growth rate of a population is often most sensitive to changes in adult survival rate, but this does not mean that increasing that rate is the best option for managing the population because it may be much more expensive than other options. To explore how managers should optimize their manipulation of vital rates, we incorporated the cost of changing those rates into matrix population models. We derived analytic expressions for locations in parameter space where managers should shift between management of fecundity and survival, for the balance between fecundity and survival management at those boundaries, and for the allocation of management resources to sustain that optimal balance. For simple matrices, the optimal budget allocation can often be expressed as simple functions of vital rates and the relative costs of changing them. We applied our method to management of the Helmeted Honeyeater (Lichenostomus melanops cassidix; an endangered Australian bird) and the koala (Phascolarctos cinereus) as examples. Our method showed that cost-efficient management of the Helmeted Honeyeater should focus on increasing fecundity via nest protection, whereas optimal koala management should focus on manipulating both fecundity and survival simultaneously. These findings are contrary to the cost-negligent recommendations of elasticity analysis, which would suggest focusing on managing survival in both cases. A further investigation of Helmeted Honeyeater management options, based on an individual-based model incorporating density dependence, spatial structure, and environmental stochasticity, confirmed that fecundity management was the most cost-effective strategy. Our results demonstrate that decisions that ignore economic factors will reduce management efficiency. ©2006 Society for Conservation Biology.

Optimal allocation of conservation effort among subpopulations of a threatened species: How important is patch quality?

Money is often a limiting factor in conservation, and attempting to conserve endangered species can be costly. Consequently, a framework for optimizing fiscally constrained conservation decisions for a single species is needed. In this paper we find the optimal budget allocation among isolated subpopulations of a threatened species to minimize local extinction probability. We solve the problem using stochastic dynamic programming, derive a useful and simple alternative guideline for allocating funds, and test its performance using forward simulation. The model considers subpopulations that persist in habitat patches of differing quality, which in our model is reflected in different relationships between money invested and extinction risk. We discover that, in most cases, subpopulations that are less efficient to manage should receive more money than those that are more efficient to manage, due to higher investment needed to reduce extinction risk. Our simple investment guideline performs almost as well as the exact optimal strategy. We illustrate our approach with a case study of the management of the Sumatran tiger, Panthera tigris sumatrae, in Kerinci Seblat National Park (KSNP), Indonesia. We find that different budgets should be allocated to the separate tiger subpopulations in KSNP. The subpopulation that is not at risk of extinction does not require any management investment. Based on the combination of risks of extinction and habitat quality, the optimal allocation for these particular tiger subpopulations is an unusual case: subpopulations that occur in higher-quality habitat (more efficient to manage) should receive more funds than the remaining subpopulation that is in lower-quality habitat. Because the yearly budget allocated to the KSNP for tiger conservation is small, to guarantee the persistence of all the subpopulations that are currently under threat we need to prioritize those that are easier to save. When allocating resources among subpopulations of a threatened species, the combined effects of differences in habitat quality, cost of action, and current subpopulation probability of extinction need to be integrated. We provide a useful guideline for allocating resources among isolated subpopulations of any threatened species. © 2010 by the Ecological Society of America.

Optimal eradication: When to stop looking for an invasive plant

The notion of being sure that you have completely eradicated an invasive species is fanciful because of imperfect detection and persistent seed banks. Eradication is commonly declared either on an ad hoc basis, on notions of seed bank longevity, or on setting arbitrary thresholds of 1% or 5% confidence that the species is not present. Rather than declaring eradication at some arbitrary level of confidence, we take an economic approach in which we stop looking when the expected costs outweigh the expected benefits. We develop theory that determines the number of years of absent surveys required to minimize the net expected cost. Given detection of a species is imperfect, the optimal stopping time is a trade-off between the cost of continued surveying and the cost of escape and damage if eradication is declared too soon. A simple rule of thumb compares well to the exact optimal solution using stochastic dynamic programming. Application of the approach to the eradication programme of Helenium amarum reveals that the actual stopping time was a precautionary one given the ranges for each parameter. © 2006 Blackwell Publishing Ltd/CNRS.