Additional scaled solutions to Richards' equation for infiltration and drainage

Warrick and Hussen developed in the nineties of the last century a method to scale Richards' equation (RE) for similar soils. In this paper, new scaled solutions are added to the method of Warrick and Hussen considering a wider range of soils regardless of their dissimilarity. Gardner-Kozeny hydraulic functions are adopted instead of Brooks-Corey functions used originally by Warrick and Hussen. These functions allow to reduce the dependence of the scaled RE on the soil properties. To evaluate the proposed method (PM), the scaled RE was solved numerically using a finite difference method with a fully implicit scheme. Three cases were considered: constant-head infiltration, constant-flux infiltration, and drainage of an initially uniform wet soil. The results for five texturally different soils ranging from sand to clay (adopted from the literature) showed that the scaled solutions were invariant to a satisfactory degree. However, slight deviations were observed mainly for the sandy soil. Moreover, the scaled solutions deviated when the soil profile was initially wet in the infiltration case or when deeply wet in the drainage condition. Based on the PM, a Philip-type model was also developed to approximate RE solutions for the constant-head infiltration. The model showed a good agreement with the scaled RE for the same range of soils and conditions, however only for Gardner-Kozeny soils. Such a procedure reduces numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils. (C) 2011 Elsevier B.V. All rights reserved.

Thermal model for charring rate calculation in wooden cellular slabs under fire

Wood is a natural and traditional building material, as popular today as ever, and presents advantages. Physically, wood is strong and stiff, but compared with other materials like steel is light and flexible. Wood material can absorb sound very effectively and it is a relatively good heat insulator. But dry wood burns quite easily and produces a great deal of heat energy. The main disadvantage is the high level of combustion when exposed to fire, where the point at which it catches fire is from 200–400°C. After fire exposure, is need to determine if the charred wooden structures are safe for future use. Design methods require the use of computer modelling to predict the fire exposure and the capacity of structures to resist those action. Also, large or small scale experimental tests are necessary to calibrate and verify the numerical models. The thermal model is essential for wood structures exposed to fire, because predicts the charring rate as a function of fire exposure. The charring rate calculation of most structural wood elements allows simple calculations, but is more complicated for situations where the fire exposure is non-standard and in wood elements protected with other materials. In this work, the authors present different case studies using numerical models, that will help professionals analysing woods elements and the type of information needed to decide whether the charred structures are adequate or not to use. Different thermal models representing wooden cellular slabs, used in building construction for ceiling or flooring compartments, will be analysed and submitted to different fire scenarios (with the standard fire curve exposure). The same numerical models, considering insulation material inside the wooden cellular slabs, will be tested to compare and determine the fire time resistance and the charring rate calculation.

Thermal model for charring rate calculation in wooden cellular slabs under fire

Wood is a natural and traditional building material, as popular today as ever, and presents advantages. Physically, wood is strong and stiff, but compared with other materiais like steel is light and flexible. Wood material can absorb sound very effectively and it is a relatively good heat insulator. But dry wood does bum quite easily md produces a great deal ofheat energy. The main disadvantage is the high levei ofcombustion when exposed to fíre, where the point at which it catches fire is fi-om 200-400°C. After fu-e exposure, is need to determine if the charred wooden stmctures are safe for future use. Design methods require the use ofcomputer modelling to predict the fíre exposure and the capacity ofstructures to resist fhose action. Also, large or small scale experimental tests are necessary to calibrate and verify the numerical models. The thermal model is essential for wood stmctures exposed to fire, because predicts the charring rate as a fünction offire exposure. The charring rate calculation ofmost stmctural wood elements allows simple calculations, but is more complicated for situations where the fire exposure is non-standard and in wood elements protected with other materiais.

A proposed qualitative framework for heterogeneous burning of metallic materials : the 'melting rate triangle'

This paper presents a proposed qualitative framework to discuss the heterogeneous burning of metallic materials, through parameters and factors that influence the melting rate of the solid metallic fuel (either in a standard test or in service). During burning, the melting rate is related to the burning rate and is therefore an important parameter for describing and understanding the burning process, especially since the melting rate is commonly recorded during standard flammability testing for metallic materials and is incorporated into many relative flammability ranking schemes. However, whilst the factors that influence melting rate (such as oxygen pressure or specimen diameter) have been well characterized, there is a need for an improved understanding of how these parameters interact as part of the overall melting and burning of the system. Proposed here is the ‘Melting Rate Triangle’, which aims to provide this focus through a conceptual framework for understanding how the melting rate (of solid fuel) is determined and regulated during heterogeneous burning. In the paper, the proposed conceptual model is shown to be both (a) consistent with known trends and previously observed results, and (b)capable of being expanded to incorporate new data. Also shown are examples of how the Melting Rate Triangle can improve the interpretation of flammability test results. Slusser and Miller previously published an ‘Extended Fire Triangle’ as a useful conceptual model of ignition and the factors affecting ignition, providing industry with a framework for discussion. In this paper it is shown that a ‘Melting Rate Triangle’ provides a similar qualitative framework for burning, leading to an improved understanding of the factors affecting fire propagation and extinguishment.

Multiscale analysis of protein functions and stochastic modelling of gene transcriptional regulatory networks

Genomic and proteomic analyses have attracted a great deal of interests in biological research in recent years. Many methods have been applied to discover useful information contained in the enormous databases of genomic sequences and amino acid sequences. The results of these investigations inspire further research in biological fields in return. These biological sequences, which may be considered as multiscale sequences, have some specific features which need further efforts to characterise using more refined methods. This project aims to study some of these biological challenges with multiscale analysis methods and stochastic modelling approach. The first part of the thesis aims to cluster some unknown proteins, and classify their families as well as their structural classes. A development in proteomic analysis is concerned with the determination of protein functions. The first step in this development is to classify proteins and predict their families. This motives us to study some unknown proteins from specific families, and to cluster them into families and structural classes. We select a large number of proteins from the same families or superfamilies, and link them to simulate some unknown large proteins from these families. We use multifractal analysis and the wavelet method to capture the characteristics of these linked proteins. The simulation results show that the method is valid for the classification of large proteins. The second part of the thesis aims to explore the relationship of proteins based on a layered comparison with their components. Many methods are based on homology of proteins because the resemblance at the protein sequence level normally indicates the similarity of functions and structures. However, some proteins may have similar functions with low sequential identity. We consider protein sequences at detail level to investigate the problem of comparison of proteins. The comparison is based on the empirical mode decomposition (EMD), and protein sequences are detected with the intrinsic mode functions. A measure of similarity is introduced with a new cross-correlation formula. The similarity results show that the EMD is useful for detection of functional relationships of proteins. The third part of the thesis aims to investigate the transcriptional regulatory network of yeast cell cycle via stochastic differential equations. As the investigation of genome-wide gene expressions has become a focus in genomic analysis, researchers have tried to understand the mechanisms of the yeast genome for many years. How cells control gene expressions still needs further investigation. We use a stochastic differential equation to model the expression profile of a target gene. We modify the model with a Gaussian membership function. For each target gene, a transcriptional rate is obtained, and the estimated transcriptional rate is also calculated with the information from five possible transcriptional regulators. Some regulators of these target genes are verified with the related references. With these results, we construct a transcriptional regulatory network for the genes from the yeast Saccharomyces cerevisiae. The construction of transcriptional regulatory network is useful for detecting more mechanisms of the yeast cell cycle.

A model of workplace safety incorporating worker interactions and simple interventions

Although there was substantial research into the occupational health and safety sector over the past forty years, this generally focused on statistical analyses of data related to costs and/or fatalities and injuries. There is a lack of mathematical modelling of the interactions between workers and the resulting safety dynamics of the workplace. There is also little work investigating the potential impact of different safety intervention programs prior to their implementation. In this article, we present a fundamental, differential equation-based model of workplace safety that treats worker safety habits similarly to an infectious disease in an epidemic model. Analytical results for the model, derived via phase plane and stability analysis, are discussed. The model is coupled with a model of a generic safety strategy aimed at minimising unsafe work habits, to produce an optimal control problem. The optimal control model is solved using the forward-backward sweep numerical scheme implemented in Matlab.

A national satellite-based land-use regression model for air pollution exposure assessment in Australia

Land-use regression (LUR) is a technique that can improve the accuracy of air pollution exposure assessment in epidemiological studies. Most LUR models are developed for single cities, which places limitations on their applicability to other locations. We sought to develop a model to predict nitrogen dioxide (NO2) concentrations with national coverage of Australia by using satellite observations of tropospheric NO2 columns combined with other predictor variables. We used a generalised estimating equation (GEE) model to predict annual and monthly average ambient NO2 concentrations measured by a national monitoring network from 2006 through 2011. The best annual model explained 81% of spatial variation in NO2 (absolute RMS error=1.4 ppb), while the best monthly model explained 76% (absolute RMS error=1.9 ppb). We applied our models to predict NO2 concentrations at the ~350,000 census mesh blocks across the country (a mesh block is the smallest spatial unit in the Australian census). National population-weighted average concentrations ranged from 7.3 ppb (2006) to 6.3 ppb (2011). We found that a simple approach using tropospheric NO2 column data yielded models with slightly better predictive ability than those produced using a more involved approach that required simulation of surface-to-column ratios. The models were capable of capturing within-urban variability in NO2, and offer the ability to estimate ambient NO2 concentrations at monthly and annual time scales across Australia from 2006–2011. We are making our model predictions freely available for research.

Optimal barrier subdivision for Kramers' escape rate

We examine the effect of subdividing the potential barrier along the reaction coordinate on Kramers' escape rate for a model potential. Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate.

Flow pattern analysis in a highly stenotic patient-specific carotid bifurcation model using a turbulence model

The aim of this study is to investigate the blood flow pattern in carotid bifurcation with a high degree of luminal stenosis, combining in vivo magnetic resonance imaging (MRI) and computational fluid dynamics (CFD). A newly developed two-equation transitional model was employed to evaluate wall shear stress (WSS) distribution and pressure drop across the stenosis, which are closely related to plaque vulnerability. A patient with an 80% left carotid stenosis was imaged using high resolution MRI, from which a patient-specific geometry was reconstructed and flow boundary conditions were acquired for CFD simulation. A transitional model was implemented to investigate the flow velocity and WSS distribution in the patient-specific model. The peak time-averaged WSS value of approximately 73Pa was predicted by the transitional flow model, and the regions of high WSS occurred at the throat of the stenosis. High oscillatory shear index values up to 0.50 were present in a helical flow pattern from the outer wall of the internal carotid artery immediately after the throat. This study shows the potential suitability of a transitional turbulent flow model in capturing the flow phenomena in severely stenosed carotid arteries using patient-specific MRI data and provides the basis for further investigation of the links between haemodynamic variables and plaque vulnerability. It may be useful in the future for risk assessment of patients with carotid disease.

Mechanism of adsorption effects on electrode kinetics: Part I: Selection rules in the case of low coverage by molecular surfactants

It is shown that the effect of adsorption of inert molecules on electrode reaction rates is completely accounted for, by introducing into the rate equation, adsorption-induced changes in both the effective electrode area as well as in the electrostatic potential at the reaction site with an additional term for the noncoulombic interaction between the reactant and the adsorbate. The electrostatic potential at the reaction site due to the adsorbed layer is calculated using a model of discretely-distributed molecules in parallel orientation when adsorbed on the electrode with an allowance for thermal agitation. The resulting expression, which is valid for the limiting case of low coverages, is used to predict the types of molecular surfactants that are most likely to be useful for acceleration and inhibition of electrode reactions.

Oxidation of acetaldehyde to acetic acid in a sparger reactor

The kinetics of oxidation of acetaldehyde to acetic acid was studied in a sparger reactor using manganese acetate as the catalyst. Data obtained in a stirred tank reactor are used for analyzing the sparger reactor data. The rate of chemical reaction is extremely fast and can be neglected for the rate equation of the sparger reactor. A kinetic model applicable at any temperature and concentration within the range of the variables studied is developed which predicts the performance of the sparger reactor satisfactorily.

A new approach to the kinetics of size reduction in ball milling

The rate of breakage of feed in ball milling is usually represented in the form of a first-order rate equation. The equation was developed by treating a simple batch test mill as a well mixed reactor. Several case of deviation from the rule have been reported in the literature. This is attributed to the fact that accumulated fines interfere with the feed material and breaking events are masked by these fines. In the present paper, a new rate equation is proposed which takes into account the retarding effect of fines during milling. For this purpose the analogy of diffusion of ions through permeable membranes is adopted, with suitable modifications. The validity of the model is cross checked with the data obtained in batch grinding of ?850/+600 ?m size quartz. The proposed equation enables calculation of the rate of breakage of the feed at any instant of time.

Mean first passage time approach to the problem of optimal barrier subdivision for Kramer's escape rate

We consider the effect of subdividing the potential barrier along the reaction coordinate on Kramer's escape rate for a model potential, Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate, We cast the problem as a mean first passage time problem of a biased random walker and obtain equivalent results, We briefly summarize the results of our investigation on the increase in the escape rate by placing a blow-torch in the unstable part of one of the potential wells. (C) 1999 Elsevier Science B.V. All rights reserved.