Using mathematical models to predict the development of aircraft cabin fires

Computer based mathematical models describing aircraft fire have a role to play in the design and development of safer aircraft, in the implementation of safer and more rigorous certification criteria and in post mortuum accident investigation. As the cost involved in performing large-scale fire experiments for the next generation 'Ultra High Capacity Aircraft' (UHCA) are expected to be prohibitively high, the development and use of these modelling tools may become essential if these aircraft are to prove a safe and viable reality. By describing the present capabilities and limitations of aircraft fire models, this paper will examine the future development of these models in the areas of large scale applications through parallel computing, combustion modelling and extinguishment modelling.

Modelling air quality in street canyons: a review

High pollution levels have been often observed in urban street canyons due to the increased traffic emissions and reduced natural ventilation. Microscale dispersion models with different levels of complexity may be used to assess urban air qualityand support decision-making for pollution control strategies and traffic planning. Mathematical models calculate pollutant concentrations by solving either analytically a simplified set of parametric equations or numerically a set of differential equations that describe in detail wind flow and pollutant dispersion. Street canyon models, which might also include simplified photochemistry and particle deposition–resuspension algorithms, are often nested within larger-scale urban dispersion codes. Reduced-scale physical models in wind tunnels may also be used for investigating atmospheric processes within urban canyons and validating mathematical models. A range of monitoring techniques is used to measure pollutant concentrations in urban streets. Point measurement methods (continuous monitoring, passive and active pre-concentration sampling, grab sampling) are available for gaseous pollutants. A number of sampling techniques (mainlybased on filtration and impaction) can be used to obtain mass concentration, size distribution and chemical composition of particles. A combination of different sampling/monitoring techniques is often adopted in experimental studies. Relativelysimple mathematical models have usually been used in association with field measurements to obtain and interpret time series of pollutant concentrations at a limited number of receptor locations in street canyons. On the other hand, advanced numerical codes have often been applied in combination with wind tunnel and/or field data to simulate small-scale dispersion within the urban canopy.

Computational modelling of particle degradation in dilute phase pneumatic conveyors

The aim of this paper is to develop a mathematical model with the ability to predict particle degradation during dilute phase pneumatic conveying. A numerical procedure, based on a matrix representation of degradation processes, is presented to determine the particle impact degradation propensity from a small number of particle single impact tests carried out in a new designed laboratory scale degradation tester. A complete model of particle degradation during dilute phase pneumatic conveying is then described, where the calculation of degradation propensity is coupled with a flow model of the solids and gas phases in the pipeline. Numerical results are presented for degradation of granulated sugar in an industrial scale pneumatic conveyor.

Computational modelling of multi-physics and multi-scale processes in parallel

This paper provides an overview of the developing needs for simulation software technologies for the computational modelling of problems that involve combinations of interactions amongst varying physical phenomena over a variety of time and space scales. Computational modelling of such problems requires software tech1nologies that enable the mathematical description of the interacting physical phenomena together with the solution of the resulting suites of equations in a numerically consistent and compatible manner. This functionality requires the structuring of simulation modules for specific physical phenomena so that the coupling can be effectively represented. These multi-physics and multi-scale computations are very compute intensive and the simulation software must operate effectively in parallel if it is to be used in this context. An approach to these classes of multi-disciplinary simulation in parallel is described, with some key examples of application to2 challenging engineering problems.

Modelling of dosator operation for improved manufacturing performance

Purpose: To develop an improved mathematical model for the prediction of dose accuracy of Dosators - based upon the geometry of the machine in conjunction with measured flow properties of the powder. Methods: A mathematical model has been created, based on a analytical method of differential slices - incorporating measured flow properties. The key flow properties of interest in this investigation were: flow function, effective angle of wall friction, wall adhesion, bulk density, stress ratio K and permeability. To simulate the real process and (very importantly) validate the model, a Dosator test-rig has been used to measure the forces acting on the Dosator during the filling stage, the force required to eject the dose and the dose weight. Results: Preliminary results were obtained from the Dosator test-rig. Figure 1 [Omitted] shows the dose weight for different depths to the bottom of the powder bed at the end of the stroke and different levels of pre-compaction of the powder bed. A strong influence over dose weight arising from the proximity between the Dosator and the bottom of the powder bed at the end of the stroke and the conditions of the powder bed has been established. Conclusions: The model will provide a useful tool to predict dosing accuracy and, thus, optimise the future design of Dosator based equipment technology – based on measured bulk properties of the powder to be handled. Another important factor (with a significant influence) on Dosator processes, is the condition of the powder bed and the clearance between the Dosator and the bottom of the powder bed.

Modelling dosator filling and discharge of powder

Dosators and other dosing mechanisms operating on generally similar principles are very widely used in the pharmaceutical industry for capsule filling, and for dosing products that are delivered to the customer in powder form such as inhalers. This is a trend that is set to increase. However a significant problem for this technology is being able to predict how accurately and reliably, new drug formulations will be dosed from these machines prior to manufacture. This paper presents a review of the literature relating to powder dosators which considers mathematical models for predicting dosator performance, the effects of the dosator geometry and machine settings on the accuracy of the dose weight. An overview of a model based on classical powder mechanics theory that has been developed at The University of Greenwich is presented. The model uses inputs from a range of powder characterisation tests including, wall friction, bulk density, stress ratio and permeability. To validate the model it is anticipated that it will be trialled for a range of powders alongside a single shot dosator test rig.

Economic modelling of antenatal screening and ultrasound scanning programmes for identification of fetal abnormalities

Objective Within the framework of a health technology assessment and using an economic model, to determine the most clinically and cost effective policy of scanning and screening for fetal abnormalities in early pregnancy. Design A discrete event simulation model of 50,000 singleton pregnancies. Setting Maternity services in Scotland. Population Women during the first 24 weeks of their pregnancy. Methods The mathematical model was populated with data on uptake of screening, prevalence, detection and false positive rates for eight fetal abnormalities and with costs for ultrasound scanning and serum screening. Inclusion of abnormalities was based on the relative prevalence and clinical importance of conditions and the availability of data. Six strategies for the identification of abnormalities prenatally including combinations of first and second trimester ultrasound scanning and first and second trimester screening for chromosomal abnormalities were compared. Main outcome measures The number of abnormalities detected and missed, the number of iatrogenic losses resulting from invasive tests, the total cost of strategies and the cost per abnormality detected were compared between strategies. Results First trimester screening for chromosomal abnormalities costs more than second trimester screening but results in fewer iatrogenic losses. Strategies which include a second trimester ultrasound scan result in more abnormalities being detected and have lower costs per anomaly detected. Conclusions The preferred strategy includes both first and second trimester ultrasound scans and a first trimester screening test for chromosomal abnormalities. It has been recommended that this policy is offered to all women in Scotland.

Linear quadratic and tumour control probability modelling in external beam radiotherapy

The standard linear-quadratic (LQ) survival model for external beam radiotherapy is reviewed with particular emphasis on studying how different schedules of radiation treatment planning may be affected by different tumour repopulation kinetics. The LQ model is further examined in the context of tumour control probability (TCP) models. The application of the Zaider and Minerbo non-Poissonian TCP model incorporating the effect of cellular repopulation is reviewed. In particular the recent development of a cell cycle model within the original Zaider and Minerbo TCP formalism is highlighted. Application of this TCP cell-cycle model in clinical treatment plans is explored and analysed.

Modelling the comet assay

The single-cell gel electrophoresis technique or comet assay is widely regarded as a quick and reliable method of analysing DNA damage in individual cells. It has a proven track record from the fields of biomonitoring to nutritional studies. The assay operates by subjecting cells that are fixed in agarose to high salt and detergent lysis, thus removing all the cellular content except the DNA. By relaxing the DNA in an alkaline buffer, strands containing breaks are released from supercoiling. Upon electrophoresis, these strands are pulled out into the agarose, forming a tail which, when stained with a fluorescent dye, can be analysed by fluorescence microscopy. The intensity of this tail reflects the amount of DNA damage sustained. Despite being such an established and widely used assay, there are still many aspects of the comet assay which are not fully understood. The present review looks at how the comet assay is being used, and highlights some of its limitations. The protocol itself varies among laboratories, so results from similar studies may vary. Given such discrepancies, it would be attractive to break the assay into components to generate a mathematical model to investigate specific parameters.

Computational simulation methodologies for mechanobiological modelling: a cell-centred approach to neointima development in stents

The design of medical devices could be very much improved if robust tools were available for computational simulation of tissue response to the presence of the implant. Such tools require algorithms to simulate the response of tissues to mechanical and chemical stimuli. Available methodologies include those based on the principle of mechanical homeostasis, those which use continuum models to simulate biological constituents, and the cell-centred approach, which models cells as autonomous agents. In the latter approach, cell behaviour is governed by rules based on the state of the local environment around the cell; and informed by experiment. Tissue growth and differentiation requires simulating many of these cells together. In this paper, the methodology and applications of cell-centred techniques-with particular application to mechanobiology-are reviewed, and a cell-centred model of tissue formation in the lumen of an artery in response to the deployment of a stent is presented. The method is capable of capturing some of the most important aspects of restenosis, including nonlinear lesion growth with time. The approach taken in this paper provides a framework for simulating restenosis; the next step will be to couple it with more patient-specific geometries and quantitative parameter data.

Modelling road traffic accidents using macroscopic second-order models of traffic flow

In this paper, we introduce a macroscopic model for road traffic accidents along highway sections. We discuss the motivation and the derivation of such a model, and we present its mathematical properties. The results are presented by means of examples where a section of a crowded one-way highway contains in the middle a cluster of drivers whose dynamics are prone to road traffic accidents. We discuss the coupling conditions and present some existence results of weak solutions to the associated Riemann Problems. Furthermore, we illustrate some features of the proposed model through some numerical simulations. © The authors 2012.

Modelling 3D camera movement for vibration characterisation and multiple object identification with application to lighting assessment

Utilising cameras as a means to survey the surrounding environment is becoming increasingly popular in a number of different research areas and applications. Central to using camera sensors as input to a vision system, is the need to be able to manipulate and process the information captured in these images. One such application, is the use of cameras to monitor the quality of airport landing lighting at aerodromes where a camera is placed inside an aircraft and used to record images of the lighting pattern during the landing phase of a flight. The images are processed to determine a performance metric. This requires the development of custom software for the localisation and identification of luminaires within the image data. However, because of the necessity to keep airport operations functioning as efficiently as possible, it is difficult to collect enough image data to develop, test and validate any developed software. In this paper, we present a technique to model a virtual landing lighting pattern. A mathematical model is postulated which represents the glide path of the aircraft including random deviations from the expected path. A morphological method has been developed to localise and track the luminaires under different operating conditions. © 2011 IEEE.