331 resultados para Curves, Algebraic


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Fluid–solid interactions in natural and engineered porous solids underlie a variety of technological processes, including geological storage of anthropogenic greenhouse gases, enhanced coal bed methane recovery, membrane separation, and heterogeneous catalysis. The size, distribution and interconnectivity of pores, the chemical and physical properties of the solid and fluid phases collectively dictate how fluid molecules migrate into and through the micro- and meso-porous media, adsorb and ultimately react with the solid surfaces. Due to the high penetration power and relatively short wavelength of neutrons, smallangle neutron scattering (SANS) as well as ultra small-angle scattering (USANS) techniques are ideally suited for assessing the phase behavior of confined fluids under pressure as well as for evaluating the total porosity in engineered and natural porous systems including coal. Here we demonstrate that SANS and USANS can be also used for determining the fraction of the pore volume that is actually accessible to fluids as a function of pore sizes and study the fraction of inaccessible pores as a function of pore size in three coals from the Illinois Basin (USA) and Bowen Basin (Australia). Experiments were performed at CO2 and methane pressures up to 780 bar, including pressures corresponding to zero average contrast condition (ZAC), which is the pressure where no scattering from the accessible pores occurs. Scattering curves at the ZAC were compared with the scattering from same coals under vacuum and analysed using a newly developed approach that shows that the volume fraction of accessible pores in these coals varies between �90% in the macropore region to �30% in the mesopore region and the variation is distinctive for each of the examined coals. The developed methodology may be also applied for assessing the volume of accessible pores in other natural underground formations of interest for CO2 sequestration, such as saline aquifers as well as for estimating closed porosity in engineered porous solids of technological importance.

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This research analyses the extent of damage to buildings in Brisbane, Ipswich and Grantham during the recent Eastern Australia flooding and explore the role planning and design/construction regulations played in these failures. It highlights weaknesses in the current systems and propose effective solutions to mitigate future damage and financial loss under current or future climates. 2010 and early 2011 saw major flooding throughout much of Eastern Australia. Queensland and Victoria were particularly hard hit, with insured losses in these states reaching $2.5 billion and many thousands of homes inundated. The Queensland cities of Brisbane and Ipswich were the worst affected; around two-thirds of all inundated property/buildings were in these two areas. Other local government areas to record high levels of inundation were Central Highlands and Rockhampton Regional Councils in Queensland, and Buloke, Campaspe, Central Gold Fields and Loddon in Victoria. Flash flooding was a problem in a number of Victorian councils, but the Lockyer Valley west of Ipswich suffered the most extensive damage with 19 lives lost and more than 100 homes completely destroyed. In all more than 28,000 properties were inundated in Queensland and around 2,500 buildings affected in Victoria. Of the residential properties affected in Brisbane, around 90% were in areas developed prior to the introduction of floodplain development controls, with many also suffering inundation during the 1974 floods. The project developed a predictive model for estimating flood loss and occupant displacement. This model can now be used for flood risk assessments or rapid assessment of impacts following a flood event.

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In this paper, we consider the problem of position regulation of a class of underactuated rigid-body vehicles that operate within a gravitational field and have fully-actuated attitude. The control objective is to regulate the vehicle position to a manifold of dimension equal to the underactuation degree. We address the problem using Port-Hamiltonian theory, and reduce the associated matching PDEs to a set of algebraic equations using a kinematic identity. The resulting method for control design is constructive. The point within the manifold to which the position is regulated is determined by the action of the potential field and the geometry of the manifold. We illustrate the performance of the controller for an unmanned aerial vehicle with underactuation degree two-a quadrotor helicopter.

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Fire incident in buildings is common in Hong Kong and this could lead to heavy casualties due to its high population density, so the fire safety design of the framed structure is an important research topic. This paper describes a computer tool for determination of capacity of structural safety against various fire scenarios and the well-accepted second-order direct plastic analysis is adopted for simulation of material yielding and buckling. A computer method is developed to predict structural behaviour of bare steel framed structures at elevated temperatures but the work can be applied to structures made of other materials. These effects of thermal expansion and material degradation due to heating are required to be considered in order to capture the actual behavior of the structure under fire. Degradation of material strength with increasing temperature is included by a set of temperature-stress-strain curves according to BS5950 Part 8 mainly, which implicitly allows for creep deformation. Several numerical and experimental verifications of framed structures are presented and compared against solutions by other researchers. The proposed method allows us to adopt the truly performance-based structural fire analysis and design with significant saving in cost and time.

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Similarity solutions are carried out for flow of power law non-Newtonian fluid film on unsteady stretching surface subjected to constant heat flux. Free convection heat transfer induces thermal boundary layer within a semi-infinite layer of Boussinesq fluid. The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. This technique reduces the number of independent variables by two, and finally the obtained ordinary differential equations are solved numerically for the temperature and velocity using the shooting method. The thermal and velocity boundary layers are studied by the means of Prandtl number and non-Newtonian power index plotted in curves.

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An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R2 value greater than 98.6% for all temperatures.

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Two varieties of grapes, white grape and red grape grown in the Campania region of Italy were selected for the study of drying characteristics, moisture diffusion, quality changes (colour) and shrinkage behaviour. Comparisons were made with treated and untreated grapes under constant drying condition of 50o C in a conventional drying system. This temperature was selected to represent farm drying conditions. Grapes were purchased from a local market from the same supplier to maintain the same size of grapes and same properties. An abrasive physical treatment was used as pretreatment. The drying curves were constructed and drying kinetics was calculated using several commonly available models. It was found that treated samples shows better drying characteristics than untreated samples. The objective of this study is to obtain drying kinetics which can be used to optimize the drying operations in grape drying.

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The unique physical and movement characteristics of children necessitate the development of accelerometer equations and cut points that are population specific. The purpose of this study is to develop an ecologically valid cut point for the Biotrainer Pro monitor that reflects a threshold for moderate-intensity physical activity in elementary school children. A sample of 30 children (ages 8-12) wore a Biotrainer monitor while completing a series of 7 movement tasks (calibration phase) and while participating in an organized group activity (cross-validation phase). Videotapes from each session were processed using a computerized direct-observation technique to provide a criterion measure of physical activity. Analyses involved the use of mixed-model regression and receiver operator characteristic (ROC) curves. The results indicated that a cut point of 4 counts/min provides the optimal balance between the related needs for sensitivity (accurately detecting activity) and specificity (limiting misclassification of activity as inactivity). Results with the cross-validation data demonstrated that this value yielded the best overall kappa (.58) and a high classification agreement (84%) for activity determination. The specificity of 93% demonstrates that the proposed cut point can accurately detect activity; however, the lower sensitivity value of 61% suggests that some minutes of activity might be incorrectly classified as inactivity. The cut point of 4 counts/min provides an ecologically valid cut point to capture physical activity in children using the Biotrainer Pro activity monitor.

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Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension .a=W D 0:5/ and three-point bend .a=W D 0:1 and 0:5/ specimens under plane stress condition. The crack growth is controlled by the experimental J -integral resistance curves measured by Sun et al. The results indicate that the distributions of opening stress, equivalent stress and equivalent strain ahead of a growing crack are not sensitive to specimen geometry. For both stationary and growing cracks, similar distributions of opening stress and triaxiality can be found along the ligament. During stable crack growth, the crack-tip opening displacement (CTOD) resistance curve and the cohesive fracture energy in the fracture process zone are independent of specimen geometry and may be suitable criteria for characterizing stable crack growth in plane stress.

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Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification of this topic can provide a discovery experience for prospective secondary teachers and information technology students. Such experience can be extended to include a transition from a computationally driven conjecturing to a formal proof based on a number of simple yet useful techniques.

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Introduction Standing radiographs are the ‘gold standard’ for clinical assessment of adolescent idiopathic scoliosis (AIS), with the Cobb Angle used to measure the severity and progression of the scoliotic curve. Supine imaging modalities can provide valuable 3D information on scoliotic anatomy, however, due to changes in gravitational loading direction, the geometry of the spine alters between the supine and standing position which in turn affects the Cobb Angle measurement. Previous studies have consistently reported a 7-10° [1-3] Cobb Angle increase from supine to standing, however, none have reported the effect of endplate pre-selection and which (if any) curve parameters affect the supine to standing Cobb Angle difference. Methods Female AIS patients with right-sided thoracic major curves were included in the retrospective study. Clinically measured Cobb Angles from existing standing coronal radiographs and fulcrum bending radiographs [4] were compared to existing low-dose supine CT scans taken within 3 months of the reference radiograph. Reformatted coronal CT images were used to measure Cobb Angle variability with and without endplate pre-selection (end-plates selected on the radiographs used on the CT images). Inter and intra-observer measurement variability was assessed. Multi-linear regression was used to investigate whether there was a relationship between supine to standing Cobb Angle change and patient characteristics (SPSS, v.21, IBM, USA). Results Fifty-two patients were included, with mean age of 14.6 (SD 1.8) years; all curves were Lenke Type 1 with mean Cobb Angle on supine CT of 42° (SD 6.4°) and 52° (SD 6.7°) on standing radiographs. The mean fulcrum bending Cobb Angle for the group was 22.6° (SD 7.5°). The 10° increase from supine to standing is consistent with existing literature. Pre-selecting vertebral endplates was found to increase the Cobb Angle difference by a mean 2° (range 0-9°). Multi-linear regression revealed a statistically significant relationship between supine to standing Cobb Angle change with: fulcrum flexibility (p=0.001), age (p=0.027) and standing Cobb Angle (p<0.001). In patients with high fulcrum flexibility scores, the supine to standing Cobb Angle change was as great as 20°.The 95% confidence intervals for intra-observer and inter-observer measurement variability were 3.1° and 3.6°, respectively. Conclusion There is a statistically significant relationship between supine to standing Cobb Angle change and fulcrum flexibility. Therefore, this difference can be considered a measure of spinal flexibility. Pre-selecting vertebral endplates causes only minor changes.

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INTRODUCTION Managing spinal deformities in young children is challenging, particularly early onset scoliosis (EOS). Surgical intervention is often required if EOS has been unresponsive to conservative treatment particularly with rapidly progressive curves. An emerging treatment option for EOS is fusionless scoliosis surgery. Similar to bracing, this surgical option potentially harnesses growth, motion and function of the spine along with correcting spinal deformity. Dual growing rods are one such fusionless treatment, which aims to modulate growth of the vertebrae. The aim of this study was to ascertain the extent to which semiconstrained growing rods (Medtronic, Sofamor, Danek, Memphis, TN) with a telescopic sleeve component, reduce rotational constraint on the spine compared with standard "constrained / rigid" rods and hence potentially provide a more physiological mechanical environment for the growing spine. METHODS Six 40-60kg English Large White porcine spines served as a model for the paediatric human spine. Each spine was dissected into a 7 level thoracolumbar multi-segment unit (MSU), removing all non-ligamentous soft tissues and leaving 3cm of ribs either side. Pure nondestructive axial rotation moments of ±4Nm at a constant rotation rate of 8deg.s-1 were applied to the mounted MSU spines using a biaxial Instron testing machine. Displacement of each vertebral level was captured using a 3D motion tracking system (Optotrak 3020, Northern Digital Inc, Waterloo, ON). Each spine was tested in an un-instrumented state first and then with appropriately sized semi-constrained growing rods and rigid rods in alternating sequence. The rods were secured by multi-axial pedicle screws (Medtronic CD Horizon) at levels 2 and 6 of the construct. The range of motion (ROM), neutral zone (NZ) size and stiffness (Nm.deg-1) were calculated from the Instron load-displacement data and intervertebral ROM was calculated through a MATLAB algorithm from Optotrak data. RESULTS Irrespective of the order of testing, rigid rods significantly reduced the total ROM compared with semi-constrained rods (p<0.05) with in a significantly stiffer spine for both left and right axial rotation (p<0.05). Analysing the intervertebral motion within the instrumented levels 2-6, rigid rods showed reduced ROM compared with semi-constrained growing rods and compared with un-instrumented motion segments. CONCLUSION Semi-constrained growing rods maintain similar stiffness in axial rotation to un-instrumented spines, while dual rigid rods significantly reduce axial rotation. Clinically the effect of semi-constrained growing rods as observed in this study is that they would be expected to allow growth via the telescopic rod components while maintaining the axial flexibility of the spine, which may reduce occurrence of the crankshaft phenomenon.

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INTRODUCTION: Increasing health care costs, limited resources and increased demand makes cost effective and cost-efficient delivery of Adolescent Idiopathic Scoliosis (AIS) management paramount. Rising implant costs in deformity correction surgery have prompted analysis of whether high implant densities are justified. The objective of this study was to analyse the costs of thoracoscopic scoliosis surgery, comparing initial learning curve costs with those of the established technique and to the costs involved in posterior instrumented fusion from the literature. METHODS: 189 consecutive cases from April 2000 to July 2011 were assessed with a minimum of 2 years follow-up. Information was gathered from a prospective database covering perioperative factors, clinical and radiological outcomes, complications and patient reported outcomes. The patients were divided into three groups to allow comparison; 1. A learning curve cohort, 2. An intermediate cohort and 3. A third cohort of patients, using our established technique. Hospital finance records and implant manufacturer figures were corrected to 2013 costs. A literature review of AIS management costs and implant density in similar curve types was performed. RESULTS: The mean pre-op Cobb angle was 53°(95%CI 0.4) and was corrected postop to mean 22.9°(CI 0.4). The overall complication rate was 20.6%, primarily in the first cohort, with a rate of 5.6% in the third cohort. The average total costs were $46,732, operating room costs of $10,301 (22.0%) and ICU costs of $4620 (9.8%). The mean number of screws placed was 7.1 (CI 0.04) with a single rod used for each case giving average implant costs of $14,004 (29.9%). Comparison of the three groups revealed higher implant costs as the technique evolved to that in use today, from $13,049 in Group 1 to $14577 in Group 3 (P<0.001). Conversely operating room costs reduced from $10,621 in Group 1 to $7573 (P<0.001) in Group 3. ICU stay was reduced from an average of 1.2 to 0 days. In-patient stay was significantly (P=0.006) lower in Groups 2 and 3 (5.4 days) than Group 1 (5.9 days) (i.e. a reduction in cost of approximately $6,140). CONCLUSIONS: The evolution of our thoracoscopic anterior scoliosis correction has resulted in an increase in the number of levels fused and reduction in complication rate. Implant costs have risen as a result, however, there has been a concurrent decrease in those costs generated by operating room use, ICU and in-patient stay with increasing experience. Literature review of equivalent curve types treated posteriorly shows similar perioperative factors but higher implant density, 69-83% compared to the 50% in this study. Thoracoscopic Scoliosis surgery presents a low density, reliable, efficient and effective option for selected curves. A cost analysis of Thoracoscopic Scoliosis Surgery using financial records and a prospectively collected database of all patients since 2000, demonstrating a clear cost advantage compared to equivalent posterior instrumentation and fusion.

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The basic principles and equations are developed for elementary finance, based on the concept of compound interest. The five quantities of interest in such problems are present value, future value, amount of periodic payment, number of periods and the rate of interest per period. We consider three distinct means of computing each of these five quantities in Excel 2007: (i) use of algebraic equations, (ii) by recursive schedule and the Goal Seek facility, and (iii) use of Excel's intrinsic financial functions. The paper is intended to be used as the basis for a lesson plan and contains many examples and solved problems. Comment is made regarding the relative difficulty of each approach, and a prominent theme is the systematic use of more than one method to increase student understanding and build confidence in the answer obtained. Full instructions to build each type of model are given and a complete set of examples and solutions may be downloaded (Examples.xlsx and Solutions.xlsx).

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Notwithstanding the problems with identifying audiences (c.f. Hartley, 1987), nor with sampling them (c.f. Turner, 2005), we contend that by using social media, it is at least possible to gain an understanding of the habits of those who chose to engage with content through social media. In this chapter, we will broadly outline the ways in which networks such as Twitter and Facebook can stand as proxies for audiences in a number of scenarios, and enable content creators, networks and researchers to understand the ways in which audiences come into existence, change over time, and engage with content. Beginning with the classic audience – television – we will consider the evolution of metrics from baseline volume metrics to the more sophisticated ‘telemetrics’ that are the focus of our current work. We discuss the evolution of these metrics, from principles developed in the field of ‘sabermetrics’, and highlight their effectiveness as both a predictor and a baseline for producers and networks to measure the success of their social media campaigns. Moving beyond the evaluation of the audiences engagement, we then move to consider the ‘audiences’ themselves. Building on Hartley’s argument that audiences are “imagined” constructs (1987, p. 125), we demonstrate the continual shift of Australian television audiences, from episode to episode and series to series, demonstrating through our map of the Australian Twittersphere (Bruns, Burgess & Highfield, 2014) both the variation amongst those who directly engage with television content, and those who are exposed to it through their social media networks. Finally, by exploring overlaps between sporting events (such as the NRL and AFL Grand Finals), reality TV (such as Big Brother, My Kitchen Rules & Biggest Loser), soaps (e.g. Bold & The Beautiful, Home & Away), and current affairs programming (e.g. Morning Television & A Current Affair), we discuss to what extent it is possible to profile and categorize Australian television audiences. Finally, we move beyond television audiences to consider audiences around social media platforms themselves. Building on our map of the Australian Twittersphere (Bruns, Burgess & Highfield, 2014), and a pool of 5000 active Australian accounts, we discuss the interconnectedness of audiences around particular subjects, and how specific topics spread throughout the Twitter Userbase. Also, by using Twitter as a proxy, we consider the career of a number of popular YouTuber’s, utilizing a method we refer to as Twitter Accession charts (Bruns & Woodford, 2014) to identify the growth curves, and relate them to specific events in the YouTubers career, be that ‘viral’ videos or collaborations, to discuss how audiences form around specific content creators.