Unsteady natural convection within a differentially heated enclosure of sinusoidal corrugated side walls

Numerically investigation of natural convection within a differentially heated modified square enclosure with sinusoidally corrugated side walls has been performed for different values of Rayleigh number. The fluid inside the enclosure considered is air and is quiescent, initially. The top and bottom surfaces are flat and considered as adiabatic. Results reveal three main stages: an initial stage, a transitory or oscillatory stage and a steady stage for the development of natural convection flow inside the corrugated cavity. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. Investigation has been performed for the Rayleigh number, Ra ranging from 105 to 108 with variation of corrugation amplitude and frequency. Constant physical properties for the fluid medium have been assumed. Results have been presented in terms of the isotherms, streamlines, temperature plots, average Nusselt numbers, traveling waves and thermal boundary layer thickness plots, temperature and velocity profiles. The effects of sudden differential heating and its consequent transient behavior on fluid flow and heat transfer characteristics have been observed for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the Rayleigh Number with corrugation amplitude and frequency.

Linear and nonlinear propagation of localised plasmon in metallic nanostructures

A major challenge in modern photonics and nano-optics is the diffraction limit of light which does not allow field localisation into regions with dimensions smaller than half the wavelength. Localisation of light into nanoscale regions (beyond its diffraction limit) has applications ranging from the design of optical sensors and measurement techniques with resolutions as high as a few nanometres, to the effective delivery of optical energy into targeted nanoscale regions such as quantum dots, nano-electronic and nano-optical devices. This field has become a major research direction over the last decade. The use of strongly localised surface plasmons in metallic nanostructures is one of the most promising approaches to overcome this problem. Therefore, the aim of this thesis is to investigate the linear and non-linear propagation of surface plasmons in metallic nanostructures. This thesis will focus on two main areas of plasmonic research –– plasmon nanofocusing and plasmon nanoguiding. Plasmon nanofocusing – The main aim of plasmon nanofocusing research is to focus plasmon energy into nanoscale regions using metallic nanostructures and at the same time achieve strong local field enhancement. Various structures for nanofocusing purposes have been proposed and analysed such as sharp metal wedges, tapered metal films on dielectric substrates, tapered metal rods, and dielectric V-grooves in metals. However, a number of important practical issues related to nanofocusing in these structures still remain unclear. Therefore, one of the main aims of this thesis is to address two of the most important of issues which are the coupling efficiency and heating effects of surface plasmons in metallic nanostructures. The method of analysis developed throughout this thesis is a general treatment that can be applied to a diversity of nanofocusing structures, with results shown here for the specific case of sharp metal wedges. Based on the geometrical optics approximation, it is demonstrated that the coupling efficiency from plasmons generated with a metal grating into the nanofocused symmetric or quasi-symmetric modes may vary between ~50% to ~100% depending on the structural parameters. Optimal conditions for nanofocusing with the view to minimise coupling and dissipative losses are also determined and discussed. It is shown that the temperature near the tip of a metal wedge heated by nanosecond plasmonic pulses can increase by several hundred degrees Celsius. This temperature increase is expected to lead to nonlinear effects, self-influence of the focused plasmon, and ultimately self-destruction of the metal tip. This thesis also investigates a different type of nanofocusing structure which consists of a tapered high-index dielectric layer resting on a metal surface. It is shown that the nanofocusing mechanism that occurs in this structure is somewhat different from other structures that have been considered thus far. For example, the surface plasmon experiences significant backreflection and mode transformation at a cut-off thickness. In addition, the reflected plasmon shows negative refraction properties that have not been observed in other nanofocusing structures considered to date. Plasmon nanoguiding – Guiding surface plasmons using metallic nanostructures is important for the development of highly integrated optical components and circuits which are expected to have a superior performance compared to their electronicbased counterparts. A number of different plasmonic waveguides have been considered over the last decade including the recently considered gap and trench plasmon waveguides. The gap and trench plasmon waveguides have proven to be difficult to fabricate. Therefore, this thesis will propose and analyse four different modified gap and trench plasmon waveguides that are expected to be easier to fabricate, and at the same time acquire improved propagation characteristics of the guided mode. In particular, it is demonstrated that the guided modes are significantly screened by the extended metal at the bottom of the structure. This is important for the design of highly integrated optics as it provides the opportunity to place two waveguides close together without significant cross-talk. This thesis also investigates the use of plasmonic nanowires to construct a Fabry-Pérot resonator/interferometer. It is shown that the resonance effect can be achieved with the appropriate resonator length and gap width. Typical quality factors of the Fabry- Pérot cavity are determined and explained in terms of radiative and dissipative losses. The possibility of using a nanowire resonator for the design of plasmonic filters with close to ~100% transmission is also demonstrated. It is expected that the results obtained in this thesis will play a vital role in the development of high resolution near field microscopy and spectroscopy, new measurement techniques and devices for single molecule detection, highly integrated optical devices, and nanobiotechnology devices for diagnostics of living cells.

Tax evasion, inequality, and progressive taxes : a political economy perspective

The standard approach to tax compliance applies the economics-of-crime methodology pioneered by Becker (1968): in its first application, due to Allingham and Sandmo (1972) it models the behaviour of agents as a decision involving a choice of the extent of their income to report to tax authorities, given a certain institutional environment, represented by parameters such as the probability of detection and penalties in the event the agent is caught. While this basic framework yields important insights on tax compliance behavior, it has some critical limitations. Specifically, it indicates a level of compliance that is significantly below what is observed in the data. This thesis revisits the original framework with a view towards addressing this issue, and examining the political economy implications of tax evasion for progressivity in the tax structure. The approach followed involves building a macroeconomic, dynamic equilibrium model for the purpose of examining these issues, by using a step-wise model building procedure starting with some very simple variations of the basic Allingham and Sandmo construct, which are eventually integrated to a dynamic general equilibrium overlapping generations framework with heterogeneous agents. One of the variations involves incorporating the Allingham and Sandmo construct into a two-period model of a small open economy of the type originally attributed to Fisher (1930). A further variation of this simple construct involves allowing agents to initially decide whether to evade taxes or not. In the event they decide to evade, the agents then have to decide the extent of income or wealth they wish to under-report. We find that the ‘evade or not’ assumption has strikingly different and more realistic implications for the extent of evasion, and demonstrate that it is a more appropriate modeling strategy in the context of macroeconomic models, which are essentially dynamic in nature, and involve consumption smoothing across time and across various states of nature. Specifically, since deciding to undertake tax evasion impacts on the consumption smoothing ability of the agent by creating two states of nature in which the agent is ‘caught’ or ‘not caught’, there is a possibility that their utility under certainty, when they choose not to evade, is higher than the expected utility obtained when they choose to evade. Furthermore, the simple two-period model incorporating an ‘evade or not’ choice can be used to demonstrate some strikingly different political economy implications relative to its Allingham and Sandmo counterpart. In variations of the two models that allow for voting on the tax parameter, we find that agents typically choose to vote for a high degree of progressivity by choosing the highest available tax rate from the menu of choices available to them. There is, however, a small range of inequality levels for which agents in the ‘evade or not’ model vote for a relatively low value of the tax rate. The final steps in the model building procedure involve grafting the two-period models with a political economy choice into a dynamic overlapping generations setting with more general, non-linear tax schedules and a ‘cost-of evasion’ function that is increasing in the extent of evasion. Results based on numerical simulations of these models show further improvement in the model’s ability to match empirically plausible levels of tax evasion. In addition, the differences between the political economy implications of the ‘evade or not’ version of the model and its Allingham and Sandmo counterpart are now very striking; there is now a large range of values of the inequality parameter for which agents in the ‘evade or not’ model vote for a low degree of progressivity. This is because, in the ‘evade or not’ version of the model, low values of the tax rate encourages a large number of agents to choose the ‘not-evade’ option, so that the redistributive mechanism is more ‘efficient’ relative to the situations in which tax rates are high. Some further implications of the models of this thesis relate to whether variations in the level of inequality, and parameters such as the probability of detection and penalties for tax evasion matter for the political economy results. We find that (i) the political economy outcomes for the tax rate are quite insensitive to changes in inequality, and (ii) the voting outcomes change in non-monotonic ways in response to changes in the probability of detection and penalty rates. Specifically, the model suggests that changes in inequality should not matter, although the political outcome for the tax rate for a given level of inequality is conditional on whether there is a large or small or large extent of evasion in the economy. We conclude that further theoretical research into macroeconomic models of tax evasion is required to identify the structural relationships underpinning the link between inequality and redistribution in the presence of tax evasion. The models of this thesis provide a necessary first step in that direction.

Assessing the impacts of lifetime sun exposure on skin damage and skin aging using a non-invasive method

Background: Ultraviolet radiation exposure during an individuals' lifetime is a known risk factor for the development of skin cancer. However, less evidence is available on assessing the relationship between lifetime sun exposure and skin damage and skin aging. Objectives: This study aims to assess the relationship between lifetime sun exposure and skin damage and skin aging using a non-invasive measure of exposure. Methods: We recruited 180 participants (73 males, 107 females) aged 18-83 years. Digital imaging of skin hyper-pigmentation (skin damage) and skin wrinkling (skin aging) on the facial region was measured. Lifetime sun exposure (presented as hours) was calculated from the participants' age multiplied by the estimated annual time outdoors for each year of life. We analyzed the effects of lifetime sun exposure on skin damage and skin aging. We adjust for the influence of age, sex, occupation, history of skin cancer, eye color, hair color, and skin color. Results: There were non-linear relationships between lifetime sun exposure and skin damage and skin aging. Younger participant's skin is much more sensitive to sun exposure than those who were over 50 years of age. As such, there were negative interactions between lifetime sun exposure and age. Age had linear effects on skin damage and skin aging. Conclusion: The data presented showed that self reported lifetime sun exposure was positively associated with skin damage and skin aging, in particular, the younger people. Future health promotion for sun exposure needs to pay attention to this group for skin cancer prevention messaging. (C) 2012 Elsevier B.V. All rights reserved.

Analytical Solution of a Walters’ Liquid B Flow Over a Linear Stretching Sheet in a Porous Medium

This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

Heteroscedastic probabilistic linear discriminant analysis for manifold learning in video-based face recognition

To recognize faces in video, face appearances have been widely modeled as piece-wise local linear models which linearly approximate the smooth yet non-linear low dimensional face appearance manifolds. The choice of representations of the local models is crucial. Most of the existing methods learn each local model individually meaning that they only anticipate variations within each class. In this work, we propose to represent local models as Gaussian distributions which are learned simultaneously using the heteroscedastic probabilistic linear discriminant analysis (PLDA). Each gallery video is therefore represented as a collection of such distributions. With the PLDA, not only the within-class variations are estimated during the training, the separability between classes is also maximized leading to an improved discrimination. The heteroscedastic PLDA itself is adapted from the standard PLDA to approximate face appearance manifolds more accurately. Instead of assuming a single global within-class covariance, the heteroscedastic PLDA learns different within-class covariances specific to each local model. In the recognition phase, a probe video is matched against gallery samples through the fusion of point-to-model distances. Experiments on the Honda and MoBo datasets have shown the merit of the proposed method which achieves better performance than the state-of-the-art technique.

Non-contact ACL injuries : association with clegg soil impact test values for sports fields, soil moisture and prevailing weather

Introduction: There is a recognised relationship between dry weather conditions and increased risk of anterior cruciate ligament (ACL) injury. Previous studies have identified 28 day evaporation as an important weather-based predictor of non-contact ACL injuries in professional Australian Football League matches. The mechanism of non-contact injury to the ACL is believed to increased traction and impact forces between footwear and playing surface. Ground hardness and the amount and quality of grass are factors that would most likely influence this and are inturn, related to the soil moisture content and prevailing weather conditions. This paper explores the relationship between soil moisture content, preceding weather conditions and the Clegg Soil Impact Test (CSIT) which is an internationally recognised standard measure of ground hardness for sports fields. Methodology: The 2.25 kg Clegg Soil Impact Test and a pair of 12 cm soil moisture probes were used to measure ground hardness and percentage moisture content. Five football fields were surveyed at 13 prescribed sites just before seven football matches from October 2008 to January 2009 (an FC Women’s WLeague team). Weather conditions recorded at the nearest weather station were obtained from the Bureau of Meteorology website and total rainfall less evaporation was calculated for 7 and 28 days prior to each match. All non-contact injuries occurring during match play and their location on the field were recorded. Results/conclusions: Ground hardness varied between CSIT 5 and 17 (x10G) (8 is considered a good value for sports fields). Variations within fields were typically greatest in the centre and goal areas. Soil moisture ranged from 3 to 40% with some fields requiring twice the moisture content of others to maintain similar CSIT values. There was a non-linear, negative relationship for ground hardness versus moisture content and a linear relationship with weather (R2, of 0.30 and 0.34, respectively). Three non-contact ACL injuries occurred during the season. Two of these were associated with hard and variable ground conditions.

Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

Refined plastic hinge analysis of steel frame structures comprising non-compact sections : II : verification

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A refined plastic hinge method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in a companion paper. The method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established in this paper by comparison with a comprehensive range of analytical benchmark frame solutions. The refined plastic hinge method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.

Distributed plasticity analysis of steel frame structures comprising non-compact sections

Application of 'advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. A primary objective was to produce a comprehensive range of new distributed plasticity analytical benchmark solutions for verification of the concentrated plasticity methods. A distributed plasticity model was developed using shell finite elements to explicitly account for the effects of gradual yielding and spread of plasticity, initial geometric imperfections, residual stresses and local buckling deformations. The model was verified by comparison with large-scale steel frame test results and a variety of existing analytical benchmark solutions. This paper presents a description of the distributed plasticity model and details of the verification study.

Pseudo plastic zone analysis of steel frame structures comprising non-compact sections

Application of `advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A concentrated plasticity method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in this paper. The pseudo plastic zone method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established by comparison with a comprehensive range of analytical benchmark frame solutions. The pseudo plastic zone method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.

Large-scale testing of steel frame structures comprising non-compact sections

Application of 'advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. A series of large-scale tests were performed in order to provide experimental results for verification of the new analytical models. Each of the test frames comprised non-compact sections, and exhibited significant local buckling behaviour prior to failure. This paper presents details of the test program including the test specimens, set-up and instrumentation, procedure, and results.

Non-invasive clinical measurement of the viscoelastic properties of tendon using acoustic wave transmission

Background. In isotropic materials, the speed of acoustic wave propagation is governed by the bulk modulus and density. For tendon, which is a structural composite of fluid and collagen, however, there is some anisotropy requiring an adjustment for Poisson's ratio. This paper explores these relationships using data collected, in vivo, on human Achilles tendon and then compares estimates of elastic modulus and hysteresis against published values from in vitro mechanical tests. Methods. Measurements using conventional B-model ultrasound imaging, inverse dynamics and acoustic transmission techniques were used to determine dimensions, loading conditions and longitudinal speed of sound in the Achilles tendon during a series of isometric plantar flexion exercises against body weight. Upper and lower bounds for speed of sound versus tensile stress in the tendon were then modelled and estimates of the elastic modulus and hysteresis of the Achilles tendon derived. Results. Axial speed of sound varied between 1850 and 2090 ms-1 with a non-linear, asymptotic dependency on the level of tensile stress (5-35 MPa) in the tendon. Estimates derived for the elastic modulus of the Achilles tendon ranged between 1-2 GPa. Hysteresis derived from models of the stress-strain relationship, ranged from 3-11%. Discussion. Estimates of elastic modulus agree closely with those previously reported from direct measurements obtained via mechanical tensile tests on major weight bearing tendons in vitro [1,2]. Hysteresis derived from models of the stress-strain relationship is consistent with direct measures from various mamalian tendon (7-10%) but is lower than previous estimates in human tendon (17-26%) [3]. This non-invasive method would appear suitable for monitoring changes in tendon properties during dynamic sporting activities.

Improved sub-cellular resolution via simultaneous analysis of organelle proteomics data across varied experimental conditions

Spatial organisation of proteins according to their function plays an important role in the specificity of their molecular interactions. Emerging proteomics methods seek to assign proteins to sub-cellular locations by partial separation of organelles and computational analysis of protein abundance distributions among partially separated fractions. Such methods permit simultaneous analysis of unpurified organelles and promise proteome-wide localisation in scenarios wherein perturbation may prompt dynamic re-distribution. Resolving organelles that display similar behavior during a protocol designed to provide partial enrichment represents a possible shortcoming. We employ the Localisation of Organelle Proteins by Isotope Tagging (LOPIT) organelle proteomics platform to demonstrate that combining information from distinct separations of the same material can improve organelle resolution and assignment of proteins to sub-cellular locations. Two previously published experiments, whose distinct gradients are alone unable to fully resolve six known protein-organelle groupings, are subjected to a rigorous analysis to assess protein-organelle association via a contemporary pattern recognition algorithm. Upon straightforward combination of single-gradient data, we observe significant improvement in protein-organelle association via both a non-linear support vector machine algorithm and partial least-squares discriminant analysis. The outcome yields suggestions for further improvements to present organelle proteomics platforms, and a robust analytical methodology via which to associate proteins with sub-cellular organelles.

Distinguishing attack on SOBER-128 with linear masking

We present a distinguishing attack against SOBER-128 with linear masking. We found a linear approximation which has a bias of 2^− − 8.8 for the non-linear filter. The attack applies the observation made by Ekdahl and Johansson that there is a sequence of clocks for which the linear combination of some states vanishes. This linear dependency allows that the linear masking method can be applied. We also show that the bias of the distinguisher can be improved (or estimated more precisely) by considering quadratic terms of the approximation. The probability bias of the quadratic approximation used in the distinguisher is estimated to be equal to O(2^− − 51.8), so that we claim that SOBER-128 is distinguishable from truly random cipher by observing O(2^103.6) keystream words.