240 resultados para Nonlinear Fredholm Alternative


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The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

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We report a new approach that uses the single beam Z-scan technique, to discriminate between excited state absorption (ESA) and two and three photon nonlinear absorption. By measuring the apparent delay or advance of the pulse in reaching the detector, the nonlinear absorption can be unambiguously identified as either instantaneous or transient. The simple method does not require a large range of input fluences or sophisticated pulse-probe experimental apparatus. The technique is easily extended to any absorption process dependent on pulse width and to nonlinear refraction measurements. We demonstrate in particular, that the large nonlinear absorption in ZnO nanocones when exposed to nanosecond 532 nm pulses, is due mostly to ESA, not pure two-photon absorption.

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Modern cancer research requires physiological, three-dimensional (3-D) cell culture platforms, wherein the physical and chemical characteristics of the extracellular matrix (ECM) can be modified. In this study, gelatine methacrylamide (GelMA)-based hydrogels were characterized and established as in vitro and in vivo spheroid-based models for ovarian cancer, reflecting the advanced disease stage of patients, with accumulation of multicellular spheroids in the tumour fluid (ascites). Polymer concentration (2.5-7% w/v) strongly influenced hydrogel stiffness (0.5±0.2kPa to 9.0±1.8kPa) but had little effect on solute diffusion. The diffusion coefficient of 70kDa fluorescein isothiocyanate (FITC)-labelled dextran in 7% GelMA-based hydrogels was only 2.3 times slower compared to water. Hydrogels of medium concentration (5% w/v GelMA) and stiffness (3.4kPa) allowed spheroid formation and high proliferation and metabolic rates. The inhibition of matrix metalloproteinases and consequently ECM degradability reduced spheroid formation and proliferation rates. The incorporation of the ECM components laminin-411 and hyaluronic acid further stimulated spheroid growth within GelMA-based hydrogels. The feasibility of pre-cultured GelMA-based hydrogels as spheroid carriers within an ovarian cancer animal model was proven and led to tumour development and metastasis. These tumours were sensitive to treatment with the anti-cancer drug paclitaxel, but not the integrin antagonist ATN-161. While paclitaxel and its combination with ATN-161 resulted in a treatment response of 33-37.8%, ATN-161 alone had no effect on tumour growth and peritoneal spread. The semi-synthetic biomaterial GelMA combines relevant natural cues with tunable properties, providing an alternative, bioengineered 3-D cancer cell culture in in vitro and in vivo model systems.

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A nonlinear finite element analysis was carried out to investigate the viscoplastic deformation of solder joints in a ball grid array (BGA) package under temperature cycle. The effects of constraint on print circuit board (PCB) and stiffness of substrate on the deformation behaviour of the solder joints were also studied. A relative damage stress was adopted to analyze the potential failure sites in the solder joints. The results indicated that high inelastic strain and strain energy density were developed in the joints close to the package center. On the other hand, high constraint and high relative damage stress were associated with the joint closest to the edge of the silicon chip. The joint closest to the edge of the silicon chip was regarded as the most susceptible failure site if cavitation instability is the dominant failure mechanism. Increase the external constraint on the print circuit board (PCB) causes a slight increase in stress triaxiality (m/eq) and relative damage stress in the joint closest to the edge of silicon die. The relative damage stress is not sensitive to the Young’s modulus of the substrate.

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This paper presents two novel nonlinear models of u-shaped anti-roll tanks for ships, and their linearizations. In addition, a third simplified nonlinear model is presented. The models are derived using Lagrangian mechanics. This formulation not only simplifies the modeling process, but also allows one to obtain models that satisfy energy-related physical properties. The proposed nonlinear models and their linearizations are validated using model-scale experimental data. Unlike other models in the literature, the nonlinear models in this paper are valid for large roll amplitudes. Even at moderate roll angles, the nonlinear models have three orders of magnitude lower mean square error relative to experimental data than the linear models.

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In moderate to high sea states, the effectiveness of ship fin stabilizers can severely deteriorate due to nonlinear effects arising from unsteady hydrodynamic characteristics of the fins: dynamic stall. These nonlinear effects take the form of a hysteresis, and they become very significant when the effective angle of attack of the fins exceeds a certain threshold angle. Dynamic stall can result in a complete loss of control action depending on how much the fins exceed the threshold angle. When this is detected, it is common to reduce the gain of the controller that commands the fins. This approach is cautious and tends to reduce performance when the conditions leading to dynamic stall disappear. An alternative approach for preventing the effects while keeping high performance, consists of estimating the effective angle of attack and set a conservative constraint on it as part of the control objectives. In this paper, we investigate the latter approach, and propose the use of a model predictive control (MPC) to prevent the development of these nonlinear effects by considering constraints on both the mechanical angle of the fins and the effective angle of attack.

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Parametric roll is a critical phenomenon for ships, whose onset may cause roll oscillations up to +-40 degrees, leading to very dangerous situations and possibly capsizing. Container ships have been shown to be particularly prone to parametric roll resonance when they are sailing in moderate to heavy head seas. A Matlab/Simulink parametric roll benchmark model for a large container ship has been implemented and validated against a wide set of experimental data. The model is a part of a Matlab/Simulink Toolbox (MSS, 2007). The benchmark implements a 3rd-order nonlinear model where the dynamics of roll is strongly coupled with the heave and pitch dynamics. The implemented model has shown good accuracy in predicting the container ship motions, both in the vertical plane and in the transversal one. Parametric roll has been reproduced for all the data sets in which it happened, and the model provides realistic results which are in good agreement with the model tank experiments.

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In this paper, we consider a passivity-based approach for the design of a control law of multiple ship-roll gyro-stabiliser units. We extend previous work on control of ship roll gyro-stabilisation by considering the problem within a nonlinear framework. In particular, we derive an energy-based model using the port-Hamiltonian theory and then design an active precession controller using passivity-based control interconnection and damping assignment. The design considers the possibility of having multiple gyro-stabiliser units, and the desired potential energy of the system (in closed loop) is chosen to behave like a barrier function, which allows us to enforce constraints on the precession angle of the gyros.

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For many years materials such as quarried sand, anthracite, and granular activated carbon have been the principal media-products traditionally used in water and wastewater filtration plants. Pebble Matrix Filtration (PMF) is a novel non-chemical, sustainable pre-treatment method of protecting Slow Sand Filters (SSF) from high turbidity during heavy monsoon periods. PMF uses sand and pebbles as the filter media and the sustainability of this new technology might depend on availability and supply of pebbles and sand, both finite resources. In many countries there are two principal methods of obtaining pebbles and sand, namely dredging from rivers and beaches, and due to the scarcity of these resources in some countries the cost of pebbles is often 4-5 times higher than that of sand. In search for an alternative medium to pebbles after some preliminary laboratory tests conducted in Colombo-Sri Lanka, Poznan-Poland and Cambridge-UK, a 100-year-old brick factory near Sudbury, Suffolk, has produced hand-made clay pebbles satisfying the PMF quality requirements. As an alternative to sand, crushed recycled glass from a UK supplier was used and the PMF system was operated together with hand-made clay balls in the laboratory for high turbidity removal effectively. The results of laboratory experiments with alternative media are presented in this paper. There are potential opportunities for recycled crushed glass and clay ball manufacturing processes in some countries where they can be used as filter media.

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Alternative schools are an emerging model of education offered to young people who have been disenfranchised from conventional schooling opportunities. The body of literature on alternative schools in Australia has not identified how many Indigenous young people are engaged with alternative schools and how alternative schools are supporting Indigenous young people to remain engaged in education. It is well documented that Aboriginal and Torres Strait Islander people experience significant disadvantage including poorer educational outcomes than their non-Indigenous peers. This study seeks to contribute to improving educational outcomes for Aboriginal and Torres Strait Islander young people through exploring Aboriginal and Torres Strait Islander interactions with alternative schools in Queensland and investigating the practices of alternative school leaders in terms of how they are supporting Indigenous young people to remain engaged in education. Critical race theory informed the development of this study. An Aboriginal researcher sought to shift the focus of this study away from Indigenous young people to Principals; to explore their perspective of their own knowledge and practices in supporting Aboriginal and Torres Strait Islander young people at their school. Using survey methodology, a web-based questionnaire was developed to survey Principals’ providing data on alternative schools in Queensland including the demographics of the alternative school; self-reported knowledge of Indigenous cultures and communities and practices that support Aboriginal and Torres Strait Islander young people at their alternative school. There are nine key findings that emerged through the analysis of this study: key finding one is the high percentage of Aboriginal and Torres Strait Islander young people enrolled in schools surveyed; key finding two is there is a high percentage of Aboriginal and Torres Strait Islander staff employed in the schools; key finding three is the majority of the schools are located in low socio-economic areas; key finding four is the strong willingness of Principals’ in this study to engage in self-directed learning in relation to Aboriginal and Torres Strait Islander cultures; key finding five is the limited demonstration of understandings of Aboriginal and Torres Strait Islander cultures and communities; key finding six is the most prevalent practice of Principals’ in this study is the celebration of cultural events and cultural activities; key finding seven is the limited Principal engagement with Aboriginal and Torres Strait Islander young people, their families and the local community; key finding eight is the practice of alternative schools provides limited support and nurturing of Aboriginal and Torres Strait Islander young person’s cultural identity and key finding nine is that Principals’ are relying heavily on informal discussions with staff to know what their staff’s knowledge and skills are in relation to supporting Aboriginal and Torres Strait Islander young people. There are multiple implications that have arisen from this study. The data demonstrated high numbers of Aboriginal and Torre Strait Islander students and staff. The data also revealed that Principal’s demonstration of knowledge in relation to Indigenous cultures and communities was limited, as well as limited Principal engagement with Indigenous young peoples, families and communities. Therefore a major practical implication of this study is the urgent need for quality cultural learning opportunities for leaders of alternative schools to improve practices. Additionally, the implications of this study support an urgent need for further research on the role alternative schools are playing in supporting Indigenous young people to remain engaged in education.

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This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel's centre of gravity due to, for example, water on deck and also in changes in the buoyancy triggered by variations in the water-plane area produced by longitudinal waves -- propagating along the fore-aft direction along the hull. These variations in the restoring can change dramatically the dynamics of the roll motion leading to dangerous resonance. Therefore, it is of interest to estimate and detect such changes.

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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.

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Currently, open circuit Bayer refineries pump seawater directly into their operations to neutralise the caustic fraction of the Bayer residue. The resulting supernatant has a reduced pH and is pumped back to the marine environment. This investigation has assessed modified seawater sources generated from different ion filtration processes to compare their relative capacities to neutralise bauxite residues. An assessment of the chemical stability of the neutralisation products, neutralisation efficiency, discharge water quality, bauxite residue composition, and associated economic benefits have been considered to determine the most preferable seawater filtration process based on implementation costs, savings to operations and environmental benefits. The mechanism of neutralisation for each technology was determined to be predominately due to the formation of Bayer hydrotalcite and calcium carbonate, however variations in neutralisation capacity and efficiencies have been observed. The neutralisation efficiency of each feed source has been found to be dependent on the concentration of magnesium, aluminium, calcium and carbonate. These studies have revealed that multiple neutralisation steps occur throughout the process. Environmental, economic and social advantages and disadvantages of the different filtration technologies have been explored to determine the most sustainable method for the neutralisation of bauxite residues. The relative degree of “green” associated with nanofiltered seawater and reverse osmosis filtered seawater are discussed.

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For users of germplasm collections, the purpose of measuring characterization and evaluation descriptors, and subsequently using statistical methodology to summarize the data, is not only to interpret the relationships between the descriptors, but also to characterize the differences and similarities between accessions in relation to their phenotypic variability for each of the measured descriptors. The set of descriptors for the accessions of most germplasm collections consists of both numerical and categorical descriptors. This poses problems for a combined analysis of all descriptors because few statistical techniques deal with mixtures of measurement types. In this article, nonlinear principal component analysis was used to analyze the descriptors of the accessions in the Australian groundnut collection. It was demonstrated that the nonlinear variant of ordinary principal component analysis is an appropriate analytical tool because subspecies and botanical varieties could be identified on the basis of the analysis and characterized in terms of all descriptors. Moreover, outlying accessions could be easily spotted and their characteristics established. The statistical results and their interpretations provide users with a more efficient way to identify accessions of potential relevance for their plant improvement programs and encourage and improve the usefulness and utilization of germplasm collections.

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A measure quantifying unequal use of carbon sources, the Gini coefficient (G), has been developed to allow comparisons of the observed functional diversity of bacterial soil communities. This approach was applied to the analysis of substrate utilisation data obtained from using BIOLOG microtiter plates in a study which compared decomposition processes in two contrasting plant substrates in two different soils. The relevance of applying the Gini coefficient as a measure of observed functional diversity, for soil bacterial communities is evaluated against the Shannon index (H) and average well colour development (AWCD), a measure of the total microbial activity. Correlation analysis and analysis of variance of the experimental data show that the Gini coefficient, the Shannon index and AWCD provided similar information when used in isolation. However, analyses based on the Gini coefficient and the Shannon index, when total activity on the microtiter plates was maintained constant (i.e. AWCD as a covariate), indicate that additional information about the distribution of carbon sources being utilised can be obtained. We demonstrate that the Lorenz curve and its measure of inequality, the Gini coefficient, provides not only comparable information to AWCD and the Shannon index but when used together with AWCD encompasses measures of total microbial activity and absorbance inequality across all the carbon sources. This information is especially relevant for comparing the observed functional diversity of soil microbial communities.