Accurate series solutions for gravity-driven Stokes waves

In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that higher order behaviour of series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Pade approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Pade approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.

Marital loss, mental health and the role of perceived social support : findings from six waves of an Australian population based panel study

Objectives: To investigate the impact of transitions out of marriage (separation, widowhood) on the self reported mental health of men and women, and examine whether perceptions of social support play an intervening role. ---------- Methods: The analysis used six waves (2001–06) of an Australian population based panel study, with an analytical sample of 3017 men and 3225 women. Mental health was measured using the MHI-5 scale scored 0–100 (α=0.97), with a higher score indicating better mental health. Perceptions of social support were measured using a 10-item scale ranging from 10 to 70 (α=0.79), with a higher score indicating higher perceived social support. A linear mixed model for longitudinal data was used, with lags for marital status, mental health and social support. ---------- Results: After adjustment for social characteristics there was a decline in mental health for men who separated (−5.79 points) or widowed (−7.63 points), compared to men who remained married. Similar declines in mental health were found for women who separated (−6.65 points) or became widowed (−9.28 points). The inclusion of perceived social support in the models suggested a small mediation effect of social support for mental health with marital loss. Interactions between perceived social support and marital transitions showed a strong moderating effect for men who became widowed. No significant interactions were found for women. ---------- Conclusion: Marital loss significantly decreased mental health. Increasing, or maintaining, high levels of social support has the potential to improve widowed men's mental health immediately after the death of their spouse.

A geometric approach to trajectory design for an autonomous underwater vehicle : surveying the bulbous bow of a ship

In this paper, we present a control strategy design technique for an autonomous underwater vehicle based on solutions to the motion planning problem derived from differential geometric methods. The motion planning problem is motivated by the practical application of surveying the hull of a ship for implications of harbor and port security. In recent years, engineers and researchers have been collaborating on automating ship hull inspections by employing autonomous vehicles. Despite the progresses made, human intervention is still necessary at this stage. To increase the functionality of these autonomous systems, we focus on developing model-based control strategies for the survey missions around challenging regions, such as the bulbous bow region of a ship. Recent advances in differential geometry have given rise to the field of geometric control theory. This has proven to be an effective framework for control strategy design for mechanical systems, and has recently been extended to applications for underwater vehicles. Advantages of geometric control theory include the exploitation of symmetries and nonlinearities inherent to the system. Here, we examine the posed inspection problem from a path planning viewpoint, applying recently developed techniques from the field of differential geometric control theory to design the control strategies that steer the vehicle along the prescribed path. Three potential scenarios for surveying a ship?s bulbous bow region are motivated for path planning applications. For each scenario, we compute the control strategy and implement it onto a test-bed vehicle. Experimental results are analyzed and compared with theoretical predictions.

Vibration of L-shaped plates under a deterministic force or moment excitation : a case of statistical energy analysis application

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary

Sloshing motion of water in a moonpool

This thesis is concerned with the sloshing motion of water in a moonpool. It is a relatively new problem, that is particularly predominant in moonpools with relatively large dimensions. The problem is further complicated by the additional behaviour of vertical oscillation. It is inevitable that large moonpools will be needed as offshore technology advances, therefore making a problem an important one. The research involves two parts, the theoretical and experimental study. The theoretical study consists of idealising the moonpool to a two dimensional system, represented by two surface piercing parallel barriers at a distance 2a apart. The barriers are forced to undergo roll motion which in turn generates waves. These travelling waves are travelling in opposite directions to each other and have the same amplitude and period, and thus can be expressed in terms of a standing wave. This is mathematically achieved by applying the theory of wavemaking, and therefore the wave amplitude at the side wall can be evaluated at near resonant conditions. The experimental study comprises of comparing the results obtained from the tank and moonpool experiments. The rolling motion creates the sloshing waves in both cases, in addition the vertical oscillation in the moonpool is produced by generating waves at one end of the towing tank. Apart from highlighting influencing parameters, the resonant frequencies obtained from these experiments are then compared with the theoretical values. Experiments in demonstrating the effect of increasing damping with the aid of baffles are also conducted. This is an important aspect which is very necessary if operations in launching and retrieving are to be carried out efficiently and safely.

Minimising wave drag for free surface flow past a two-dimensional stern

Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving for the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results found using a forced KdV equation are also presented, as are numerical solutions to the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely.

Predicting wave glider speed from environmental measurements

In the ocean science community, researchers have begun employing novel sensor platforms as integral pieces in oceanographic data collection, which have significantly advanced the study and prediction of complex and dynamic ocean phenomena. These innovative tools are able to provide scientists with data at unprecedented spatiotemporal resolutions. This paper focuses on the newly developed Wave Glider platform from Liquid Robotics. This vehicle produces forward motion by harvesting abundant natural energy from ocean waves, and provides a persistent ocean presence for detailed ocean observation. This study is targeted at determining a kinematic model for offline planning that provides an accurate estimation of the vehicle speed for a desired heading and set of environmental parameters. Given the significant wave height, ocean surface and subsurface currents, wind speed and direction, we present the formulation of a system identification to provide the vehicle’s speed over a range of possible directions.

Modelling travelling waves in spatially constrained environment solutions

In this study, we consider how Fractional Differential Equations (FDEs) can be used to study the travelling wave phenomena in parabolic equations. As our method is conducted under intracellular environments that are highly crowded, it was discovered that there is a simple relationship between the travelling wave speed and obstacle density.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

The allocation of taxing rights of ship and aircraft leasing profits under Australia's tax treaties

The Australian Federal Commissioner of Taxation recently released Draft Taxation Ruling TR 2008/D3 with the stated purpose of clarifying ‘what profits derived from the leasing of ships or aircraft fall within the ship and aircraft articles of each of Australia’s tax treaties’. In particular, TR 2008/D3 explains the taxing rights over different types of leasing profits, such as a full basis lease in respect of any transport by a ship operated in international traffic and bareboat leases which are ancillary to the lessor transport operations of ships in international traffic. This article outlines the Commissioner’s views on the application of the standard ships and aircraft articles in the tax treaties to which it is a party as well as considering the major variations on the standard adoption. In doing so, guidance is provided as to the allocation of taxing rights of ship and aircraft leasing profits under Australia’s tax treaties.

The taxation of international maritime leasing profits : has the commissioners ship come in?

In light of McDermott Industries (AUST) Pty Ltd v Commissioner of Taxation, and Draft Taxation Ruling TR 2006/D8, this article considers the current Australian taxation position of profits arising from the cross-border leasing of vessels in the maritime industry. It focuses on the tax treaties to which Australia is a party, in particular the application of the business profits provisions of those treaties, and the deemed existence of a permanent establishment where substantial equipment, owned by a fiscal non-resident, is used within Australian waters.

Cold and heat waves in the United States

Extreme cold and heat waves, characterised by a number of cold or hot days in succession, place a strain on people’s cardiovascular and respiratory systems. The increase in deaths due to these waves may be greater than that predicted by extreme temperatures alone. We examined cold and heat waves in 99 US cities for 14 years (1987–2000) and investigated how the risk of death depended on the temperature threshold used to define a wave, and a wave’s timing, duration and intensity. We defined cold and heat waves using temperatures above and below cold and heat thresholds for two or more days. We tried five cold thresholds using the first to fifth percentiles of temperature, and five heat thresholds using the ninety-fifth to ninety-ninth percentiles. The extra wave effects were estimated using a two-stage model to ensure that their effects were estimated after removing the general effects of temperature. The increases in deaths associated with cold waves were generally small and not statistically significant, and there was even evidence of a decreased risk during the coldest waves. Heat waves generally increased the risk of death, particularly for the hottest heat threshold. Cold waves of a colder intensity or longer duration were not more dangerous. Cold waves earlier in the cool season were more dangerous, as were heat waves earlier in the warm season. In general there was no increased risk of death during cold waves above the known increased risk associated with cold temperatures. Cold or heat waves earlier in the cool or warm season may be more dangerous because of a build up in the susceptible pool or a lack of preparedness for cold or hot temperatures.

Tactically-driven nonmonotone travelling waves

Models of cell invasion incorporating directed cell movement up a gradient of an external substance and carrying capacity-limited proliferation give rise to travelling wave solutions. Travelling wave profiles with various shapes, including smooth monotonically decreasing, shock-fronted monotonically decreasing and shock-fronted nonmonotone shapes, have been reported previously in the literature. The existence of tacticallydriven shock-fronted nonmonotone travelling wave solutions is analysed for the first time. We develop a necessary condition for nonmonotone shock-fronted solutions. This condition shows that some of the previously reported shock-fronted nonmonotone solutions are genuine while others are a consequence of numerical error. Our results demonstrate that, for certain conditions, travelling wave solutions can be either smooth and monotone, smooth and nonmonotone or discontinuous and nonmonotone. These different shapes correspond to different invasion speeds. A necessary and sufficient condition for the travelling wave with minimum wave speed to be nonmonotone is presented. Several common forms of the tactic sensitivity function have the potential to satisfy the newly developed condition for nonmonotone shock-fronted solutions developed in this work.