On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Opportunities for enhancing the Australian national road safety strategy

With the current National Road Safety Strategy [1] coming to the end of its term, it is timely to consider ways in which the next iteration of this strategy can be enhanced. Strategic planning should be a cyclic process in which learning and adaptation are just as important as planning and implementation. It will always be the case that some actions are not as effective as expected, or that barriers to effective implementation will emerge. Rather than being setbacks, these are opportunities for learning about the validity of our assumptions. They are also opportunities for us to adapt to meet unanticipated or emerging challenges. One of the positive aspects of the implementation of the first and second National Road Safety Strategies has been the willingness of road safety agencies to critically assess progress and to identify where and how actions would be better focused. This has been reflected in the evolving nature of the periodic National Road Safety Action Plans. As the decade of the current Strategy reaches an end, there is a need to take this process further, and undertake a thorough critical evaluation of the Strategy development and implementation. While not an attempt to be exhaustive, the following article will identify some key priorities for consideration as part of this process.

Cyclic strain disrupts endothelial network formation on Matrigel

Most forms of tissue healing depend critically on revascularisation. In soft tissues and in vitro, mechanical stimuli have been shown to promote vessel-forming activity. However, in bone defects, increased interfragmentary motion impairs vascular regeneration. Because these effects seem contradictory, we aimed to determine whether a range of mechanical stimuli exists in which angiogenesis is favoured. A series of cyclic strain magnitudes were applied to a Matrigel-based “tube formation” assay and the total lengths of networks formed by human microvascular endothelial cells measured at 24 h. Network lengths were reduced at all strain levels, compared to unstretched controls. However, the levels of pro-angiogenic matrix metalloproteases-2 and -9 in the corresponding conditioned media were unchanged by strain, and vascular endothelial growth factor was uniformly elevated in stretched conditions. By repeating the assay with the addition of conditioned media from mesenchymal stem cells cultivated in similar conditions, paracrine stimuli were shown to increase network lengths, but not to alter the negative effect of cyclic stretching. Together, these results demonstrate that directly applied periodic strains can inhibit endothelial organisation in vitro, and suggest that this may be due to physical disruption rather than biochemical modulation. Most importantly, the results indicate that the straining of endothelial cells and their assembly into vascular-like structures must be studied simultaneously to adequately characterise the mechanical influence on vessel formation.

Application of a continuum theory to vertical vibrations of a layer of granular material

Many interesting phenomena have been observed in layers of granular materials subjected to vertical oscillations; these include the formation of a variety of standing wave patterns, and the occurrence of isolated features called oscillons, which alternately form conical heaps and craters oscillating at one-half of the forcing frequency. No continuum-based explanation of these phenomena has previously been proposed. We apply a continuum theory, termed the double-shearing theory, which has had success in analyzing various problems in the flow of granular materials, to the problem of a layer of granular material on a vertically vibrating rigid base undergoing vertical oscillations in plane strain. There exists a trivial solution in which the layer moves as a rigid body. By investigating linear perturbations of this solution, we find that at certain amplitudes and frequencies this trivial solution can bifurcate. The time dependence of the perturbed solution is governed by Mathieu’s equation, which allows stable, unstable and periodic solutions, and the observed period-doubling behaviour. Several solutions for the spatial velocity distribution are obtained; these include one in which the surface undergoes vertical velocities that have sinusoidal dependence on the horizontal space dimension, which corresponds to the formation of striped standing waves, and is one of the observed patterns. An alternative continuum theory of granular material mechanics, in which the principal axes of stress and rate-of-deformation are coincident, is shown to be incapable of giving rise to similar instabilities.

Thermal tweezers for manipulation of adatoms and nanoparticles on surfaces heated by interfering laser pulses

We conduct the detailed numerical investigation of a nanomanipulation and nanofabrication technique—thermal tweezers with dynamic evolution of surface temperature, caused by absorption of interfering laser pulses in a thin metalfilm or any other absorbing surface. This technique uses random Brownian forces in the presence of strong temperature modulation (surfacethermophoresis) for effective manipulation of particles/adatoms with nanoscale resolution. Substantial redistribution of particles on the surface is shown to occur with the typical size of the obtained pattern elements of ∼100 nm, which is significantly smaller than the wavelength of the incident pulses used (532 nm). It is also demonstrated that thermal tweezers based on surfacethermophoresis of particles/adatoms are much more effective in achieving permanent high maximum-to-minimum concentration ratios than bulk thermophoresis, which is explained by the interaction of diffusing particles with the periodic lattice potential on the surface. Typically required pulse regimes including pulse lengths and energies are also determined. The approach is applicable for reproducing any holographically achievable surfacepatterns, and can thus be used for engineering properties of surfaces including nanopatterning and design of surface metamaterials.

Vibration of ship structures and its control

Noise and vibration in complex ship structures are becoming a prominent issue for ship building industry and ship companies due to the constant demand of building faster ships of lighter weight, and the stringent noise and libration regulation of the industry. In order to retain the full benefit of building faster ships without compromising too much on ride comfort and safety, noise and vibration control needs to be implemented. Due to the complexity of ship structures, the coupling of different wave types and multiple wave propagation paths, active control of global hull modes is difficult to implement and very expensive. Traditional passive control such as adding damping materials is only effective in the high frequency range. However, most severe damage to ship structures is caused by large structural deformation of hull structures and high dynamic stress concentration at low frequencies. The most discomfort and fatigue of passengers and the crew onboard ships is also due to the low frequency noise and vibration. Innovative approaches are therefore, required to attenuate the noise and vibration at low frequencies. This book was developed from several specialized research topics on vibration and vibration control of ship structures, mostly from the author's own PhD work at the University of Western Australia. The book aims to provide a better understanding of vibration characteristics of ribbed plate structures, plate/plate coupled structures and the mechanism governing wave propagation and attenuation in periodic and irregular ribbed structures as well as in complex ship structures. The book is designed to be a reference book for ship builders, vibro-acoustic engineers and researchers. The author also hopes that the book can stimulate more exciting future work in this area of research. It is the author's humble desire that the book can be some use for those who purchase it. This book is divided into eight chapters. Each chapter focuses on providing solution to address a particular issue on vibration problems of ship structures. A brief summary of each chapter is given in the general introduction. All chapters are inter-dependent to each other to form an integration volume on the subject of vibration and vibration control of ship structures and alike. I am in debt to many people in completing this work. In particular, I would like to thank Professor J. Pan, Dr N.H. Farag, Dr K. Sum and many others from the University of Western Australia for useful advices and helps during my times at the University and beyond. I would also like to thank my wife, Miaoling Wang, my children, Anita, Sophia and Angela Lin, for their sacrifice and continuing supports to make this work possible. Financial supports from Australian Research Council, Australian Defense Science and Technology Organization and Strategic Marine Pty Ltd at Western Australia for this work is gratefully acknowledged.

Evaluation of piezoelectric PVDF polymers for use in space environments. II. Effects of atomic oxygen and vacuum UV exposure

The effects of atomic oxygen (AO) and vacuum UV radiation simulating low Earth orbit conditions on two commercially available piezoelectric polymer films, poly(vinylidene fluoride) (PVDF) and poly(vinylidene fluoride-trifluoroethylene) P(VDF-TrFE), have been studied. Surface erosion and pattern development are significant for both polymers. Erosion yields were determined as 2.8 � 10�24 cm3/atom for PVDF and 2.5 � 10�24 cm3/atom for P(VDF-TrFE). The piezoelectric properties of the residual material of both polymers were largely unchanged after exposure, although a slight shift in the Curie transition of the P(VDF-TrFE) was observed. A lightly cross-linked network was formed in the copolymer presumably because of penetrating vacuum ultraviolet (VUV) radiation, while the homopolymer remained uncross-linked. These differences were attributed to varying degrees of crystallinity and potentially greater absorption, and hence damage, of VUV radiation in P(VDFTrFE) compared with PVDF.

Selection and optimization of piezoelectric polyvinylidene fluoride polymers for adaptive optics in space environments

Various piezoelectric polymers based on polyvinylidene fluoride (PVDF) are of interest for large aperture space-based telescopes. Dimensional adjustments of adaptive polymer films depend on charge deposition and require a detailed understanding of the piezoelectric material responses which are expected to deteriorate owing to strong vacuum UV, � -, X-ray, energetic particles and atomic oxygen exposure. We have investigated the degradation of PVDF and its copolymers under various stress environments detrimental to reliable operation in space. Initial radiation aging studies have shown complex material changes with lowered Curie temperatures, complex material changes with lowered melting points, morphological transformations and significant crosslinking, but little influence on piezoelectric d33 constants. Complex aging processes have also been observed in accelerated temperature environments inducing annealing phenomena and cyclic stresses. The results suggest that poling and chain orientation are negatively affected by radiation and temperature exposure. A framework for dealing with these complex material qualification issues and overall system survivability predictions in low earth orbit conditions has been established. It allows for improved material selection, feedback for manufacturing and processing, material optimization/stabilization strategies and provides guidance on any alternative materials.

Effect of simulated space environments on piezoelectric vinylidene flouride-based polymers

Piezoelectric polymers based on polyvinylidene flouride (PVDF) are of interest as adaptive materials for large aperture space-based telescopes. In this study, two piezoelectric polymers, PVDF and P(VDF-TrFE), were exposed to conditions simulating the thermal, radiative and atomic oxygen conditions of low Earth orbit. The degradation pathways were governed by a combination of chemical and physical degradation processes with the molecular changes primarily induced via radiative damage, and physical damage from temperature and atomic oxygen exposure, as evident from depoling, loss of orientation and surface erosion. The piezoelectric responsiveness of each polymer was strongly dependent on exposure temperature. Radiation and atomic oxygen exposure caused physical and chemical degradation, which would ultimately cause terminal damage of thin films, but did not adversely affect the piezoelectric properties.

Degradation of piezoelectric fluropolymers in space environments

The performance criteria of piezoelectric polymers based on polyvinylidene flouride (PVDF) in complex space environments have been evaluated. Thin films of these materials are being explored as in-situ responsive materials for large aperture space-based telescopes with the shape deformation and optical features dependent on long-term deformation and optical features dependent on long-term degradation effects, mainly due to thermal cycling, vacuum UV exposure and atomic oxygen. A summary of previous studies related to materials testing and performance prediction based on a laboratory environment is presented. The degradation pathways are a combination of molecular chemical changes primarily induced via radiative damage and physical degradation processes due to temperature and atomic oxygen exposure resulting in depoling, loss of orientation and surface erosing. Experimental validation for these materials to be used in space is being conducted as part of MISSE-6 (Materials International Space Station Experiment) with an overview of the experimental strategies discussed here.

Piezoelectric vinylidene-fluoride based polymers for use in space environments

The effects of simulated low earth orbit conditions on vinylidene-fluoride based thin-film piezoelectrics for use in lightweight, large surface area spacecraft such as telescope mirrors and antennae is presented. The environmental factors considered as having the greatest potential to cause damage are temperature, atomic oxygen and vacuum UV radiation. Using the piezoelectric strain coefficients and bimorph deflection measurements the piezoelectric performance over the temperature range -100 to +150°C was studied. The effects of simultaneous AO/VUV exposure were also examined and films characterized by their piezoelectric, surface, and thermal properties. Two fluorinated piezoelectric polymers, poly(vinylidene fluoride) and poly(vinylidene fluoride-co-trifluoroethylene), were adversely affected at elevated temperatures due to depoling caused by randomization of the dipole orientation, while AO/VUV contributed little to depoling but did cause significant surface erosion and, in the case of P(VDF-TrFE), bulk crosslinking. These results highlight the importance of materials selection for use in space environments.

Piezoelectric PVDF materials performance and operation limits in space environments

Piezoelectric polymers based on polyvinylidene fluoride (PVDF) are of interest for large aperture space-based telescopes. Dimensional adjustments of adaptive polymer films are achieved via charge deposition and require a detailed understanding of the piezoelectric material responses which are expected to suffer due to strong vacuum UV, gamma, X-ray, energetic particles and atomic oxygen under low earth orbit exposure conditions. The degradation of PVDF and its copolymers under various stress environments has been investigated. Initial radiation aging studies using gamma- and e-beam irradiation have shown complex material changes with significant crosslinking, lowered melting and Curie points (where observable), effects on crystallinity, but little influence on overall piezoelectric properties. Surprisingly, complex aging processes have also been observed in elevated temperature environments with annealing phenomena and cyclic stresses resulting in thermal depoling of domains. Overall materials performance appears to be governed by a combination of chemical and physical degradation processes. Molecular changes are primarily induced via radiative damage, and physical damage from temperature and AO exposure is evident as depoling and surface erosion. Major differences between individual copolymers have been observed providing feedback on material selection strategies.

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.