Nonlinear mode coupling of surface acoustic waves on an isotropic solid

The nonlinear mode coupling between two co-directional quasi-harmonic Rayleigh surface waves on an isotropic solid is analysed using the method of multiple scales. This procedure yields a system of six semi-linear hyperbolic partial differential equations with the same principal part governing the slow variations in the (complex) amplitudes of the two fundamental, the two second harmonic and the two combination frequency waves at the second stage of the perturbation expansion. A numerical solution of these equations for excitation by monochromatic signals at two arbitrary frequencies, indicates that there is a continuous transfer of energy back and forth among the fundamental, second harmonic and combination frequency waves due to mode coupling. The mode coupling tends to be more pronounced as the frequencies of the interacting waves approach each other.

Nonlinear surface acoustic waves on an isotropic solid

A systematic derivation of the approximate coupled amplitude equations governing the propagation of a quasi-monochromatic Rayleigh surface wave on an isotropic solid is presented, starting from the non-linear governing differential equations and the non-linear free-surface boundary conditions, using the method of mulitple scales. An explicit solution of these equations for a signalling problem is obtained in terms of hyperbolic functions. In the case of monochromatic excitation, it is shown that the second harmonic amplitude grows initially at the expense of the fundamental and that the amplitudes of the fundamental and second harmonic remain bounded for all time.

Polybridge Technical Report

This study examined the physical and chemical properties of a novel, fully-recirculated prawn and polychaete production system that incorporated polychaete-assisted sand filters (PASF). The aims were to assess and demonstrate the potential of this system for industrialisation, and to provide optimisations for wastewater treatment by PASF. Two successive seasons were studied at commercially-relevant scales in a prototype system constructed at the Bribie Island Research Centre in Southeast Queensland. The project produced over 5.4 tonnes of high quality black tiger prawns at rates up to 9.9 tonnes per hectare, with feed conversion of up to 1.1. Additionally, the project produced about 930 kg of high value polychaete biomass at rates up to 1.5 kg per square metre of PASF, with the worms feeding predominantly on waste nutrients. Importantly, this closed production system demonstrated rapid growth of healthy prawns at commercially relevant production levels, using methods that appear feasible for application at large scale. Deeper (23 cm) PASF beds provided similar but more reliable wastewater treatment efficacies compared with shallower (13 cm) beds, but did not demonstrate significantly greater polychaete productivity than (easier to harvest) shallow beds. The nutrient dynamics associated with seasonal and tidal operations of the system were studied in detail, providing technical and practical insights into how PASF could be optimised for the mitigation of nutrient discharge. The study also highlighted some of the other important advantages of this integrated system, including low sludge production, no water discharge during the culture phase, high ecosystem health, good prospects for biosecurity controls, and the sustainable production of a fishery-limited resource (polychaetes) that may be essential for the expansion of prawn farming industries throughout the world. Regarding nutrient discharge from this prototype mariculture system, when PASF was operating correctly it proved feasible to have no water (or nutrient) discharge during the entire prawn growing season. However, the final drain harvest and emptying of ponds that is necessary at the end of the prawn farming season released 58.4 kg ha-1 of nitrogen and 6 kg ha-1 of phosphorus (in Season 2). Whilst this is well below (i.e., one-third to one-half of) the current load-based licencing conditions for many prawn farms in Australia, the levels of nitrogen and chlorophyll a in the ponds remained higher than the more-stringent maximum limits at the Bribie Island study site. Zero-net-nutrient discharge was not achieved, but waste nutrients were low where 5.91 kg of nitrogen and 0.61 kg of phosphorus was discharged per tonne of prawns produced. This was from a system that deployed PASF at 14.4% of total ponded farm area which treated an average of 5.8% of pond water daily and did not use settlement ponds or other natural or artificial water remediation systems. Four supplemental appendices complement this research by studying several additional aspects that are central to the industrialisation of PASF. The first details an economic model and decision tool which allows potential users to interactively assess construction and operational variables of PASF at different scales. The second provides the qualitative results of a prawn maturation trial conducted collaboratively with the Commonwealth Scientific and Industrial Research Organisation (CSIRO) to assess dietary inclusions of PASF-produced worms. The third provides the reproductive results from industry-based assessments of prawn broodstock produced using PASF. And the fourth appendix provides detailed elemental and nutritional analyses of bacterial biofilm produced by PASF and assesses its potential to improve the growth of prawns in recirculated culture systems.

Head motion and Inattention/Hyperactivity share common genetic influences: Implications for fMRI studies of ADHD

Head motion (HM) is a well known confound in analyses of functional MRI (fMRI) data. Neuroimaging researchers therefore typically treat HM as a nuisance covariate in their analyses. Even so, it is possible that HM shares a common genetic influence with the trait of interest. Here we investigate the extent to which this relationship is due to shared genetic factors, using HM extracted from resting-state fMRI and maternal and self report measures of Inattention and Hyperactivity-Impulsivity from the Strengths and Weaknesses of ADHD Symptoms and Normal Behaviour (SWAN) scales. Our sample consisted of healthy young adult twins (N = 627 (63% females) including 95 MZ and 144 DZ twin pairs, mean age 22, who had mother-reported SWAN; N = 725 (58% females) including 101 MZ and 156 DZ pairs, mean age 25, with self reported SWAN). This design enabled us to distinguish genetic from environmental factors in the association between head movement and ADHD scales. HM was moderately correlated with maternal reports of Inattention (r = 0.17, p-value = 7.4E-5) and Hyperactivity-Impulsivity (r = 0.16, p-value = 2.9E-4), and these associations were mainly due to pleiotropic genetic factors with genetic correlations [95% CIs] of rg = 0.24 [0.02, 0.43] and rg = 0.23 [0.07, 0.39]. Correlations between self-reports and HM were not significant, due largely to increased measurement error. These results indicate that treating HM as a nuisance covariate in neuroimaging studies of ADHD will likely reduce power to detect between-group effects, as the implicit assumption of independence between HM and Inattention or Hyperactivity-Impulsivity is not warranted. The implications of this finding are problematic for fMRI studies of ADHD, as failing to apply HM correction is known to increase the likelihood of false positives. We discuss two ways to circumvent this problem: censoring the motion contaminated frames of the RS-fMRI scan or explicitly modeling the relationship between HM and Inattention or Hyperactivity-Impulsivity

The structure of turbulent boundary layers along mildly curved surfaces

This paper describes a detailed study of the structure of turbulence in boundary layers along mildly curved convex and concave surfaces. The surface curvature studied corresponds to δ/Rw = ± 0·01, δ being the boundary-layer thickness and Rw the radius of curvature of the wall, taken as positive for convex and negative for concave curvature. Measurements of turbulent energy balance, autocorrelations, auto- and cross-power spectra, amplitude probability distributions and conditional correlations are reported. It is observed that even mild curvature has very strong effects on the various aspects of the turbulent structure. For example, convex curvature suppresses the diffusion of turbulent energy away from the wall, reduces drastically the integral time scales and shifts the spectral distributions of turbulent energy and Reynolds shear stress towards high wavenumbers. Exactly opposite effects, though generally of a smaller magnitude, are produced by concave wall curvature. It is also found that curvature of either sign affects the v fluctuations more strongly than the u fluctuations and that curvature effects are more significant in the outer region of the boundary layer than in the region close to the wall. The data on the conditional correlations are used to study, in detail, the mechanism of turbulent transport in curved boundary layers. (Published Online April 12 2006)

Elements of Volatility at High Frequency

Volatility is central in options pricing and risk management. It reflects the uncertainty of investors and the inherent instability of the economy. Time series methods are among the most widely applied scientific methods to analyze and predict volatility. Very frequently sampled data contain much valuable information about the different elements of volatility and may ultimately reveal the reasons for time varying volatility. The use of such ultra-high-frequency data is common to all three essays of the dissertation. The dissertation belongs to the field of financial econometrics. The first essay uses wavelet methods to study the time-varying behavior of scaling laws and long-memory in the five-minute volatility series of Nokia on the Helsinki Stock Exchange around the burst of the IT-bubble. The essay is motivated by earlier findings which suggest that different scaling laws may apply to intraday time-scales and to larger time-scales, implying that the so-called annualized volatility depends on the data sampling frequency. The empirical results confirm the appearance of time varying long-memory and different scaling laws that, for a significant part, can be attributed to investor irrationality and to an intraday volatility periodicity called the New York effect. The findings have potentially important consequences for options pricing and risk management that commonly assume constant memory and scaling. The second essay investigates modelling the duration between trades in stock markets. Durations convoy information about investor intentions and provide an alternative view at volatility. Generalizations of standard autoregressive conditional duration (ACD) models are developed to meet needs observed in previous applications of the standard models. According to the empirical results based on data of actively traded stocks on the New York Stock Exchange and the Helsinki Stock Exchange the proposed generalization clearly outperforms the standard models and also performs well in comparison to another recently proposed alternative to the standard models. The distribution used to derive the generalization may also prove valuable in other areas of risk management. The third essay studies empirically the effect of decimalization on volatility and market microstructure noise. Decimalization refers to the change from fractional pricing to decimal pricing and it was carried out on the New York Stock Exchange in January, 2001. The methods used here are more accurate than in the earlier studies and put more weight on market microstructure. The main result is that decimalization decreased observed volatility by reducing noise variance especially for the highly active stocks. The results help risk management and market mechanism designing.