Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Secular series and renormalization group for amplitude equations

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

Renormalization group interpretation of the Born and Rytov approximations

In this paper the method of renormalization group (RG) [Phys. Rev. E 54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. © 2008 Optical Society of America.

A non-malleable group key exchange protocol robust against active insiders

In this paper we make progress towards solving an open problem posed by Katz and Yung at CRYPTO 2003. We propose the first protocol for key exchange among n ≥2k+1 parties which simultaneously achieves all of the following properties: 1. Key Privacy (including forward security) against active attacks by group outsiders, 2. Non-malleability — meaning in particular that no subset of up to k corrupted group insiders can ‘fix’ the agreed key to a desired value, and 3. Robustness against denial of service attacks by up to k corrupted group insiders. Our insider security properties above are achieved assuming the availability of a reliable broadcast channel.

Testing the international linkage in the platinum-group metal futures markets

This study tests whether an international market exists in the platinum-group metal (PGM) futures markets. For this purpose, we tested the law of one price (LOP) and the causality between the U.S. and Japanese platinum and palladium futures markets. We also performed the test when structural breaks are considered. Long-run price relationships were found in both platinum and palladium markets but the LOP only sustained in the palladium market. The causality test revealed that it is the U.S. market that leads the price to transmit information between the U.S. and Japanese markets. Structural breaks had large impacts on the test results, suggesting that incorporating breaks is important when investigating the international price linkage in the PGM futures markets.

Sentencing and public confidence in Australia: The dynamics and foci of small group deliberations

This study is the first of its kind in Australia to use the deliberative small group methodology to explore participants’ deeper, nuanced thoughts on specific criminal justice issues in order to gain insight into the underlying beliefs that influence people’s opinions on sentencing. The use of small group discussions allows an analysis of the dynamics of people’s interactions and the potential of these to elicit deeper, more thoughtful deliberation. Participants’ comments around two policy areas – mandatory sentencing and the use of alternatives to imprisonment – were founded on concerns about the need for judges to tailor the sentence to fit the specific circumstances of each case. The methodology itself has shown that people may change their initial opinions on complex issues when given the opportunity to discuss and reflect on their beliefs.

Socio-demographic vulnerability to heatwave impacts in Brisbane, Australia : a time series analysis

Objective: Examining the association between socioeconomic disadvantage and heat-related emergency department (ED) visits during heatwave periods in Brisbane, 2000–2008. Methods: Data from 10 public EDs were analysed using a generalised additive model for disease categories, age groups and gender. Results: Cumulative relative risks (RR) for non-external causes other than cardiovascular and respiratory diseases were 1.11 and 1.05 in most and least disadvantaged areas, respectively. The pattern persisted on lags 0–2. Elevated risks were observed for all age groups above 15 years in all areas. However, with RRs of 1.19–1.28, the 65–74 years age group in more disadvantaged areas stood out, compared with RR=1.08 in less disadvantaged areas. This pattern was observed on lag 0 but did not persist. The RRs for male presentations were 1.10 and 1.04 in most and less disadvantaged areas; for females, RR was 1.04 in less disadvantaged areas. This pattern persisted across lags 0–2. Conclusions: Heat-related ED visits increased during heatwaves. However, due to overlapping confidence intervals, variations across socioeconomic areas should be interpreted cautiously. Implications: ED data may be utilised for monitoring heat-related health impacts, particularly on the first day of heatwaves, to facilitate prompt interventions and targeted resource allocation.

‘It's all scientific to me’ : focus group insights into why young people do not apply safe-sex knowledge

Despite rising levels of safe-sex knowledge in Australia, sexually transmitted infection notifications continue to increase. A culture-centred approach suggests it is useful in attempting to reach a target population first to understand their perspective on the issues. Twenty focus groups were conducted with 89 young people between the ages of 14 and 16 years. Key findings suggest that scientific information does not articulate closely with everyday practice, that young people get the message that sex is bad and they should not be preparing for it and that it is not appropriate to talk about sex. Understanding how young people think about these issues is particularly important because the focus groups also found that young people disengage from sources of information that do not match their own experiences.

A time series analysis of presentations to Queensland health facilities for alcohol-related conditions, following the increase in 'alcopops' tax

Objective: In response to concerns about the health consequences of high-risk drinking by young people, the Australian Government increased the tax on pre-mixed alcoholic beverages ('alcopops') favoured by this demographic. We measured changes in admissions for alcohol-related harm to health throughout Queensland, before and after the tax increase in April 2008. Methods: We used data from the Queensland Trauma Register, Hospitals Admitted Patients Data Collection, and the Emergency Department Information System to calculate alcohol-related admission rates per 100,000 people, for 15 - 29 year-olds. We analysed data over 3 years (April 2006 - April 2009), using interrupted time-series analyses. This covered 2 years before, and 1 year after, the tax increase. We investigated both mental and behavioural consequences (via F10 codes), and intentional/unintentional injuries (S and T codes). Results: We fitted an auto-regressive integrated moving average (ARIMA) model, to test for any changes following the increased tax. There was no decrease in alcohol-related admissions in 15 - 29 year-olds. We found similar results for males and females, as well as definitions of alcohol-related harms that were narrow (F10 codes only) and broad (F10, S and T codes). Conclusions: The increased tax on 'alcopops' was not associated with any reduction in hospital admissions for alcohol-related harms in Queensland 15 - 29 year-olds.

Amino group positions dependent morphology and coverage of electropolymerized metallophthalocyanine (M = Ni and Co) films on electrode surfaces

Electropolymerized films of teraaminometallophthalocyanines (MTAPc; M = Ni and Co) with amino groups at α- (4α-MTAPc) and β- (4β-MTAPc) positions were prepared on glassy carbon (GC) and indium tin oxide (ITO) electrodes. It was found that the electropolymerization growth rate of 4α-MTAPc was less than that of 4β-MTAPc prepared under identical conditions. Further, the surface coverage of the polymerized 4β-MTAPc film was greater than that of 4α-MTAPc polymerized film. Atomic force microscopy (AFM), X-ray diffraction (XRD) and UV–visible spectroscopic studies were carried out for the polymerized films of 4α-NiIITAPc (p-4α-NiIITAPc) and 4β-NiIITAPc (p-4β-NiIITAPc) alone because both Ni(II) and Co(II) polymerized films show similar trend in electropolymerization and surface coverage values. AFM images show that p-4α-NiIITAPc film contains islands and the thickness of this film was nearly three times less than that of p-4β-NiIITAPc. XRD patterns for the two polymerized films reveal that p-4β-NiIITAPc film was relatively more crystalline than p-4α-NiIITAPc film. Further, the compactness of these films was scrutinized from their barrier properties toward [Fe(CN)6]3−/4− redox couple. The differences in the polymerization growth rate of 4α-MTAPc and 4β-MTAPc, and the thicknesses of the resultant polymerized films suggest that unlike 4β-MTAPc one or two amino groups might have not involved in electropolymerization in the case of 4α-MTAPc. Further, the influence of surface coverage on the electrocatalytic properties of the polymerized films was studied by taking p-4β-CoIITAPc and p-4α-CoIITAPc films as examples. The electrocatalytic oxygen reduction current was almost same at both the electrodes suggesting that only the surface species were involved in the electrocatalytic reduction of oxygen.

Amino group position dependent orientation of self-assembled monomolecular films of tetraaminophthalocyanatocobalt(II) on Au surfaces

Self-assembled monomolecular films of 1,8,15,22-tetraaminophthalocyanatocobalt(II) (4α-CoIITAPc) and 2,9,16,23-tetraaminophthalocyanatocobalt(II) (4β-CoIITAPc) on Au surfaces were prepared by spontaneous adsorption from solution. These films were characterized by cyclic voltammetry and Raman spectroscopy. Both the surface coverage (Γ) and intensity of the in-plane stretching bands obtained from Raman studies vary for these monomolecular films, indicating different orientations adopted by them on Au surfaces. The 4α-CoIITAPc-modified electrode exhibits an E1/2 of 0.35 V, while the 4β-CoIITAPc-modified electrode exhibits an E1/2 of 0.19 V, corresponding to the CoII/CoIII redox couple in 0.1 M H2SO4. The Γ estimated from the charge associated with the oxidation of Co(II) gives (2.62 ± 0.10) × 10-11 mol cm-2 for 4α-CoIITAPc and (3.43 ± 0.14) × 10-10 mol cm-2 for 4β-CoIITAPc. In Raman spectral studies, the intensity ratio between in-plane phthalocyanine (Pc) stretching and the Au−N stretching was found to be 6.6 for 4β-CoIITAPc, while it was 1.6 for 4α-CoIITAPc. The obtained lower Γ and intensity ratio values suggest that 4α-CoIITAPc adopts nearly a parallel orientation on the Au surface, while the higher Γ and intensity ratio values suggest that 4β-CoIITAPc adopts a perpendicular orientation. The electrochemical reduction of dioxygen was carried out using these differently oriented Pc's in phosphate buffer solution (pH 7.2). Both the Pc's catalyze the reduction of dioxygen; however, the 4α-CoIITAPc-modified electrode greatly reduces the dioxygen reduction overpotential compared to 4β-CoIITAPc-modified and bare Au electrodes.

Indigenous livelihoods policy reference group: Research priorities identified from the first meeting, 28th April 2010

The CSIRO Indigenous Livelihoods Project sought to work with Indigenous communities, government and non-government stakeholders to bring together western science and Indigenous knowledge in order to understand the potential livelihood benefits of enterprises based on natural resource management. The research focus was to enhance livelihood opportunities for Indigenous communities derived from new enterprises and activities based on natural resource management in regional and remote Australia. Underpinning outcomes were: · Identification of effective policy and institutional arrangements required to establish and maintain sustainable livelihoods; · Improved systems understanding of factors that enhance or inhibit sustainable livelihoods based on natural resource management; · Tools and methods for measuring the livelihood benefits of natural resource management; · Education, training, employment and capacity building for Indigenous communities and researchers.