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.

The BRICS and R2P : contestation, re-interpretation and norm entrepreneurship

The intra-state humanitarian crises in Libya and Syria have led to renewed debate over the content and implementation of pillar three of the responsibility to protect (R2P). This paper examines the BRICS’ (Brazil, Russia, India, China, South Africa) current perspectives on R2P and their recent efforts to shape the concept’s evolution. While Brazil’s “Responsibility while Protecting” (RwP) proposal has been widely discussed, the central focus here is on the lesser-known, semi-official Chinese idea of “Responsible Protection” (RP). Like RwP, RP proposes decision-making criteria and accountability mechanisms for UN-authorised military intervention under R2P’s third pillar. This paper argues that although RP draws heavily on previous R2P proposals such as the original 2001 ICISS report and Brazil’s RwP, by amalgamating and re-packaging these earlier ideas in a more restrictive form the Chinese initiative represents a new and distinctive interpretation of R2P. However, as it currently stands, some aspects of RP appear to be framed too strictly to provide workable guidelines for determining the permissibility of R2P military intervention, and would, therefore, benefit from clarification and refinement. Of broader significance, China’s RP and Brazil’s RwP initiatives point to the growing willingness of rising, non-Western powers to articulate and promote their own normative preferences on sovereignty, intervention and global governance. This development has potential implications both for R2P’s evolution and for the structure of the international system.

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.

‘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.

Managing identity transitions during radical change in nuclear engineering organizations

This study reports the construction and reconstruction of identities of new and existing employees during a significant transition phase of a nuclear engineering organization. We followed a group of new and existing employees over the period of three years, during which the organization constructed a greenfield nuclear facility with new generational technologies whilst in parallel, decommissioned the older reactor. This change led to the transfer and integration of existing trade-based employees with the newly recruited, primarily university educated graduates in the new site. Three waves of interview data were collected, in conjunction with the cognitive mapping of social grouping and photo elicitation portrayed the stories of different group of employees who either succeeded or failed at embracing their new professional identity. In contrast with the new recruits who constructed new identities as they join this organization, we identify and report on the number of enabling and disabling factors that influence the process of professional identity construction and reconstruction during gamma change.

National working group meeting on ALK diagnostics in lung cancer

The global landscape of molecular testing is rapidly changing, with the recent publication of the International Association for the Study of Lung Cancer (IASLC)/College of American Pathologists (CAP) guidelines and the ALK Atlas. The IASLC/CAP guidelines recommend that tumors from patients with non-small cell lung cancer (NSCLC) be tested for ALK rearrangements in addition to epidermal growth factor receptor (EGFR) mutations. The spur for this recommendation is the availability of novel therapies that target these rearrangements. This article is based on coverage of a Pfizer-sponsored National Working Group Meeting on ALK Diagnostics in Lung Cancer, held around the 15th World Lung Cancer Conference, in Sydney on October 31, 2013. It is based on the presentations given by the authors at the meeting and the discussion that ensued. The content for this article was discussed and agreed on by the authors.

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.