The renormalization group: A perturbation method for the graduate curriculum

In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. Lett., 73 (1994), pp.1311-1315; Phys. Rev. E, 54 (1996), pp.376-394] is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum.The method is illustrated by some linear and nonlinear singular perturbation problems. Key word. © 2012 Society for Industrial and Applied Mathematics.

A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms. © 2010 by the Massachusetts Institute of Technology.

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.

Architecture in the South Pacific : the Ocean of Islands

Architecture in the South Pacific: The Ocean of Islands recounts the recent developments of the South Pacific and its fascinating architecture. This volume traces the European architectural overlay onto this scattered group of islands as well as the transition of these same islands towards a regional identity that has been fashioned by the remoteness of each location, the incomparable setting, and the distinctive ethnic mix of its inhabitants. A series of themed essays present the story of architectural development in the Solomon Islands, Vanuatu, New Caledonia, Fiji, Wallis and Futuna, Tonga, the Cook Islands, Samoa and American Samoa, and French Polynesia. Recent architecture typifies the evolution of the islands as they have been subjected to the transformative waves of alien trade, religion, colonization, war and tourism, followed by post-colonialism and revived nationalism. As with the Pacific region itself, the most prominent characteristic of the architecture is its diversity. The blending of the universal and the local sets the stage for a fresh vision of the South Pacific across a wide range of building types, from spectacular mission churches to sensational resorts in paradise. This book, in full colour, will appeal to architects, armchair-tourists, students and all those for whom the South Pacific is the idyll of their dreams.

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.

User-led innovation in call center knowledge work

So called “knowledge work” is seen as integral to post-industrial society and, for some, information and communications technologies (ICTs) are critical enablers of the associated practices. Many still propose the technologically deterministic route of rolling out ICTs and expecting that users will, and indeed can, “download” what they know into a system that can then be used in a number of ways. This approach is usually underpinned by the predominant assumption that the system will be developed by one group (developers) and used by another group (users). In this paper, we report on an exploratory case study of the enactment of ICT supported knowledge work in a human resources contact center which illustrates the negotiable boundary between the developer and user in local level innovation processes. Drawing upon ideas from the social shaping of technology, we examine how discussions regarding producer-user relations in innovation processes require a degree of greater sophistication as we show how users often develop (or produce) technologies and work practices in situ—in this case, to enable knowledge work practices and contribute to the project of constructing the knowledge component of professional identity. Much has been made of contextualizing the user; further work is required to contextualize the developer as a user and understand the social actors in ICT innovation environments who straddle both domains

‘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.

‘He has a way gayer Facebook than I do’ : investigating sexual identity disclosure and context collapse on a social networking site

This study extends previous research into social networking sites (SNSs) as environments that often reduce spatial, temporal, and social boundaries, which can result in collapsed contexts for social situations. Context collapse was investigated through interviews and Facebook walkthroughs with 27 LGBTQ young people in the United Kingdom. Since diverse sexualities are often stigmatized, participants’ sexual identity disclosure decisions were shaped by both the social conditions of their online networks and the technological architecture of SNSs. Context collapse was experienced as an event through which individuals intentionally redefined their sexual identity across audiences or managed unintentional disclosure. To prevent unintentional context collapse, participants frequently reinstated contexts through tailored performances and audience separation. These findings provide insight into stigmatized identity performances in networked publics while situating context collapse within a broader understanding of impression management, which paves the way for future research exploring the identity implications of everyday SNS use.