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.

Minimum cost of transport in human running is not ubiquitous

Purpose This study explores recent claims that humans exhibit a minimum cost of transport (CoTmin) for running which occurs at an intermediate speed, and assesses individual physiological, gait and training characteristics. Methods Twelve healthy participants with varying levels of fitness and running experience ran on a treadmill at six self-selected speeds in a discontinuous protocol over three sessions. Running speed (km[middle dot]hr-1), V[spacing dot above]O2 (mL[middle dot]kg-1[middle dot]km-1), CoT (kcal[middle dot]km-1), heart rate (beats[middle dot]min-1) and cadence (steps[middle dot]min-1) were continuously measured. V[spacing dot above]O2 max was measured on a fourth testing session. The occurrence of a CoTmin was investigated and its presence or absence examined with respect to fitness, gait and training characteristics. Results Five participants showed a clear CoTmin at an intermediate speed and a statistically significant (p < 0.05) quadratic CoT-speed function, while the other participants did not show such evidence. Participants were then categorized and compared with respect to the strength of evidence for a CoTmin (ClearCoTmin and NoCoTmin). The ClearCoTmin group displayed significantly higher correlation between speed and cadence; more endurance training and exercise sessions per week; than the NoCoTmin group; and a marginally non-significant but higher aerobic capacity. Some runners still showed a CoTmin at an intermediate speed even after subtraction of resting energy expenditure. Conclusion The findings confirm the existence of an optimal speed for human running, in some but not all participants. Those exhibiting a COTmin undertook a higher volume of running, ran with a cadence that was more consistently modulated with speed, and tended to be aerobically fitter. The ability to minimise the energetic cost of transport appears not to be ubiquitous feature of human running but may emerge in some individuals with extensive running experience.

Intervertebral staple grading system with micro-CT

Introduction Intervertebral stapling is a leading method of fusionless scoliosis treatment which attempts to control growth by applying pressure to the convex side of a scoliotic curve in accordance with the Hueter-Volkmann principle. In addition to that, staples have the potential to damage surrounding bone during insertion and subsequent loading. The aim of this study was to assess the extent of bony structural damage including epiphyseal injury as a result of intervertebral stapling using an in vitro bovine model. Materials and Methods Thoracic spines from 6-8 week old calves were dissected and divided into motion segments including levels T4-T11 (n=14). Each segment was potted in polymethylemethacrylate. An Instron Biaxial materials testing machine with a custom made jig was used for testing. The segments were tested in flexion/extension, lateral bending and axial rotation at 37⁰C and 100% humidity, using moment control to a maximum 1.75 Nm with a loading rate of 0.3 Nm per second for 10 cycles. The segments were initially tested uninstrumented with data collected from the tenth load cycle. Next an anterolateral 4-prong Shape Memory Alloy (SMA) staple (Medtronic Sofamor Danek, USA) was inserted into each segment. Biomechanical testing was repeated as before. The staples were cut in half with a diamond saw and carefully removed. Micro-CT scans were performed and sagittal, transverse and coronal reformatted images were produced using ImageJ (NIH, USA).The specimens were divided into 3 grades (0, 1 and 2) according to the number of epiphyses damaged by the staple prongs. Results: There were 9 (65%) segments with grade 1 staple insertions and 5 (35%) segments with grade 2 insertions. There were no grade 0 staples. Grade 2 spines had a higher stiffness level than grade 1 spines, in all axes of movement, by 28% (p=0.004). This was most noted in flexion/extension with an increase of 49% (p=0.042), followed by non-significant change in lateral bending 19% (p=0.129) and axial rotation 8% (p=0.456) stiffness. The cross sectional area of bone destruction from the prongs was only 0.4% larger in the grade 2 group compared to the grade 1 group (p=0.961). Conclusion Intervertebral staples cause epiphyseal damage. There is a difference in stiffness between grade 1 and grade 2 staple insertion segments in flexion/extension only. There is no difference in the cross section of bone destruction as a result of prong insertion and segment motion.

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.

Gentrification and the artistic dividend : the role of the arts in neighborhood change

Problem, research strategy, and findings: There is a conflict between recent creative placemaking policies intended to promote positive neighborhood development through the arts and the fact that the arts have long been cited as contributing to gentrification and the displacement of lower-income residents. Unfortunately, we do not have data to demonstrate widespread evidence of either outcome. We address the dearth of comprehensive research and inform neighborhood planning efforts by statistically testing how two different groups of arts activities—the fine arts and commercial arts industries—are associated with conditions indicative of revitalization and gentrification in 100 large U.S. metropolitan areas. We find that different arts activities are associated with different types and levels of neighborhood change. Commercial arts industries show the strongest association with gentrification in rapidly changing areas, while the fine arts are associated with stable, slow-growth neighborhoods. Takeaway for practice: This research can help planners to more effectively incorporate the arts into neighborhood planning efforts and to anticipate the potential for different outcomes in their arts development strategies, including gentrification-related displacement.

Drawing out critical thinking : testing the methodological value of drawing collaboratively

Early childhood research has long established that drawing is a central, and important activity for young children. Less common are investigations into the drawing activity of adults involved in early childhood. A team of adult early childhood researchers, with differing exposures and familiarities with drawing, experimented with intergenerational collaborative drawing with colleagues, students, family members and others, to explore the effectiveness of drawing as a research process and as an arts-based methodology. This testing prompted critical thinking into how drawing might facilitate research that involves young children, to operate in more communicable ways, and how research-focused drawings might occur in reference to a research project.

An orientation to early childhood education for sustainability and research : framing the text

This publication arose from the interests of the chapter authors, ‘a small group of thoughtful people’ almost all of whom participated in one or both Transnational Dialogues in Research in Early Childhood Education for Sustainability, held in Stavanger, Norway in 2010 and Brisbane, Australia in 2011 (Refer Appendix 1 for list of participants). These meetings were the first time that a critical mass of researchers from vastly different parts of the globe - Norway, Sweden, Australia and New Zealand at the inaugural meeting, with additional participants from Korea, Japan and Singapore attending the second - had come together to debate, discuss and share ideas about research and theory in the emerging field of Early Childhood Education for Sustainability (ECEfS. Some of the researchers who joined these Transnational Dialogues, had met serendipitously at earlier conferences and meetings, or corresponded via email, but many had never met face-to-face. Now a significant number are contributing authors in this text. It is a testament to these researchers’ interest in this agenda that they mostly self-funded their travel and other costs to attend the Transnational Dialogues research meetings. While most chapter authors come from the field of early childhood education, a few are more aligned with education for sustainability/environmental education, while a much smaller number are already working at the intersection of early childhood education and education for sustainability. What we share as a group is a range of perspectives and orientations to research and to the research focus at the heart of this book - young children and their actual and potential capabilities as agents of change for sustainability. As researchers, regardless of experience and perspectives, participants knew they had something extra to offer - their expertise as researchers - providing scholarly insights into the work of practitioners, applying critically reflective lenses to curricula, pedagogies and assumptions, testing of ideas and theories, and presenting a sense for where ECEfS might fit or, indeed, go beyond norms and orthodoxies. This is a text, then, for both researchers and those whose primary interests lie in daily interactions with children, families and communities.

Nonvolatile multilevel data storage memory device from controlled ambipolar charge trapping mechanism

The capability of storing multi-bit information is one of the most important challenges in memory technologies. An ambipolar polymer which intrinsically has the ability to transport electrons and holes as a semiconducting layer provides an opportunity for the charge trapping layer to trap both electrons and holes efficiently. Here, we achieved large memory window and distinct multilevel data storage by utilizing the phenomena of ambipolar charge trapping mechanism. As fabricated flexible memory devices display five well-defined data levels with good endurance and retention properties showing potential application in printed electronics.

Testing the effects of the Japanese vehicle emission-control law on the international palladium futures market

This paper tested the effects of the 2005 vehicle emission-control law issued in Japan on the market linkages between the U.S. and Japanese palladium futures markets, To determine these effects, we applied a cointegration test both with and without break points in the time series and found that the market linkages between the two countries changed after the break in October 2005. Our results show that the 2005 long-term regulation of vehicle emissions enacted in Japan influenced the international palladium futures market.

Total factor productivity growth and convergence in the petroleum industry : empirical analysis testing for convexity

While economic theory acknowledges that some features of technology (e.g., indivisibilities, economies of scale and specialization) can fundamentally violate the traditional convexity assumption, almost all empirical studies accept the convexity property on faith. In this contribution, we apply two alternative flexible production technologies to measure total factor productivity growth and test the significance of the convexity axiom using a nonparametric test of closeness between unknown distributions. Based on unique field level data on the petroleum industry, the empirical results reveal significant differences, indicating that this production technology is most likely non-convex. Furthermore, we also show the impact of convexity on answers to traditional convergence questions in the productivity growth literature.

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.