Non-Gaussian numerical errors versus mass hierarchy

We probe the numerical errors made in renormalization group calculations by varying slightly the rescaling factor of the fields and rescaling back in order to get the same (if there were no round-off errors) zero momentum 2-point function (magnetic susceptibility). The actual calculations were performed with Dyson's hierarchical model and a simplified version of it. We compare the distributions of numerical values obtained from a large sample of rescaling factors with the (Gaussian by design) distribution of a random number generator and find significant departures from the Gaussian behavior. In addition, the average value differ (robustly) from the exact answer by a quantity which is of the same order as the standard deviation. We provide a simple model in which the errors made at shorter distance have a larger weight than those made at larger distance. This model explains in part the non-Gaussian features and why the central-limit theorem does not apply.Comment: 26 pages, 7 figures, uses Revte

High-Accuracy Calculations of the Critical Exponents of Dyson's Hierarchical Model

We calculate the critical exponent gamma of Dyson's hierarchical model by direct fits of the zero momentum two-point function, calculated with an Ising and a Landau-Ginzburg measure, and by linearization about the Koch-Wittwer fixed point. We find gamma= 1.299140730159 plus or minus 10^(-12). We extract three types of subleading corrections (in other words, a parametrization of the way the two-point function depends on the cutoff) from the fits and check the value of the first subleading exponent from the linearized procedure. We suggest that all the non-universal quantities entering the subleading corrections can be calculated systematically from the non-linear contributions about the fixed point and that this procedure would provide an alternative way to introduce the bare parameters in a field theory model.Comment: 15 pages, 9 figures, uses revte

Digital analysis of the geometric variability of Guadua, Moso and Oldhamii bamboo

The implementation of sustainable building materials is currently one of the principal global challenges faced by the construction industry. Natural bamboo culms are a potential alternative to tackle this challenge due to its favourable environmental credentials as well as affordability. However, the organic geometry of bamboo culms is one of the barriers that prevents them from being implemented in formal design procedures. This work presents the details of a new digitisation workflow to systematically capture the geometry of bamboo culms through the application of 3D scanning technologies and reverse engineering principles. This workflow is applied to carry out a comprehensive analysis of the geometric variability of Guadua angustifolia kunth (Guadua), Phillostachys pubescens (Moso) and Bambusa oldhamii (Oldhamii) to identify potential correlation patterns. This geometric analysis showed a wide variation in the geometric properties of all species and no particular pattern was found which could be adopted for a potential visual grading system. These results highlight the challenges that the use of bamboo culms pose for the traditional design and fabrication processes developed for manufactured structural elements. The proposed reverse engineering methodology adopted for this study can be used to quantify and manage the geometric variability of bamboo culms to support the development of new formal design and fabrication processes for this natural structural element

Determination of the physical and mechanical properties of moso, guadua and oldhamii bamboo assisted by robotic fabrication

The large-scale urbanisation taking place in the developing world requires the construction industry to adopt alternative non-conventional renewable materials to reduce the unsustainable level of greenhouse gas emissions associated with the production of industrialised building materials. Bamboo is one of the most promising non-conventional building materials endemic to most developing countries, but there is still insufcient consistent information on the physical and mechanical properties of the numerous species suitable for construction. This study shows the potential of robotic fabrication to accelerate testing programmes on small clear samples of bamboo required to compare physical and mechanical properties across diferent species and difering plantation management practices. This fabrication method is applied on an experimental testing programme to determine the characteristic values of density, compressive strength, elastic modulus and shear strength of Phyllostachys pubescens (moso), Guadua angustifolia Kunth (guadua) and Guadua angustifolia (oldhamii). The efcient development of comprehensive experimental datasets of clear samples of bamboo is fundamental to inform the development of future design guidelines for bamboo as a construction material

T-violation in Kμ3K_{\mu3} decay in a general two-Higgs doublet model

We calculate the transverse muon polarization in the $K^+_{\mu3}$ process arising from the Yukawa couplings of charged Higgs boson in a general two-Higgs doublet model where spontaneous violation of CP is presentComment: 6 pages, latex, accepted for publication in Phys. Rev.

Additive manufacturing: exploring the social changes and impacts

Despite the myriad of possibilities and applications of additive manufacturing (AM) technology, knowledge about the social impacts of this technology is very scarce and very limited in some areas. This paper explores how factors generated by the development of AM technology may create social impacts, affecting the health and social well-being of people, quality of life, working conditions, and the creation of wealth. This paper presents the results of an exploratory multiple case study conducted among four Portuguese organizations that use AM technology, aiming to determine their perceptions regarding the social impacts of AM, its effects, and causes. The results confirm that AM technology is mainly seen to create positive impacts on health and safety (regarding physical hazards), on expectations for the future, on leisure and recreation, on low disruption with the local economy, on economic prosperity, on the professional status, and on innovative employment types. Nevertheless, a negative impact was also found on health and safety (concerning hazardous substances), as well as several mixed and null impacts. The main limitations of the research arise from the use of a case study methodology, since the results can be influenced by contextual factors, such as the size of the organizations in the sample, and/or social, cultural, technological, political, economic, and ecological factors. This study gives an up-to-date contribution to the topic of AM social impacts and social changes, an area which is still little-explored in the literature.info:eu-repo/semantics/publishedVersio

Framework for life cycle sustainability assessment of additive manufacturing

Additive manufacturing (AM) is a group of technologies that create objects by adding material layer upon layer, in precise geometric shapes. They are amongst the most disruptive technologies nowadays, potentially changing value chains from the design process to the end-of-life, providing significant advantages over traditional manufacturing processes in terms of flexibility in design and production and waste minimization. Nevertheless, sustainability assessment should also be included in the research agenda as these technologies affect the People, the Planet and the Profit: the three-bottom line (3BL) assessment framework. Moreover, AM sustainability depends on each product and context that strengthens the need for its assessment through the 3BL framework. This paper explores the literature on AM sustainability, and the results are mapped in a framework aiming to support comprehensive assessments of the AM impacts in the 3BL dimensions by companies and researchers. To sustain the coherence of boundaries, three life cycle methods are proposed, each one for a specific dimension of the 3BL analysis, and two illustrative case studies are shown to exemplify the model.info:eu-repo/semantics/publishedVersio

On the universality of the Carter and McLenaghan formula

It is shown that the formula of the isometry generators of the spinor representation given by Carter and McLenaghan is universal in the sense that this holds for any representation either in local frames or even in natural ones. The point-dependent spin matrices in natural frames are introduced for any tensor representation deriving the covariant form of the isometry generators in these frames.Comment: 7 pages, no figure

The Lie derivative of spinor fields: theory and applications

Starting from the general concept of a Lie derivative of an arbitrary differentiable map, we develop a systematic theory of Lie differentiation in the framework of reductive G-structures P on a principal bundle Q. It is shown that these structures admit a canonical decomposition of the pull-back vector bundle i_P^*(TQ) = P\times_Q TQ over P. For classical G-structures, i.e. reductive G-subbundles of the linear frame bundle, such a decomposition defines an infinitesimal canonical lift. This lift extends to a prolongation Gamma-structure on P. In this general geometric framework the concept of a Lie derivative of spinor fields is reviewed. On specializing to the case of the Kosmann lift, we recover Kosmann's original definition. We also show that in the case of a reductive G-structure one can introduce a "reductive Lie derivative" with respect to a certain class of generalized infinitesimal automorphisms, and, as an interesting by-product, prove a result due to Bourguignon and Gauduchon in a more general manner. Next, we give a new characterization as well as a generalization of the Killing equation, and propose a geometric reinterpretation of Penrose's Lie derivative of "spinor fields". Finally, we present an important application of the theory of the Lie derivative of spinor fields to the calculus of variations.Comment: 28 pages, 1 figur

A Guide to Precision Calculations in Dyson's Hierarchical Scalar Field Theory

The goal of this article is to provide a practical method to calculate, in a scalar theory, accurate numerical values of the renormalized quantities which could be used to test any kind of approximate calculation. We use finite truncations of the Fourier transform of the recursion formula for Dyson's hierarchical model in the symmetric phase to perform high-precision calculations of the unsubtracted Green's functions at zero momentum in dimension 3, 4, and 5. We use the well-known correspondence between statistical mechanics and field theory in which the large cut-off limit is obtained by letting beta reach a critical value beta_c (with up to 16 significant digits in our actual calculations). We show that the round-off errors on the magnetic susceptibility grow like (beta_c -beta)^{-1} near criticality. We show that the systematic errors (finite truncations and volume) can be controlled with an exponential precision and reduced to a level lower than the numerical errors. We justify the use of the truncation for calculations of the high-temperature expansion. We calculate the dimensionless renormalized coupling constant corresponding to the 4-point function and show that when beta -> beta_c, this quantity tends to a fixed value which can be determined accurately when D=3 (hyperscaling holds), and goes to zero like (Ln(beta_c -beta))^{-1} when D=4.Comment: Uses revtex with psfig, 31 pages including 15 figure