259 research outputs found
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
Accurate Checks of Universality for Dyson's Hierarchical Model
Using recently developed methods, we perform high-accuracy calculations of
the susceptibility near beta_c for the D=3 version of Dyson's hierarchical
model. Using linear fits, we estimate the leading gamma and subleading Delta
exponents. Independent estimates are obtained by calculating the first two
eigenvalues of the linearized renormalization group transformation. We found
gamma = 1.29914073 (with an estimated error of 10^{-8}) and, Delta=0.4259469
(with an estimated error of 10^{-7}) independently of the choice of local
integration measure (Ising or Landau-Ginzburg). After a suitable rescaling, the
approximate fixed points for a large class of local measure coincide accurately
with a fixed point constructed by Koch and Wittwer.Comment: 9 pages, Revtex, 1 figur
High-accuracy critical exponents of O(N) hierarchical sigma models
We perform high-accuracy calculations of the critical exponent gamma and its
subleading exponent for the 3D O(N) Dyson's hierarchical model, for N up to 20.
We calculate the critical temperatures for the nonlinear sigma model measure.
We discuss the possibility of extracting the first coefficients of the 1/N
expansion from our numerical data. We show that the leading and subleading
exponents agreewith Polchinski equation and the equivalent Litim equation, in
the local potential approximation, with at least 4 significant digits.Comment: 4 pages, 2 Figs., uses revte
Calibrating a composite material model for analysis and design of bamboo structures
This paper proposes a methodology to develop a material model for bamboo culms to use it in a more
rigorous structural analysis and design. The study presented here is part of a broader research with the
aim of exploiting the mechanical properties of bamboo in lightweight structures that may transfer
predominantly axial compressive forces. The methodology is based on theoretical analysis and
experimental tests. Composite material theory has been adopted to describe the mathematical model
that can realistically reproduce the behaviour of bamboo culms. The composite material model is
linear elastic and describes the axial and flexural stiffness, and the stress distribution across the culm
wall thickness. For this study a series of experimental tests of the bamboo species Moso
(Phyllostachys Pubescens) were devised to obtain the Modulus of Elasticity ďż˝ under axial
compressive loads. Establishing suitable test methods to determine material properties is not an easy
task due to the difficulty of working with a non-isotropic and variable material. Experimental tests
were based on two different codified methods (JG/T 199-2007; ISO 22157-2004) with the aim of
reviewing the differences in the results of small coupons and full culm specimens, as well as
emphasising the issues related to the measurement of strains in a material with through-thickness
gradient fibre distribution under axial compression. In order to model the variability across the culm
wall, the volume fraction of the fibres was calculated by image analysis. In addition, assessment of
through-thickness strain distributions of small coupons using digital image correlation (DIC) was
carried out and is discussed in this paper. The validation process for the composite material model is
ongoing
T-violation in decay in a general two-Higgs doublet model
We calculate the transverse muon polarization in the 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.
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
Inducing Barbero-Immirzi Connections along SU(2)-reductions of Bundles on Spacetime
We shall present here a general apt technique to induce connections along
bundle reductions which is different from the standard restriction. This
clarifies and generalizes the standard procedure to define Barbero-Immirzi (BI)
connection, though on spacetime. The standard spacial BI connection used in LQG
is then obtained by its spacetime version by standard restriction. The general
prescription to define such a reduced connection is interesting from a
mathematical viewpoint and it allows a general and direct control on
transformation laws of the induced object. Moreover, unlike what happens by
using standard restriction, we shall show that once a bundle reduction is
given, then any connection induces a reduced connection with no constraint on
the original holonomy as it happens when connections are simply restricted.Comment: 6 pages, some comments adde
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
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