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

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

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 � 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

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

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.

Hyperscaling in the Broken Symmetry Phase of Dyson's Hierarchical Model

We use polynomial truncations of the Fourier transform of the local measure to calculate the connected q-point functions of Dyson's hierarchical model in the broken symmetry phase. We show that accurate values of the connected 1, 2 and 3 point functions can be obtained at large volume and in a limited range of constant external field coupled linearly to the field variable. We introduce a new method to obtain the correct infinite volume and zero external field extrapolations. We extract the leading critical exponents and show that they obey the scaling and hyperscaling relations with an accuracy ranging from 10^-5 to 5 10^-3. We briefly discuss how to improve the method of calculation

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

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