An Efficient Method for the Solution of Schwinger--Dyson equations for propagators

Efficient computation methods are devised for the perturbative solution of Schwinger--Dyson equations for propagators. We show how a simple computation allows to obtain the dominant contribution in the sum of many parts of previous computations. This allows for an easy study of the asymptotic behavior of the perturbative series. In the cases of the four-dimensional supersymmetric Wess--Zumino model and the $\phi_6^3$ complex scalar field, the singularities of the Borel transform for both positive and negative values of the parameter are obtained and compared.Comment: 9 pages, no figures. Match of the published version, with the corrections in proo

The Standard Model of Leptons as a Purely Vectorial Theory

We propose a way to reconcile the Standard Model of leptons with a purely vectorial theory. The observed neutrino is predicted to be massless. The unobservability of its partner and the $V-A$ structure of the weak currents are given the same origin.Comment: 10 pages. Latex, 8 postscript figures included. We have corrected 2 (cancelling) sign misprints, and made explicit that we also recover the usual couplings of the U(1) gauge field B. The conclusions are unchanged. PAR-LPTHE 93/1

Integrable mappings and polynomial growth

We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds of transformations on $q \times q$ matrices: the inversion of the $q \times q$ matrix and an (involutive) permutation of the entries of the matrix. We concentrate on the case where these permutations are elementary transpositions of two entries. In this case the birational transformations fall into six different classes. For each class we analyze the factorization properties of the iteration of these transformations. These factorization properties enable to define some canonical homogeneous polynomials associated with these factorization properties. Some mappings yield a polynomial growth of the complexity of the iterations. For three classes the successive iterates, for $q=4$, actually lie on elliptic curves. This analysis also provides examples of integrable mappings in arbitrary dimension, even infinite. Moreover, for two classes, the homogeneous polynomials are shown to satisfy non trivial non-linear recurrences. The relations between factorizations of the iterations, the existence of recurrences on one or several variables, as well as the integrability of the mappings are analyzed.Comment: 45 page

A comment on free-fermion conditions for lattice models in two and more dimensions

We analyze free-fermion conditions on vertex models. We show --by examining examples of vertex models on square, triangular, and cubic lattices-- how they amount to degeneration conditions for known symmetries of the Boltzmann weights, and propose a general scheme for such a process in two and more dimensions.Comment: 12 pages, plain Late

Singularity, complexity, and quasi--integrability of rational mappings

We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of the structure of invariants of such mappings. We discuss some characteristic conditions for their (quasi)--integrability, and in particular its links with their singularities (in the 2--plane). Finally, we describe some of their properties {\it qua\/} dynamical systems, making contact with Arnol'd's notion of complexity, and exemplify remarkable behaviours.Comment: Latex file. 17 pages. To appear in CM

Electrical noise properties in aging materials

The electric thermal noise has been measured in two aging materials, a colloidal suspension (Laponite) and a polymer (polycarbonate), presenting very slow relaxation towards equilibrium. The measurements have been performed during the transition from a fluid-like to a solid-like state for the gel and after a quench for the polymer. For both materials we have observed that the electric noise is characterized by a strong intermittency, which induces a large violation of the Fluctuation Dissipation Theorem (FDT) during the aging time, and may persist for several hours at low frequency. The statistics of these intermittent signals and their dependance on the quench speed for the polymer or on sample concentration for the gel are studied. The results are in a qualitative agreement with recent models of aging, that predict an intermittent dynamics.Comment: SPIE Proceeding Journa

On-farm influence of production patterns on total polyphenol content in peach

Peach production in France is constantly confronted with marketing problems due to a decrease in fruit consumption and increasing competition with neighbouring Mediterranean countries. The production of higher quality products using production methods such as organic farming (OF) appears to be a tangible way of differentiating and enhancing peach production. To test this hypothesis, an on-farm study was conducted in one of the major production areas in South-eastern France. Focussing on the peach cultivar, cv. Spring Lady®, paired comparisons were conducted between plots in OF and conventional farming (CF). Farmers' practices were identified and checked against crop measurements and performances (yield, sugar content, size classes) in 2004 (12 plots) and in 2005 (10 plots). Polyphenol contents were assessed as an additional component of fruit quality, using the Folin-Ciocalteu colorimetric method. Organic peaches have a higher polyphenol content at harvest. Contents were 4.8 times higher in 2004, whereas the same phenomenon was not observed in 2005. Levels of nitrogen, yield and tree vigour management appeared to be the key elements responsible for the synthesis of total polyphenols and sugar content This implies new opportunities for improving the nutritional quality of peaches, based on production methods

Coupling between aging and convective motion in a colloidal glass of Laponite

We study thermal convection in a colloidal glass of Laponite in formation. Low concentration preparation are submitted to destabilizing vertical temperature gradient, and present a gradual transition from a turbulent convective state to a steady conductive state as their viscosity increases. The time spent under convection is found to depend strongly on sample concentration, decreasing exponentially with mass fraction of colloidal particles. Moreover, at fixed concentration, it also depends slightly on the pattern selected by the Rayleigh B\'{e}nard instability: more rolls maintain the convection state longer. This behavior can be interpreted with recent theoretical approaches of soft glassy material rheology.Comment: Eur. Phys. J. B 55, 101-107 (2007) The original publication is available at http://www.springerlink.co