Equivalent of a Thouless energy in lattice QCD Dirac spectra

Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. In addition, RMT provides efficient means to separate different scales in spectra. Recently RMT has found application in quantum chromodynamics (QCD). In mesoscopic physics, the Thouless energy sets the universal scale for which RMT applies. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator with staggered fermions and $SU_c(2)$ lattice gauge fields. Comparing lattice data with RMT predictions we find deviations which allow us to give an estimate for this scale.Comment: LATTICE99 (theor. devel.), 3 pages, 4 figure

Universal and non-universal behavior in Dirac spectra

We have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum, we compare the lattice data with predictions from chiral random matrix theory for the distribution of the low-lying eigenvalues. Good agreement is found up to some limiting energy, the so-called Thouless energy, above which random matrix theory no longer applies. We determine the dependence of the Thouless energy on the simulation parameters using the scalar susceptibility and the number variance.Comment: LATTICE98(confine), 9 pages, 11 figure

Spectrum of the SU(3) Dirac operator on the lattice: Transition from random matrix theory to chiral perturbation theory

We calculate complete spectra of the Kogut-Susskind Dirac operator on the lattice in quenched SU(3) gauge theory for various values of coupling constant and lattice size. From these spectra we compute the connected and disconnected scalar susceptibilities and find agreement with chiral random matrix theory up to a certain energy scale, the Thouless energy. The dependence of this scale on the lattice volume is analyzed. In the case of the connected susceptibility this dependence is anomalous, and we explain the reason for this. We present a model of chiral perturbation theory that is capable of describing the data beyond the Thouless energy and that has a common range of applicability with chiral random matrix theory.Comment: 8 pages, RevTeX, 15 .eps figure

Randomness on the Lattice

In this lecture we review recent lattice QCD studies of the statistical properties of the eigenvalues of the QCD Dirac operator. We find that the fluctuations of the smallest Dirac eigenvalues are described by chiral Random Matrix Theories with the global symmetries of the QCD partition function. Deviations from chiral Random Matrix Theory beyond the Thouless energy can be understood analytically by means of partially quenched chiral perturbation theory.Comment: Invited talk at the International Light-Cone Meeting on Non-Perturbative QCD and Hadron Phenomenology, Heidelberg 12-17 June 2000. 12 pages, 7 figures, Late

Homogénéisation des matériaux hétérogènes élastoviscoplastiques basée sur la technique des « champs translatés » : extension « affine » au cas non linéaire pour des composites biphasés

Dans cette contribution, on passe tout d’abord en revue les principales étapes de la technique à « champs translatés » pour déterminer le comportement effectif de matériaux élasto-viscoplastiques dont les phases suivent un couplage spatio-temporel de type Maxwellien et dont le comportement est supposé dans un premier temps linéaire. L’application de l’approche à « champs translatés » au problème de l’inclusion d’Eshelby viscoélastique linéaire est également présentée dans cette première partie. Le traitement de cas particuliers montre la pertinence de l’approche en viscoélasticité linéaire par rapport aux solutions obtenues classiquement par transformées de Laplace-Carson. Ensuite, l’extension de la méthode à « champs translatés » au comportement local élasto-viscoplastique avec une viscoplasticité non linéaire est résolue par le biais d’une linéarisation du comportement viscoplastique des phases de type « affine ». Cette extension couplée à un schéma d’homogénéisation à champs moyens (Mori-Tanaka ou schéma autocohérent) pour le problème hétérogène élastoviscoplastique donne une nouvelle loi d’interaction qui contient les interactions mécaniques entre les champs moyens par phase et les grandeurs macroscopiques. Dans le but de situer la validité de l’approximation à « champs moyens », les réponses mécaniques du modèle sont reportées pour des composites biphasés et sont comparées aux résultats d’autres approches d’homogénéisation de type analytique ou numériques existants dans la littérature

A time-incremental Eshelby-based homogenization scheme for viscoelastic heterogeneous materials

International audienceA time-incremental Eshelby-based homogenization scheme for Maxwellian heterogeneous materials is proposed and discussed. This is based on the exact solution of the heterogeneous Eshelby ellipsoidal inclusion problem obtained in the time domain. In contrast with hereditary methods, the effective behavior as well as the evolution laws of the averaged stresses per phase are solved incrementally in the time domain without need to inverse Laplace or Laplace-Carson transforms. This is made through a time-differential equation to exactly solve a volume term in the integral equation that was generally approximated in previous internal variable methods. The present formulation works for any arbitrary anisotropic ellipsoidal Maxwellian inclusion embedded in an isotropic Maxwellian matrix without any other restrictive assumptions. In order to show the interest of the present approach, a Mori-Tanaka homogenization scheme is applied to two-phase composites using the developed strain rate concentration equations. The results are reported and discussed in comparisons with other existing methods, including hereditary approaches and more recent internal variable approaches, in order to show the efficiency of the present time-incremental homogenization scheme

Fast Fourier transform-based micromechanics of interfacial line defects in crystalline materials

International audienceSpectral methods using Fast Fourier Transform (FFT) algorithms have recently seen a surge in interest in the mechanics community. The present contribution addresses the critical question of determining local mechanical fields using the FFT method in the presence of interfacial defects. Precisely, the present work introduces a numerical approach based on intrinsic discrete Fourier transforms for the simultaneous treatment of material discontinuities arising from the presence of disclinations, i.e., rotational discontinuities, and inhomogeneities. A centered finite difference scheme for differential rules are first used for numerically solving the Poisson-type equations in the Fourier space to get the incompatible elastic fields due to disclinations and dislocations. Second, centered finite differences on a rotated grid are chosen for the computation of the modified Fourier-Green's operator in the Lippmann-Schwinger-Dyson type equation for heterogeneous media. Elastic fields of disclination dipole distributions interacting with inhomogeneities of varying stiffnesses, grain boundaries seen as DSUM (Disclina-tion Structural Unit Model), grain boundary disconnection defects and phase boundary "terraces" in anisotropic bi-materials are numerically computed as applications of the method

Lattice strain measurements using synchrotron diffraction to calibrate a micromechanical modeling in a ferrite–cementite steel

In situ tensile tests were performed at room temperature on a ferrite–cementite steel specifically designed for this study. The evolution of the average stress in ferrite during loading was analyzed by X-ray diffraction.Lattice strain measurements were performed with synchrotron ring diffraction in both ferrite and cementite.These in situ tests were complemented by macroscopic tensile and reversible tensile-compression tests to study the Bauschinger effect. In order to reproduce stresses in ferrite and cementite particles,a recently developed micromechanical Internal Length Mean Field (ILMF) model based on a generalized self-consistent scheme is applied. In this designed ferrite–cementite steel,the third ‘‘phase’’of the model represents finite intermediate‘‘layers’’in ferrite due to large geometrically necessary dislocation (GND) densities around cementite particles. The assumed constant thickness of the layers is calibrated thanks to the obtained experimental data.The ILMF model is validated by realistic estimates of the Bauschinger stress and the large difference between mean stresses in ferrite and in cementite phases.This difference cannot be reproduced by classic two-phase homogenization schemes without intermediate GND layers

Kramers Equation Algorithm with Kogut-Susskind Fermions on Lattice

We compare the performance of the Kramers Equation Monte Carlo (KMC) Algorithm with that of the Hybrid Monte Carlo (HMC) algorithm for numerical simulations with dynamical Kogut-Susskind fermions. Using the lattice Gross-Neveu model in 2 space-time dimensions, we calculate the integrated autocorrelation time of different observables at a number of couplings in the scaling region on 16^2 and 32^2 lattices while varying the parameters of the algorithms for optimal performance. In our investigation the performance of KMC is always significantly below than that of HMC for the observables used. We also stress the importance of having a large number of configurations for the accurate estimation of the integrated autocorrelation time.Comment: revised version to appear in Phys. Lett. B, 9 pages, 3 ps figure

Thermogravimetry and X-ray diffraction study of the thermal decomposition processes in Li2CO3-MnCO3 mixtures

The thermal decomposition processes taking place in solid state mixtures Li2CO3–MnCO3 (xLi=0.10–0.50, xLi=lithium cathionic fraction) have been studied (both in air and nitrogen flow) by thermogravimetric analysis (TGA), in order to get a better understanding of the different possible by-products, and by X-ray powder diffractometry (XRD) to assess the equilibrium compounds. As concerns the measurements performed in air, LiMn2O4 and excess Mn2O3 are the equilibrium products obtained for xLi up to 0.33. By 0.33xLi0.50 a mixture of LiMn2O4 and Li2MnO3 is obtained. In this case the TGA data show that an excess lithiated spinel phase (Li1+xMn2O4) is obtained as an intermediate phase. The measurements performed in nitrogen (xLi up to 0.33) show, when examined by TGA, the formation reaction of LiMn2O4 and Mn3O4 which is completed within about 720°C. At higher temperatures a rather complex reaction takes place between LiMn2O4 and the excess Li2O present at 720°C, leading to the formation of the compounds Li2Mn2O4 and LiMnO2 again with excess of Mn3O4. At higher mixture lithium content (0.33xLi0.50) LiMn2O4, Li2MnO3 and Mn3O4 form up to about 720°C. At higher temperatures LiMnO2 is by far the majority phase present which is formed by solid state reactions occurring between LiMn2O4 and Li2MnO3 and between Li2MnO3 and Mn3O4