The role of intra- and inter-site exchange correlations in the extended Falicov-Kimball model on a triangular lattice

Ground state magnetic properties of the spin-dependent Falicov-Kimball model (FKM) are studied by incorporating the intrasite exchange correlation J (between itinerant d- and localized f-electrons) and intersite (superexchange) correlation J (between localized f-electrons) on a triangular lattice for two different fillings. Numerical diagonalization and Monte-Carlo techniques are used to determine the ground state magnetic properties. Transitions from antiferromagnetic to ferromagnetic and again to re-entrant antiferromagnetic phase is observed in a wide range of parameter space. The magnetic moments of d- and f-electrons are observed to depend strongly on the value off, J and also on the total number of d-electrons (N-d). (C) 2015 Elsevier Ltd. All rights reserved.

Traveling waves in trimer granular lattice I: Bifurcation structure of traveling waves in the unit-cell model

Present paper is the first one in the series devoted to the dynamics of traveling waves emerging in the uncompressed, tri-atomic granular crystals. This work is primarily concerned with the dynamics of one-dimensional periodic granular trimer (tri-atomic) chains in the state of acoustic vacuum. Each unit cell consists of three spherical particles of different masses subject to periodic boundary conditions. Hertzian interaction law governs the mutual interaction of these particles. Under the assumption of zero pre-compression, this interaction is modeled as purely nonlinear, which means the absence of linear force component. The dynamics of such chains is governed by the two system parameters that scale the mass ratios between the particles of the unit cell. Such a system supports two different classes of periodic solutions namely the traveling and standing waves. The primary objective of the present study is the numerical analysis of the bifurcation structure of these solutions with emphasis on the dynamics of traveling waves. In fact, understanding of the bifurcation structure of the traveling wave solutions emerging in the unit-cell granular trimer is rather important and can shed light on the more complex nonlinear wave phenomena emerging in semi-infinite trimer chains. (c) 2016 Elsevier B.V. All rights reserved.

Lattice type of fracture model for concrete

Concrete is usually described as a three-phase material, where matrix, aggregate and interface zones are distinguished. The beam lattice model has been applied widely by many investigators to simulate fracture processes in concrete. Due to the extremely large computational effort, however, the beam lattice model faces practical difficulties. In our investigation, a new lattice called generalized beam (GB) lattice is developed to reduce computational effort. Numerical experiments conducted on a panel subjected to uniaxial tension show that the GB lattice model can reproduce the load-displacement curves and crack patterns in agreement to what are observed in tests. Moreover, the effects of the particle overlay on the fracture process are discussed in detail. (C) 2007 Elsevier Ltd. All rights reserved.

Numerical investigation of crack growth in concrete subjected to compression by the generalized beam lattice model

The beam lattice-type models, such as the Euler-Bernoulli (or Timoshenko) beam lattice and the generalized beam (GB) lattice, have been proved very effective in simulating failure processes in concrete and rock due to its simplicity and easy implementation. However, these existing lattice models only take into account tensile failures, so it may be not applicable to simulation of failure behaviors under compressive states. The main aim in this paper is to incorporate Mohr-Coulomb failure criterion, which is widely used in many kinds of materials, into the GB lattice procedure. The improved GB lattice procedure has the capability of modeling both element failures and contact/separation of cracked elements. The numerical examples show its effectiveness in simulating compressive failures. Furthermore, the influences of lateral confinement, friction angle, stiffness of loading platen, inclusion of aggregates on failure processes are respectively analyzed in detail.

The study of banded spherulite patterns by coupled logistic map lattice model

Banded spherulite patterns are simulated in two dimensions by means of a coupled logistic map lattice model. Both target pattern and spiral pattern which have been proved to be existent experimentally in banded spherulite are obtained by choosing suitable parameters in the model. The simulation results also indicate that the band spacing is decreased with the increase of parameter mu in the logistic map and increased with the increase of the coupling parameter epsilon, which is quite similar to the results in some experiments. Moreover, the relationship between the parameters and the corresponding patterns is obtained, and the target patterns and spiral patterns are distinguished for a given group of initial values, which may guide the study of banded spherulite.

Simulation of Banded Spherulite Patterns by Coupled Logistic Map Lattice Model in Three Dimensions

Banded spherulite patterns are simulated in three dimensions by means of a Coupled Logistic map lattice model. The patterns obtained by numerical calculation are consistent with those in experiments. The simulation results also indicate that the hand spacing is decreased with the increase of parameter mu in the Logistic map and increased with the increase of the coupling parameter e for cube lattices, and increased with the increase of the thickness of the lattice for polymer film, which is quite similar to the results in some experiments. Spiral pattern in three dimensions is also shown in this paper, which helps us understand the form of banded spherulite in polymers.

A novel self-consistent-field lattice model for block copolymers

We develop a self-consistent-field lattice model for block copolymers and propose a novel and general method to solve the self-consistent-field equations. The approach involves describing the polymer chains in a lattice and employing a two-stage relaxation procedure to evolve a system as rapidly as possible to a free-energy minimum. In order to test the validity of this approach, we use the method to study the microphases of rod-coil diblock copolymers. In addition to the lamellar and cylindrical morphologies, micellar, perforated lamellar, gyroid, and zigzag structures have been identified without any prior assumption of the microphase symmetry. Furthermore, this approach can also give the possible orientation of the rods in different structures.

Application of the Sanchez-Lacombe lattice fluid theory to the system pvme/ps and model calculations

Cloud point curves reported in the literature for five representatives of the system poly(vinyl methyl ether)/polystyrene were evaluated theoretically by means of the Sanchez-Lacombe lattice fluid theory. The measured phase separation behavior can be described within experimental error using only one adjustable parameter (quantifying the interaction between the unlike mers). The Flory-Huggins interaction parameters calculated from this theoretical description depend in good approximation linearly on composition (volume fractions) and on the inverse temperature. An evaluation of these data yields a maximum heat effect which is almost one order of magnitude less (ca. -0.25 J/cm(3)) than obtained via Hess's cycle (dissolution of the components and of the blend) from calorimetric measurements. Model calculations on the basis of the present theory demonstrate that the critical points shift to a different extent upon a certain relative change in the molar mass of the blend components. The sensitivity of the calculated phase diagrams against changes in the scaling parameter decreases in the following order: interaction energies between unlike mers, differences in the scaling temperatures, pressures and densities.

Rotating-frame nuclear magnetic relaxation of spins diffusing on a disordered lattice: a Monte Carlo model

The rotating-frame nuclear magnetic relaxation rate of spins diffusing on a disordered lattice has been calculated by Monte Carlo methods. The disorder includes not only variation in the distances between neighbouring spin sites but also variation in the hopping rate associated with each site. The presence of the disorder, particularly the hopping rate disorder, causes changes in the time-dependent spin correlation functions which translate into asymmetry in the characteristic peak in the temperature dependence of the dipolar relaxation rate. The results may be used to deduce the average hopping rate from the relaxation but the effect is not sufficiently marked to enable the distribution of the hopping rates to be evaluated. The distribution, which is a measure of the degree of disorder, is the more interesting feature and it has been possible to show from the calculation that measurements of the relaxation rate as a function of the strength of the radiofrequency spin-locking magnetic field can lead to an evaluation of its width. Some experimental data on an amorphous metal - hydrogen alloy are reported which demonstrate the feasibility of this novel approach to rotating-frame relaxation in disordered materials.

Case study of the uniaxial anisotropic spin-1 bilinear-biquadratic Heisenberg model on a triangular lattice

We study the spin-1 model on a triangular lattice in the presence of a uniaxial anisotropy field using a cluster mean-field (CMF) approach. The interplay among antiferromagnetic exchange, lattice geometry, and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF method yields two supersolid phases compatible with those present in the spin-1/2 XXZ model onto which the spin-1 system maps. Between these two supersolid phases, the three-sublattice order is broken and the results of the CMF approach depend heavily on the geometry and size of the cluster. We discuss the possible presence of a spin liquid in this region.

Improving sampling, optimization and feature extraction in Boltzmann machines

L’apprentissage supervisé de réseaux hiérarchiques à grande échelle connaît présentement un succès fulgurant. Malgré cette effervescence, l’apprentissage non-supervisé représente toujours, selon plusieurs chercheurs, un élément clé de l’Intelligence Artificielle, où les agents doivent apprendre à partir d’un nombre potentiellement limité de données. Cette thèse s’inscrit dans cette pensée et aborde divers sujets de recherche liés au problème d’estimation de densité par l’entremise des machines de Boltzmann (BM), modèles graphiques probabilistes au coeur de l’apprentissage profond. Nos contributions touchent les domaines de l’échantillonnage, l’estimation de fonctions de partition, l’optimisation ainsi que l’apprentissage de représentations invariantes. Cette thèse débute par l’exposition d’un nouvel algorithme d'échantillonnage adaptatif, qui ajuste (de fa ̧con automatique) la température des chaînes de Markov sous simulation, afin de maintenir une vitesse de convergence élevée tout au long de l’apprentissage. Lorsqu’utilisé dans le contexte de l’apprentissage par maximum de vraisemblance stochastique (SML), notre algorithme engendre une robustesse accrue face à la sélection du taux d’apprentissage, ainsi qu’une meilleure vitesse de convergence. Nos résultats sont présent ́es dans le domaine des BMs, mais la méthode est générale et applicable à l’apprentissage de tout modèle probabiliste exploitant l’échantillonnage par chaînes de Markov. Tandis que le gradient du maximum de vraisemblance peut-être approximé par échantillonnage, l’évaluation de la log-vraisemblance nécessite un estimé de la fonction de partition. Contrairement aux approches traditionnelles qui considèrent un modèle donné comme une boîte noire, nous proposons plutôt d’exploiter la dynamique de l’apprentissage en estimant les changements successifs de log-partition encourus à chaque mise à jour des paramètres. Le problème d’estimation est reformulé comme un problème d’inférence similaire au filtre de Kalman, mais sur un graphe bi-dimensionnel, où les dimensions correspondent aux axes du temps et au paramètre de température. Sur le thème de l’optimisation, nous présentons également un algorithme permettant d’appliquer, de manière efficace, le gradient naturel à des machines de Boltzmann comportant des milliers d’unités. Jusqu’à présent, son adoption était limitée par son haut coût computationel ainsi que sa demande en mémoire. Notre algorithme, Metric-Free Natural Gradient (MFNG), permet d’éviter le calcul explicite de la matrice d’information de Fisher (et son inverse) en exploitant un solveur linéaire combiné à un produit matrice-vecteur efficace. L’algorithme est prometteur: en terme du nombre d’évaluations de fonctions, MFNG converge plus rapidement que SML. Son implémentation demeure malheureusement inefficace en temps de calcul. Ces travaux explorent également les mécanismes sous-jacents à l’apprentissage de représentations invariantes. À cette fin, nous utilisons la famille de machines de Boltzmann restreintes “spike & slab” (ssRBM), que nous modifions afin de pouvoir modéliser des distributions binaires et parcimonieuses. Les variables latentes binaires de la ssRBM peuvent être rendues invariantes à un sous-espace vectoriel, en associant à chacune d’elles, un vecteur de variables latentes continues (dénommées “slabs”). Ceci se traduit par une invariance accrue au niveau de la représentation et un meilleur taux de classification lorsque peu de données étiquetées sont disponibles. Nous terminons cette thèse sur un sujet ambitieux: l’apprentissage de représentations pouvant séparer les facteurs de variations présents dans le signal d’entrée. Nous proposons une solution à base de ssRBM bilinéaire (avec deux groupes de facteurs latents) et formulons le problème comme l’un de “pooling” dans des sous-espaces vectoriels complémentaires.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.