Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

Liquid polymorphism, order-disorder transitions and anomalous behavior: A Monte Carlo study of the Bell-Lavis model for water

The Bell-Lavis model for liquid water is investigated through numerical simulations. The lattice-gas model on a triangular lattice presents orientational states and is known to present a highly bonded low density phase and a loosely bonded high density phase. We show that the model liquid-liquid transition is continuous, in contradiction with mean-field results on the Husimi cactus and from the cluster variational method. We define an order parameter which allows interpretation of the transition as an order-disorder transition of the bond network. Our results indicate that the order-disorder transition is in the Ising universality class. Previous proposal of an Ehrenfest second order transition is discarded. A detailed investigation of anomalous properties has also been undertaken. The line of density maxima in the HDL phase is stabilized by fluctuations, absent in the mean-field solution. (C) 2009 American Institute of Physics. [doi:10.1063/1.3253297]

Approximation to density functional theory for the calculation of band gaps of semiconductors

The local-density approximation (LDA) together with the half occupation (transitionstate) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half occupation is equivalent to introducing the hole self-energy (electrostatic and exchange correlation) into the Schrodinger equation. The argument then becomes simple: The eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the self- interaction correction equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self- energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

Nonuniversal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

This paper addresses the development of several alternative novel hybrid/multi-field variational formulations of the geometrically exact three-dimensional elastostatic beam boundary-value problem. In the framework of the complementary energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of stresses only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value problem. Both weak and linearized weak forms of the principles are presented. The main features of the principles are highlighted, giving special emphasis to their relationships from both theoretical and computational standpoints. (C) 2010 Elsevier Ltd. All rights reserved.

Discrete approximation to the global spectrum of the tangent operator for flow past a circular cylinder

This paper deals with the calculation of the discrete approximation to the full spectrum for the tangent operator for the stability problem of the symmetric flow past a circular cylinder. It is also concerned with the localization of the Hopf bifurcation in laminar flow past a cylinder, when the stationary solution loses stability and often becomes periodic in time. The main problem is to determine the critical Reynolds number for which a pair of eigenvalues crosses the imaginary axis. We thus present a divergence-free method, based on a decoupling of the vector of velocities in the saddle-point system from the vector of pressures, allowing the computation of eigenvalues, from which we can deduce the fundamental frequency of the time-periodic solution. The calculation showed that stability is lost through a symmetry-breaking Hopf bifurcation and that the critical Reynolds number is in agreement with the value presented in reported computations. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

On Seliger and Whitham`s variational principle for hydrodynamic systems from the point of view of `fictitious particles`

FAPESP, the Sao Paulo State Research Foundation[04/04611-5]

On the convergence of successive Galerkin approximation for nonlinear output feedback H(infinity) control

Although the formulation of the nonlinear theory of H(infinity) control has been well developed, solving the Hamilton-Jacobi-Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H(infinity) control via output feedback are presented. An example is presented illustrating the application of the algorithm.

Expectation Propagation with Factorizing Distributions: A Gaussian Approximation and Performance Results for Simple Models

We discuss the expectation propagation (EP) algorithm for approximate Bayesian inference using a factorizing posterior approximation. For neural network models, we use a central limit theorem argument to make EP tractable when the number of parameters is large. For two types of models, we show that EP can achieve optimal generalization performance when data are drawn from a simple distribution.

Numerical test of Born-Oppenheimer approximation in chaotic systems

We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators. we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic region in phase space. (C) 2009 Elsevier B.V. All rights reserved.

First-principles calculation of the AlAs/GaAs interface band structure using a self-energy-corrected local density approximation

We apply a self-energy-corrected local density approximation (LDA) to obtain corrected bulk band gaps and to study the band offsets of AlAs grown on GaAs (AlAs/GaAs). We also investigate the Al(x)Ga(1-x)As/GaAs alloy interface, commonly employed in band gap engineering. The calculations are fully ab initio, with no adjustable parameters or experimental input, and at a computational cost comparable to traditional LDA. Our results are in good agreement with experimental values and other theoretical studies. Copyright (C) EPLA, 2011

Finite temperature correction to the Thomas-Fermi approximation for a Bose-Einstein condensate: comparison between theory and experiment

We observe experimentally a deviation of the radius of a Bose-Einstein condensate from the standard Thomas-Fermi prediction, after free expansion, as a function of temperature. A modified Hartree-Fock model is used to explain the observations, mainly based on the influence of the thermal cloud on the condensate cloud.

Dependence of Response Functions and Orbital Functionals on Occupation Numbers

Explicitly orbital-dependent approximations to the exchange-correlation energy functional of density functional theory typically not only depend on the single-particle Kohn-Sham orbitals but also on their occupation numbers in the ground-state Slater determinant. The variational calculation of the corresponding exchange-correlation potentials with the optimized effective potential (OEP) method therefore also requires a variation of the occupation numbers with respect to a variation in the effective single-particle potential, which is usually not taken into account. Here it is shown under which circumstances this procedure is justified.

The n-site approximation for the triplet-creation model

The nonequilibrium phase transition of the one-dimensional triplet-creation model is investigated using the n-site approximation scheme. We find that the phase diagram in the space of parameters (gamma, D), where gamma is the particle decay probability and D is the diffusion probability, exhibits a tricritical point for n >= 4. However, the fitting of the tricritical coordinates (gamma(t), D(t)) using data for 4 <= n <= 13 predicts that gamma(t) becomes negative for n >= 26, indicating thus that the phase transition is always continuous in the limit n -> infinity. However, the large discrepancies between the critical parameters obtained in this limit and those obtained by Monte Carlo simulations, as well as a puzzling non-monotonic dependence of these parameters on the order of the approximation n, argue for the inadequacy of the n-site approximation to study the triplet-creation model for computationally feasible values of n.