An introduction to numerical methods in low-dimensional quantum systems

This is an introductory course to the Lanczos Method and Density Matrix Renormalization Group Algorithms (DMRG), two among the leading numerical techniques applied in studies of low-dimensional quantum models. The idea of studying the models on clusters of a finite size in order to extract their physical properties is briefly discussed. The important role played by the model symmetries is also examined. Special emphasis is given to the DMRG.

Development and applications of three-dimensional gamma ray tomography system using ray casting volume rendering techniques

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Study of stress distribution with finite element method in a root with prefabricated threaded split shaft post - Part I

A finite element analysis was carried out to study the role of prefabricated threaded split shaft post (Flexi-Post) on dentinal stress in pulpless tooth. Three dimensional plane strain model of mesio-distal section of a human maxillary central incisor without restoration was analysed with the MSC/NASTRAN (MacNeal/ Schwendler) general purpose finite analysis program was executed on a microcomputer. The model as discretized into 48.954 axisymmetric finite elements defined by 10.355 nodes. Each element was assigned unique elastic properties to represent the materials modeled. Homogeneity, isotropy and linear elasticity were assume for all material. A simulation of static load of 100N was applied to the incisal edge of the post; vertical. Maximal principal stresses and von Mises equivalent stress were calculated. Using the element analysis model employed in this study, the following can be concluded concerning threaded split shaft post (Flexi-Post): Maximum principal stresses in dentin were located at cervical place and at the post apex. The apical threads of the post not redirecting stresses away from the root.

Two-dimensional induced gravity in reduced phase-space

We discuss the Dirac method analysis of two-dimensional induced gravity, coupled to bosonic matter fields, in reduced phase-space. After defining the extended Hamiltonian it is possible to fix the gauge completely. The Dirac brackets can all be obtained in closed form; nevertheless, the results are not particularly simple.

Multiloop superstring amplitudes from non-minimal pure spinor formalism

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of theta's.

Grain boundary electric characterization of Zn7Sb2O12 semiconducting ceramic: A negative temperature coefficient thermistor

The electrical properties of the grain boundary region of electroceramic sensor temperature based on inverse spinel Zn7Sb2O12 were investigated at high temperature. The zinc antimoniate was synthesized by a chemical route based on the modified Pechini method. The electric properties of Zn7Sb2O12 were investigated by impedance spectroscopy in the frequency range from 5 Hz to 13 MHz and from 250 up to 600 degreesC. The grain boundary conductivity follows the Arrhenius law, with two linear branches of different slopes. These branches exhibit activation energies with very similar values; the low-temperature (less than or equal to350 degreesC) and high-temperature (greater than or equal to400 degreesC) regions are equal to 1.15 and 1.16 eV, respectively. Dissimilar behavior is observed on the relaxation time (tau) curve as a function of temperature, where a single slope is identified. The negative temperature coefficient parameters and nature of the polarization phenomenon of the grain boundary are discussed. (C) 2003 American Institute of Physics.

SMALLEST UNIVERSE OF NEGATIVE CURVATURE

The smallest known three-dimensional closed manifold of curvature k = -1 was discovered a few years ago by Weeks. This kind of manifold is constructed from a hyperbolic polyhedron with faces pair-wise identified. Here it is used as the comoving spatial section of a Friedmann cosmological model, in the spirit of Ellis and Schreiber's idea of small universes. Its nontrivial global topology has the effect of producing multiple images of single cosmic sources, and this is the basis of an attempt to solve a famous controversy about the redshifts of quasars.

Negative temperature coefficient thermistor based on Bi3Zn2Sb3O14 ceramic: An oxide semiconductor at high temperature

Bi1.5ZnSb1.5O7 dielectric ceramic with pyrochlore structure was investigated by impedance spectroscopy from 400 to 750 degreesC. Pyrochlore was synthesized by the polymeric precursor method, a chemical synthesis route derived from Pechini's method. The grain or bulk resistance exhibits a sensor temperature characteristic, being a thermistor with a negative temperature coefficient (NTC). Only a single region was identified on the resistance curve investigated. The NTC thermistor characteristic parameter (beta) is equal to 7140 degreesC, in the temperature range investigated. The temperature coefficient of the resistance (alpha) was derived, being equal to -4.46x10(-2) degreesC(-1) at 400 degreesC. The conduction mechanism and relaxation are discussed. (C) 2003 American Institute of Physics.

Simple generalization of Wisdom's perturbative method

A simple generalization of Wisdom's perturbative method, as originally proposed by Wisdom (1985), is obtained. Any number of resonant cosines can be handled and the method can also accommodate more involved disturbing functions. Averaged trajectories are easily obtained by drawing level curves of the action. Here, the method is first tested for simple models of 3:1 and 2:1 resonant problems. Comparisons with numerical integration and surface-section curves show very good agreements.

The non-adiabatic hyperspherical approach to the two-dimensional D- ion in the presence of a magnetic field

We have used the adiabatic hyperspherical approach to determine the energies and wave functions of the ground state and first excited states of a two-dimensional D- ion in the presence of a magnetic field. Using a modified hyperspherical angular variable, potential energy curves are analytically obtained, allowing an accurate determination of the energy levels of this system. Upper and lower bounds for the ground-state energy have been determined by a non-adiabatic procedure, as the purpose is to improve the accuracy of method. The results are shown to be comparable to the best variational calculations reported in the literature.

The element-free Galerkin method applied to the study of fully developed magnetohydrodynamic duct flows

In this paper, the meshless method is introduced to magnetohydrodynamics. A numerical scheme based on the element-free Galerkin method is used to solve the laminar steady-state two-dimensional fully developed magnetohydrodynamic flow in a rectangular duct. Accurate and convergent solutions are achieved for low to moderately high Hartmann numbers.

A new implementation of population based incremental learning method for optimizations in electromagnetics

To enhance the global search ability of population based incremental learning (PBIL) methods, it is proposed that multiple probability vectors are to be included on available PBIL algorithms. The strategy for updating those probability vectors and the negative learning and mutation operators are thus re-defined correspondingly. Moreover, to strike the best tradeoff between exploration and exploitation searches, an adaptive updating strategy for the learning rate is designed. Numerical examples are reported to demonstrate the pros and cons of the newly implemented algorithm.

ANALYSIS OF CURVED EDGE PLATES BY THE BOUNDARY-ELEMENT METHOD

The aim of this work is to present a formulation of the boundary element method to analyse elastic and isotropic plates with curved boundaries. In this study the plate boundary is approximated, along each element, by a second degree polynomial relation or by a circular arch, in order to better represent the real boundary. The numerical integration is performed by the self-adaptive coordinate transformation proposed by Telles. The effective shear forces are approximated by concentrated reactions applied at the boundary element nodes, according to the alternative formulation introduced by Paiva. Some examples are presented to demonstrate the better accuracy obtained with the proposed elements.

Numerical study of low-cost alternative orbits around the Moon

In this paper, we have investigated a region of direct stable orbits around the Moon, whose stability is related to the H2 Family of periodic orbits and to the quasi-periodic orbits that oscillate around them. The stability criteria adopted was that the path did not escape from the Moon during an integration period of 1000 days (remaining with negative two-body Moon-probe orbital energy during this period). Considering the three-dimensional four-body Sun-Earth-Moon-probe problem, we investigated the evolution of the size of the stability region, taking into account the eccentricity of the Earth's orbit, the eccentricity and inclination of the Moon's orbit, and the solar radiation pressure on the probe. We also investigated the evolution of the region's size and its location by varying the inclination of the probe's initial osculating orbit relative to the Moon's orbital plane between 0 degrees and 180 degrees. The size of the stability region diminishes; nevertheless, it remains significant for 0 <= i <= 25 degrees and 35 degrees <= i <= 45 degrees. The orbits of this region could be useful for missions by space vehicles that must remain in orbit around the Moon for periods of up to 1000 days, requiring low maintenance costs. (c) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

Three-dimensional finite element analysis of MHD duct flow by the penalty function formulation

A numerical scheme based on the Finite Element Method (FEM) is presented to calculate the full solution of a three-dimensional steady magnetohydrodynamic (MHD) flow with moderately high Hartmann numbers and interaction parameters. An incompressible, viscous and electrically conducting liquid-metal is considered. Assuming a low magnetic Reynolds number, the solution method solves the coupled Navier-Stokes and Maxwell's equations through the use of a penalty function method. Results are presented for Hartmann numbers in the range 10(2)-10(3).