Linear analysis of building floor structures by a BEM formulation based on Reissner's theory

In this work, the plate bending formulation of the boundary element method (BEM) based on the Reissner's hypothesis is extended to the analysis of zoned plates in order to model a building floor structure. In the proposed formulation each sub-region defines a beam or a slab and depending on the way the sub-regions are represented, one can have two different types of analysis. In the simple bending problem all sub-regions are defined by their middle surface. on the other hand, for the coupled stretching-bending problem all sub-regions are referred to a chosen reference surface, therefore eccentricity effects are taken into account. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. The bending and stretching values defined on the interfaces are approximated along the beam width, reducing therefore the number of degrees of freedom. Then, in the proposed model the set of equations is written in terms of the problem values on the beam axis and on the external boundary without beams. Finally some numerical examples are presented to show the accuracy of the proposed model.

The BCS-Bose crossover theory

We contrast four distinct versions of the BCS-Bose statistical crossover theory according to the form assumed for the electron-number equation that accompanies the BCS gap equation. The four versions correspond to explicitly accounting for two-hole-(2h) as well as two-electron-(2e) Cooper pairs (CPs), or both in equal proportions, or only either kind. This follows from a recent generalization of the Bose-Einstein condensation (GBEC) statistical theory that includes not boson-boson interactions but rather 2e- and also (without loss of generality) 2h-CPs interacting with unpaired electrons and holes in a single-band model that is easily converted into a two-band model. The GBEC theory is essentially an extension of the Friedberg-Lee 1989 BEC theory of superconductors that excludes 2h-CPs. It can thus recover, when the numbers of 2h- and 2e-CPs in both BE-condensed and non-condensed states are separately equal, the BCS gap equation for all temperatures and couplings as well as the zero-temperature BCS (rigorous-upper-bound) condensation energy for all couplings. But ignoring either 2h- or 2e-CPs it can do neither. In particular, only half the BCS condensation energy is obtained in the two crossover versions ignoring either kind of CPs. We show how critical temperatures T-c from the original BCS-Bose crossover theory in 2D require unphysically large couplings for the Cooper/BCS model interaction to differ significantly from the T(c)s of ordinary BCS theory (where the number equation is substituted by the assumption that the chemical potential equals the Fermi energy). (c) 2007 Published by Elsevier B.V.

Methods to estimate the number of surface nucleation sites on glass particles

Based on the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory, we propose two new models to describe the crystallisation kinetics of glass particles and use them to determine the density of nucleation sites, N(s), on glass powders. We tested these models with sintered compacts of diopside glass particles using sinter-crystallisation treatments at 825 degrees C (T(g)similar to 727 degrees C), that covered from null to almost 100% crystallised volume time fraction. We measured and compared the evolution of the crystallised volume fractions by optical microscopy and x-ray diffraction. Then we fit our expressions to experimental data using Ns and R (the average particle radius) as adjustable parameters. For comparison, we also fit to our data existing expressions that describe the crystallised volume fraction in glass powders. We demonstrate that all the methods allow one to estimate N(s) with reasonable accuracy. For our ground and water washed diopside glass powder, N(s) is between 10(10)-10(11) sites.m(-2). The reasonable agreement between experimental and adjusted R confirms the consistency of all five models tested. However, one of our equations does not require taking into account the change of crystallisation mode from 3-dimensional to 1-dimensional, and this is advantageous.

A BEM formulation based on Reissner's theory to perform simple bending analysis of plates reinforced by rectangular beams

In this work, the plate bending formulation of the boundary element method (BEM), based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by rectangular beams. This composed structure is modelled by a zoned plate, being the beams represented by narrow sub-regions with larger thickness. The integral equations are derived by applying the weighted residual method to each sub-region, and summing them to get the equation for the whole plate. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to decrease the number of degrees of freedom, some approximations are considered for both displacements and tractions along the beam width. The accuracy of the proposed model is illustrated by simple examples whose exact solution are known as well as by more complex examples whose numerical results are compared with a well-known finite element code.

On the number of critical periods for planar polynomial systems

In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree l with at least 2[(l - 2)/2] critical periods as well as study concrete families of potential, reversible and Lienard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not. increases with the order of the perturbation. (C) 2007 Elsevier Ltd. All rights reserved.

Correlation functions in super liouville theory

We calculate three- and four-point functions in super Liouville theory coupled to a super Coulomb gas on world sheets with spherical topology. We first integrate over the zero mode and assume that a parameter takes an integer value. We find the amplitudes, give plausibility arguments in favor of the result, and formally continue the parameter to an arbitrary real number. Remarkably the result is completely parallel to the bosonic case.

New phenomenon of nonlinear Regge trajectory and quantum dual string theory

The relation between the spin and the mass of an infinite number of particles in a q-deformed dual string theory is studied. For the deformation parameter q a root of unity, in addition to the relation of such values of q with the rational conformal field theory, the Fock space of each oscillator mode in the Fubini-Veneziano operator formulation becomes truncated. Thus, based on general physical grounds, the resulting spin-(mass)2 relation is expected to be below the usual linear trajectory. For such specific values of q, we find that the linear Regge trajectory turns into a square-root trajectory as the mass increases.

Tachyon condensation in superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the D-brane-anti-D-brane pair or for the non-BPS D-brane of superstring theories, the negative energy density cancels the brane tensions. We study this conjecture using a Wess-Zumino-Witten-like open superstring field theory free of contact term divergences and recently shown to give 60% of the vacuum energy by condensation of the tachyon field alone. While the action is non-polynomial, the multiscalar tachyon potential to any fixed level involves only a finite number of interactions. We compute this potential to level three, obtaining 85% of the expected vacuum energy, a result consistent with convergence that can also be viewed as a successful test of the string field theory. The resulting effective tachyon potential is bounded below and has two degenerate global minima. We calculate the energy density of the kink solution interpolating between these minima finding good agreement with the tension of the D-brane of one lower dimension. © 2000 Elsevier Science B.V.

Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

The critical number of atoms for Bose-Einstein condensates with cylindrically symmetrical traps were calculated. The time evolution of the condensate was also studied at changing ground state. A conjecture on higher-order nonlinear effects was also discussed to determine its signal and strength. The results show that by exchanging frequencies, the geometry favors the condensation of larger number of particles.

Effect of anharmonicities in the critical number of trapped condensed atoms with an attractive two-body interaction

The quantitative effect in the maximum number of particles and other static observables was determined. A deviation in the harmonic trap potential that is effective only outside the central part of the potential, with the addition of a term that is proportional to a cubic or quartic power of the distance was considered. Results showed that this study could be easily transferred to other trap geometries to estimate anharmonic effects.

Noncoaxial multivortices in the complex sine-Gordon theory on the plane

We construct explicit multivortex solutions for the complex sine-Gordon equation (the Lund-Regge model) in two Euclidean dimensions. Unlike the previously found (coaxial) multivortices, the new solutions comprise n single vortices placed at arbitrary positions (but confined within a finite part of the plane.) All multivortices, including the single vortex, have an infinite number of parameters. We also show that, in contrast to the coaxial complex sine-Gordon multivortices, the axially-symmetric solutions of the Ginzburg-Landau model (the stationary Gross-Pitaevskii equation) do not belong to a broader family of noncoaxial multivortex configurations.

The Lamination of Infinitely Renormalizable Dissipative Gap Maps: Analyticity, Holonomies and Conjugacies

Motivated by return maps near saddles for three-dimensional flows and also by return maps in the torus associated to Cherry flows, we study gap maps with derivative positive and smaller than one outside the discontinuity point. We prove that the lamination of infinitely renormalizable maps (or else maps with irrational rotation numbers) has analytic leaves in a natural subset of a Banach space of analytic maps of this kind. With maps having Hölder continuous derivative and derivative bounded away from zero, we also prove Hölder continuity of holonomies of the lamination and also of conjugacies between maps having the same combinatorics. © 2011 Springer Basel AG.

Principal components and factor analytic models for birth to mature weights in Nellore cattle

A total of 61,528 weight records from 22,246 Nellore animals born between 1984 and 2002 were used to compare different multiple-trait analysis methods for birth to mature weights. The following models were used: standard multivarite model (MV), five reduced-rank models fitting the first 1, 2, 3, 4 and 5 genetic principal components, and five models using factor analysis with 1, 2, 3, 4 and 5 factors. Direct additive genetic random effects and residual effects were included in all models. In addition, maternal genetic and maternal permanent environmental effects were included as random effects for birth and weaning weight. The models included contemporary group as fixed effect and age of animal at recording (except for birth weight) and age of dam at calving as linear and quadratic effects (for birth weight and weaning weight). The maternal genetic, maternal permanent environmental and residual (co)variance matrices were assumed to be full rank. According to model selection criteria, the model fitting the three first principal components (PC3) provided the best fit, without the need for factor analysis models. Similar estimates of phenotypic, direct additive and maternal genetic, maternal permanent environmental and residual (co)variances were obtained with models MV and PC3. Direct heritability ranged from 0.21 (birth weight) to 0.45 (weight at 6 years of age). The genetic and phenotypic correlations obtained with model PC3 were slightly higher than those estimated with model MV. In general, the reduced-rank model substantially decreased the number of parameters in the analyses without reducing the goodness-of-fit. © 2013 Elsevier B.V.

Comparison of factor-analytic and reduced rank models for test-day milk yield in Gyr dairy cattle (Bos indicus)

We analyzed 46,161 monthly test-day records of milk production from 7453 first lactations of crossbred dairy Gyr (Bos indicus) x Holstein cows. The following seven models were compared: standard multivariate model (M10), three reduced rank models fitting the first 2, 3, or 4 genetic principal components, and three models considering a 2-, 3-, or 4-factor structure for the genetic covariance matrix. Full rank residual covariance matrices were considered for all models. The model fitting the first two principal components (PC2) was the best according to the model selection criteria. Similar phenotypic, genetic, and residual variances were obtained with models M10 and PC2. The heritability estimates ranged from 0.14 to 0.21 and from 0.13 to 0.21 for models M10 and PC2, respectively. The genetic correlations obtained with model PC2 were slightly higher than those estimated with model M10. PC2 markedly reduced the number of parameters estimated and the time spent to reach convergence. We concluded that two principal components are sufficient to model the structure of genetic covariances between test-day milk yields. © FUNPEC-RP.

As dificuldades relacionadas à aprendizagem do conceito de vetor à luz da teoria dos registros de representação semiótica

Esta dissertação foi desenvolvida no sentido de contribuir para o ensino e para aprendizagem da Geometria Analítica no ensino superior. Para realizar esta tarefa contamos com o referencial teórico de Raymond Duval - com a teoria dos Registros de Representação Semiótica - em aulas expositivas, atividades em classe e na exploração de um maior número de representações do objeto matemático Vetor. Nosso objetivo foi o de identificar e analisar as dificuldades na produção e no tratamento de representações dos vetores que caracterizam lacunas ao aprendizado do conceito desse objeto. Os sujeitos da pesquisa foram alunos de uma turma de Licenciatura em Matemática da Universidade do Estado do Pará – UEPA, Núcleo Regional do Baixo Tocantins – NURBAT localizado em Moju – PA. A pesquisa foi dividida em etapas, onde na primeira, a turma presenciou aulas teóricas com foco principal no estudo de vetores, explorando as várias representações do objeto bem como as operações básicas; a segunda etapa consistiu na resolução de lista de exercícios (atividades 1 e 2), contendo questões retiradas da indicação bibliográfica da disciplina e a avaliação individual. E por último a análise das resoluções feitas pelos sujeitos. Os instrumentos de coleta de dados envolveram questões de representação de vetores nos registros algébrico, figural e da língua natural, assim como, as conversões entre esses registros. Após analisar as resoluções, estas foram agrupadas por categorias as quais: confusão entre coordenadas de ponto e coordenadas de vetor, dificuldade na aplicação da regra do paralelogramo, dificuldade em identificar vetores iguais e conversão entre registros envolvendo o registro geométrico. Ao final das análises apontamos onde os alunos sentem mais dificuldades de acordo com as peculiaridades dos mesmos nas resoluções apresentadas e ainda, propomos a possibilidade de continuidade da pesquisa sobre o mesmo objeto.