Effectiveness-ntu computation with a mathematical model for cross-flow heat exchangers

Due to the wide range of design possibilities, simple manufactured, low maintenance and low cost, cross-flow heat exchangers are extensively used in the petroleum, petrochemical, air conditioning, food storage, and others industries. In this paper a mathematical model for cross-flow heat exchangers with complex flow arrangements for determining epsilon -NTU relations is presented. The model is based on the tube element approach, according to which the heat exchanger outlet temperatures are obtained by discretizing the coil along the tube fluid path. In each cross section of the element, tube-side fluid temperature is assumed to be constant because the heat capacity rate ratio C*=Cmin/Cmax tends toward zero in the element. Thus temperature is controlled by effectiveness of a local element corresponding to an evaporator or a condenser-type element. The model is validated through comparison with theoretical algebraic relations for single-pass cross-flow arrangements with one or more rows. Very small relative errors are obtained showing the accuracy of the present model. epsilon -NTU curves for several complex circuit arrangements are presented. The model developed represents a useful research tool for theoretical and experimental studies on heat exchangers performance.

Universal zero-bias conductance through a quantum wire side-coupled to a quantum dot

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Universal zero-bias conductance for the single-electron transistor

The thermal dependence of the zero-bias conductance for the single electron transistor is the target of two independent renormalization-group approaches, both based on the spin-degenerate Anderson impurity model. The first approach, an analytical derivation, maps the Kondo-regime conductance onto the universal conductance function for the particle-hole symmetric model. Linear, the mapping is parametrized by the Kondo temperature and the charge in the Kondo cloud. The second approach, a numerical renormalization-group computation of the conductance as a function the temperature and applied gate voltages offers a comprehensive view of zero-bias charge transport through the device. The first approach is exact in the Kondo regime; the second, essentially exact throughout the parametric space of the model. For illustrative purposes, conductance curves resulting from the two approaches are compared.

Fixed points on torus fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S-1 for spaces which axe fibrations over S-1 and the fiber is the torus T. For the case where the fiber is a surface with nonpositive Euler characteristic, we establish general algebraic conditions, in terms of the fundamental group and the induced homomorphism, for the existence of a deformation of a map over S-1 to a fixed point, free map. For the case where the fiber is a torus, we classify all maps over S-1 which can be deformed fiberwise to a fixed point free map.

Some results on vector bundle monomorphisms

In this paper we use the singularity method of Koschorke [2] to study the question of how many different nonstable homotopy classes of monomorphisms of vector bundles lie in a stable class and the percentage of stable monomorphisms which are not homotopic to stabilized nonstable monomorphisms. Particular attention is paid to tangent vector fields. This work complements some results of Koschorke [3; 4], Libardi-Rossini [7] and Libardi-do Nascimento-Rossini [6].

Medida da permeabilidade magnética em fio delgado ferromagnético

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Um estudo sobre formação de conceitos algébricos

Neste artigo relatamos uma investigação sobre a formação dos conceitos algébricos iniciais realizada com estudantes de uma classe de 7ª série de uma escola estadual de ensino fundamental e médio. Como suporte teórico para esta investigação, foi empregada a teoria de formação de conceitos elaborada por Lev Semenovich Vygotsky e descrita no seu livro Pensamento e Linguagem.

Potenciais delta revisitados via transformada de Fourier

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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)

Competition between local potentials and attractive particle-particle interactions in superlattices

Naturally occuring or man-made systems displaying periodic spatial modulations of their properties on a nanoscale constitute superlattices. Such modulated structures are important both as prototypes of simple nanotechnological devices and as particular examples of emerging spatial inhomogeneity in interacting many-electron systems. Here we investigate the effect different types of modulation of the system parameters have on the ground-state energy and the charge-density distribution of the system. The superlattices are described by the inhomogeneous attractive Hubbard model, and the calculations are performed by density-functional and density-matrix renormalization group techniques. We find that modulations in local electric potentials are much more effective in shaping the system's properties than modulations in the attractive on-site interaction. This is the same conclusion we previously [M.F. Silva, N.A. Lima, A.L. Malvezzi, K. Capelle, Phys. Rev. B 71 (2005) 125130.] obtained for repulsive interactions, suggesting that it is not an artifact of a specific state, but a general property of modulated structures. (c) 2007 Elsevier Ltd. All rights reserved.

The symmetry group of Z(q)(n) in the Lee space and the Z(qn)-linear codes

The Z(4)-linearity is a construction technique of good binary codes. Motivated by this property, we address the problem of extending the Z(4)-linearity to Z(q)n-linearity. In this direction, we consider the n-dimensional Lee space of order q, that is, (Z(q)(n), d(L)), as one of the most interesting spaces for coding applications. We establish the symmetry group of Z(q)(n) for any n and q by determining its isometries. We also show that there is no cyclic subgroup of order q(n) in Gamma(Z(q)(n)) acting transitively in Z(q)(n). Therefore, there exists no Z(q)n-linear code with respect to the cyclic subgroup.

A RIEMANN INTEGRAL APPROACH TO FEYNMANS PATH-INTEGRAL

It is a well known result that the Feynman's path integral (FPI) approach to quantum mechanics is equivalent to Schrodinger's equation when we use as integration measure the Wiener-Lebesgue measure. This results in little practical applicability due to the great algebraic complexibity involved, and the fact is that almost all applications of (FPI) - ''practical calculations'' - are done using a Riemann measure. In this paper we present an expansion to all orders in time of FPI in a quest for a representation of the latter solely in terms of differentiable trajetories and Riemann measure. We show that this expansion agrees with a similar expansion obtained from Schrodinger's equation only up to first order in a Riemann integral context, although by chance both expansions referred to above agree for the free. particle and harmonic oscillator cases. Our results permit, from the mathematical point of view, to estimate the many errors done in ''practical'' calculations of the FPI appearing in the literature and, from the physical point of view, our results supports the stochastic approach to the problem.

Non-Abelian Sugawara construction and the q-deformed N=2 superconformal algebra

The construction of a q-deformed N = 2 superconformal algebra is proposed in terms of level-1 currents of the U-q(<(su)over cap>(2)) quantum affine Lie algebra and a single real Fermi field. In particular, it suggests the expression for the q-deformed energy-momentum tensor in the Sugawara form. Its constituents generate two isomorphic quadratic algebraic structures. The generalization to U-q(<(su)over cap>(N + 1)) is also proposed.

THE REDUCTIVE PERTURBATION METHOD AND THE KORTEWEG-DE VRIES HIERARCHY

By using the reductive perturbation method of Taniuti with the introduction of an infinite sequence of slow time variables tau(1), tau(3), tau(5), ..., we study the propagation of long surface-waves in a shallow inviscid fluid. The Korteweg-de Vries (KdV) equation appears as the lowest order amplitude equation in slow variables. In this context, we show that, if the lowest order wave amplitude zeta(0) satisfies the KdV equation in the time tau(3), it must satisfy the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1), With n = 2, 3, 4,.... AS a consequence of this fact, we show with an explicit example that the secularities of the evolution equations for the higher-order terms (zeta(1), zeta(2),...) of the amplitude can be eliminated when zeta(0) is a solitonic solution to the KdV equation. By reversing this argument, we can say that the requirement of a secular-free perturbation theory implies that the amplitude zeta(0) satisfies the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1) This essentially means that the equations of the KdV hierarchy do play a role in perturbation theory. Thereafter, by considering a solitary-wave solution, we show, again with an explicit, example that the elimination of secularities through the use of the higher order KdV hierarchy equations corresponds, in the laboratory coordinates, to a renormalization of the solitary-wave velocity. Then, we conclude that this procedure of eliminating secularities is closely related to the renormalization technique developed by Kodama and Taniuti.