Approximations for the generalized temperature integral: a method based on quadrature rules

The generalized temperature integral I(m, x) appears in non-isothermal kinetic analysis when the frequency factor depends on the temperature. A procedure based on Gaussian quadrature to obtain analytical approximations for the integral I(m, x) was proposed. The results showed good agreement between the obtained approximation values and those obtained by numerical integration. Unless other approximations found in literature, the methodology presented in this paper can be easily generalized in order to obtain approximations with the maximum of accurate.

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.

Numerical chromosome polymorphism in Mikania cordifolia Willd. (Asteraceae)

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

Application of a meshless method in electromagnetics

An improved meshless method is presented with an emphasis on the detailed description of this new computational technique and its numerical implementations by investigating the usefulness of a commonly neglected parameter in this paper. Two approaches to enforce essential boundary conditions are also thoroughly investigated. Numerical tests on a mathematical function is carried out as a means of validating the proposed method. It will be seen that the proposed method is more robust than the conventional ones. Applications in solving electromagnetic problems are also presented.

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.

An application of the Element Free Galerkin Method to the analysis of quantum well structures

In order to obtain the quantum-mechanical properties of layered semicondutor structures (quantum well and superlattice structures, for instance), solutions of the Schrodinger equation should be obtained for arbitrary potential profiles. In this paper, it is shown that such problems may be also studied by the Element Free Galerkin Method.

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 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.

NUMERICAL DETERMINATION OF THE ORDER OF PHASE-TRANSITIONS IN ISING SYSTEMS WITH MULTISPIN INTERACTIONS

The method of the fourth-order cumulant of Challa, Landau, and Binder is used together with the Monte Carlo histogram technique of Ferrenberg and Swendsen to study the order of the phase transitions of two-dimensional Ising systems with multispin interactions in the horizontal direction and two-body interactions in the vertical direction.

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.

ITERATIVE NUMERICAL-SOLUTION OF SCATTERING PROBLEMS

An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10(10) after some 8-10 iterations.

Integration Methods Used in Numerical Simulations of Electromagnetic Transients

This paper made an analysis of some numerical integration methods that can be used in electromagnetic transient simulations. Among the existing methods, we analyzed the trapezoidal integration method (or Heun formula), Simpson's Rule and Runge-Kutta. These methods were used in simulations of electromagnetic transients in power systems, resulting from switching operations and maneuvers that occur in transmission lines. Analyzed the characteristics such as accuracy, computation time and robustness of the methods of integration.

Non-linear analysis of reinforced concrete plates by the boundary element method and continuum damage mechanics

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

Chawla-Numerov method revisited

The well-known two-step fourth-order Numerov method was shown to have better interval of periodicity when made explicit, see Chawla (1984). It is readily verifiable that the improved method still has phase-lag of order 4. We suggest a slight modification from which linear problems could benefit. Phase-lag of any order can be achieved, but only order 6 is derived. © 1991.