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.

PHENOMENOLOGICAL APPLICATION OF THE PROJECTION-OPERATOR METHOD AND ITS CONNECTION WITH CRITICAL-DYNAMICS

We consider the dynamics of a system of interacting spins described by the Ginzburg-Landau Hamiltonian. The method used is Zwanzig's version of the projection-operator method, in contrast to previous derivations in which we used Mori's version of this method. It is proved that both methods produce the same answer for the Green's function. We also make contact between the projection-operator method and critical dynamics.

SUPERSYMMETRY, VARIATIONAL METHOD AND HULTHEN POTENTIAL

The formalism of supersymmetric quantum mechanics provides us with the eigenfunctions to be used in the variational method to obtain the eigenvalues for the Hulthen potential.

Synthesis by the polymeric precursor method and characterization of undoped and Sn, Cr and V-doped ZrTiO4

In this work, zirconium titanate doped with 0. 1, 0.2, and 0.4 mole% of tin, chromium and vanadium was synthesized by the polymeric precursors method and characterized by thermal analysis (TG/DTA), X-ray diffraction (XRD), nitrogen adsorption and scanning electronic microscopy (SEM). The powder presented two mass losses attributed to the exit of water and to the pyrolysis of the organic material. The surface area reduction observed from 500 degrees C indicates the beginning of the sintering process. All the dopants led to changes in the lattice parameters and to the decrease of both crystallite size and particle size. (c) 2005 Elsevier B.V. All rights reserved.

Supersymmetry, variational method and the Lennard-Jones (12,6) potential

The formalism of supersymmetric quantum mechanics is used to determine trial functions in order to obtain eigenvalues for the Lennard-Jones (12, 6) potential from variational method. The superpotential obtained provides an effective potential which can be directly comparable to the original one.

Zirconia foams prepared by integration of the sol-gel method and dual soft template techniques

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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)

Fungus incidence on peanut grains as affected by drying method and Ca nutrition

An experiment was conducted to study the effects of liming and drying method on Ca nutrition, fungus infection and aflatoxin production potential on peanut (Arachis hypogea) grains. Peanut cv. Botutatu was grown in the absence or presence of liming to raise the base saturation of the soil from 20 to 56%. Calcium contents of the soil were increased from 5.5 to 14.6 mmol((c))kg-1 and pH from 4.2 to 4.9. After harvest, plants and pods were dried in (1) shade, (2) field down to 100 g water kg-1 (3) field down to 250 g water kg-1 and transferred to a forced-air oven at 30°C, (4) field down to 360 g water kg-1 and transferred to a forced-air oven at 30°C. Calcium contents were analyzed in the grains, pericarps and seed coats. The incidence of Aspergillus spp., Penicillium spp., Rhizopus spp. and potential aflatoxin production in vitro were evaluated, as well as the seed coat thickness. The seed coat was thicker when peanut was grown in the presence of lime, leading to a decrease in seed infection by Aspergillus spp. and Penicillium spp. When plants were dried in shade, the growth of aflatoxinogenic fungi was independent of liming. However, in plants dried in the field or field + oven, the development of these fungi was decreased and even suppressed when the Ca content of the seed coat was increased from 2.2 to 5.5 g kg-1.

Morse potential energy spectra through the variational method and supersymmetry

The Variational Method is applied within the context of Supersymmetric Quantum Mechanics to provide information about the energy and eigenfunction of the lowest levels of a Hamiltonian. The approach is illustrated by the case of the Morse potential applied to several diatomic molecules and the results are compared with stabilished results. (C) 2000 Elsevier Science B.V.

Investigations into the use of the finite element method and artificial neural networks in the non-destructive analysis of metallic tubes

This work presents an investigation into the use of the finite element method and artificial neural networks in the identification of defects in industrial plants metallic tubes, due to the aggressive actions of the fluids contained by them, and/or atmospheric agents. The methodology used in this study consists of simulating a very large number of defects in a metallic tube, using the finite element method. Both variations in width and height of the defects are considered. Then, the obtained results are used to generate a set of vectors for the training of a perceptron multilayer artificial neural network. Finally, the obtained neural network is used to classify a group of new defects, simulated by the finite element method, but that do not belong to the original dataset. The reached results demonstrate the efficiency of the proposed approach, and encourage future works on this subject.

Influence of microwave polymerization method and thickness on porosity of acrylic resin

Purpose: This study evaluated the influence of polymerization cycle and thickness of maxillary complete denture bases on the porosity of acrylic resin. Materials and Methods: Two heat-activated denture base resins - one conventional (Clássico) and one designed for microwave polymerization (Onda-Cryl) - were used. Four groups were established, according to polymerization cycles: A (Onda-Cryl, short microwave cycle), B (Onda-Cryl, long microwave cycle), C (Onda-Cryl, manufacturing microwave cycle), and T (Clássico, water bath). Porosity was evaluated for different thicknesses (2.0, 3.5, and 5.0 mm; thicknesses I, II, and III, respectively) by measurement of the specimen volume before and after its immersion in water. The percent porosity data were submitted to Kruskal-Wallis for comparison among the groups. Results: The Kruskal-Wallis test detected that the combinations of the different cycles and thicknesses showed significant differences, and the mean ranks of percent porosity showed differences only in the thinnest (2.0 mm) microwave-polymerized specimens (A = 53.55, B = 40.80, and C = 90.70). Thickness did not affect the results for cycle T (I = 96.15, II = 70.20, and III = 82.70), because porosity values were similar in the three thicknesses. Conclusions: Microwave polymerization cycles and the specimen thickness of acrylic resin influenced porosity. Porosity differences were not observed in the polymerized resin bases in the water bath cycle for any thickness. © 2007 by The American College of Prosthodontists.

Effect of light-curing method and indirect veneering materials on the Knoop hardness of a resin cement

This study evaluated the Knoop hardness of a dual-cured resin cement (Rely-X ARC) activated solely by chemical reaction (control group) or by chemical / physical mode, light-cured through a 1.5 mm thick ceramic (HeraCeram) or composite (Artglass) disc. Light curing was carried out using conventional halogen light (XL2500) for 40 s (QTH); light emitting diodes (Ultrablue Is) for 40 s (LED); and Xenon plasma arc (Apollo 95E) for 3 s (PAC). Bovine incisors had their buccal face flattened and hybridized. On this surface a rubber mold (5 mm in diameter and 1 mm in height) was bulk filled with the resin cement. A polyester strip was seated for direct light curing or through the discs of veneering materials. After dry storage in the dark (24 h 37°C), the samples (n = 5) were sectioned for hardness (KHN) measurements, taken in a microhardness tester (50 gF load 15 s). The data were statistically analyzed by ANOVA and Tukey's test (α = 0.05). The cement presented higher Knoop hardness values with Artglass for QTH and LED, compared to HeraCeram. The control group and the PAC/Artglass group showed lower hardness values compared to the groups light-cured with QTH and LED. PAC/HeraCeram resulted in the worst combination for cement hardness values. © 2009 Sociedade Brasileira de Pesquisa Odontológica.

Economic growth in Latin America in the late 20th century: evidence and interpretation

Includes bibliography

Simulation of dynamic pinion course using Runge-Kutta's method and impact modeling

Once defined the relationship between the Starter Motor components and their functions, it is possible to develop a mathematical model capable to predict the Starter behavior during operation. One important aspect is the engagement system behavior. The development of a mathematical tool capable of predicting it is a valuable step in order to reduce the design time, cost and engineering efforts. A mathematical model, represented by differential equations, can be developed using physics laws, evaluating force balance and energy flow through the systems degrees of freedom. Another important physical aspect to be considered in this modeling is the impact conditions (particularly on the pinion and ring-gear contact). This work is a report of those equations application on available mathematical software and the resolution of those equations by Runge-Kutta's numerical integration method, in order to build an accessible engineering tool. Copyright © 2011 SAE International.