935 resultados para Non linear systems of ordinary differential equations


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The understanding of the kinetics of devitrification of a glass is important for anticipating its stability in a particular purpose, such as fiber-drawing processes. The crystallization kinetics of (BaF2)16(ZnF2)20(SrF 2)20(NaF)2 (GaF3)5(InF3)36(GdF 3)1 glass prepared by quenching were studied by differential scanning calorimetry (DSC). Avrami's exponent (n) obtained by a non-isothermal method was 4.3 for a solid and 2.4 for a powdered sample. According to the classical interpretation of n, these magnitudes correspond to an interface-controlled crystal growth and a diffusion-controlled crystal growth, respectively. The activation energies for crystallization (E) was 62 ± 1 kJ/mol for solid glass and 245 ± 2 kJ/mol for powdered glass. These results are discussed in terms of glass particle size. © 2000 Elsevier Science B.V. All rights reserved.

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The kinetics of crystallization in an indium fluoride-based glass was studied by a non-isothermal method using differential scanning calorimetry. The experiments led to an Avrami's exponent of 4.6 for solid glass and 2.2 for a powdered sample. The apparent activation energy for crystallization was found to be 130 kJ/mol for solid glass and 354 kJ/mol for the powder. These results express the profound effect of glass particle size on those kinetic parameters, as different crystallization mechanisms take place during sample heating.

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The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We concentrate on the case when A(x) has only real zeros aj and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients rj in the partial fraction decomposition B(x)/A(x) = ∑j p=0 rj/(x - aj), we allow the presence of both positive and negative coefficients rj. The corresponding electrostatic interpretation of the zeros of the solution y(x) as points of equilibrium in an electrostatic field generated by charges rj at aj is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges. © 2000 American Mathematical Society.

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We apply a five-dimensional formulation of Galilean covariance to construct non-relativistic Bhabha first-order wave equations which, depending on the representation, correspond either to the well known Dirac equation (for particles with spin 1/2) or the Duffin-Kemmer-Petiau equation (for spinless and spin 1 particles). Here the irreducible representations belong to the Lie algebra of the 'de Sitter group' in 4 + 1 dimensions, SO(5, 1). Using this approach, the non-relativistic limits of the corresponding equations are obtained directly, without taking any low-velocity approximation. As a simple illustration, we discuss the harmonic oscillator.

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This work reports a conception phase of a piston engine global model. The model objective is forecast the motor performance (power, torque and specific consumption as a function of rotation and environmental conditions). Global model or Zero-dimensional is based on flux balance through each engine component. The resulting differential equations represents a compressive unsteady flow, in which, all dimensional variables are areas or volumes. A review is presented first. The ordinary differential equation system is presented and a Runge-Kutta method is proposed to solve it numerically. The model includes the momentum conservation equation to link the gas dynamics with the engine moving parts rigid body mechanics. As an oriented to objects model the documentation follows the UML standard. A discussion about the class diagrams is presented, relating the classes with physical model related. The OOP approach allows evolution from simple models to most complex ones without total code rewrite. Copyright © 2001 Society of Automotive Engineers, Inc.

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Here we present two-phase flow nonlinear parameter estimation for HFC's flow through capillary tube-suction line heat exchangers, commonly used as expansion devices in small refrigeration systems. The simplifying assumptions adopted are: steady state, pure refrigerant, one-dimensional flow, negligible axial heat conduction in the fluid, capillary tube and suction line walls. Additionally, it is considered that the refrigerant is free from oil and both phases are assumed to be at the same pressure, that is, surface tension effects are neglected. Metastable flow effects are also disregarded, and the vapor is assumed to be saturated at the local pressure. The so-called homogeneous model, involving three, first order, ordinary differential equations is applied to analyze the two-phase flow region. Comparison is done with experimental measurements of the mass flow rate and temperature distribution along capillary tubes working with refrigerant HFC-134a in different operating conditions.

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A study was conducted on the dynamics of 2D and 3D Bose-Einstein condensates in the case when the scattering length in the Gross-Pitaevskii (GP) equation which contains constant (dc) and time-variable (ac) parts. Using the variational approximation (VA), simulating the GP equation directly, and applying the averaging procedure to the GP equation without the use of the VA, it was demonstrated that the ac component of the nonlinearity makes it possible to maintain the condensate in a stable self-confined state without external traps.

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This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.

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The study on several components of intervertebral joints is essential to understand the spine's degenerative mechanisms and to assess the best method for their treatment. For such study it is necessary to know the mechanical properties of the isolated intervertebral disc (ID) mechanical properties and, it is necessary to evaluate its stresses and strains. In order to assess the ID displacements, a fine, U-shaped blade was developed, over which two extensometers connected in a Wheatstone bridge were placed. The device was then tested on porcine spine ID, where compression loads were applied and the extremities displacements of the blade coupled to the intervertebral disc were measured. Stress/strain diagram, both on the compression and on the decompression phases, evidencing the non-linear nature of such relationship. With the experiment, it was possible to obtain approximate values of the longitudinal elasticity module (E) of the disc material and of the Poisson coefficient (n ). After several tests, E results are compatible with those obtained by others studies, with very simple and low-cost device. This experiments can be used for obtained others mechanical properties of isolated ID with precision and accuracy.

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This work considers the vibrating system that consists of a snap-through truss absorber coupled to an oscillator under excitation of an electric motor with an eccentricity and limited power, characterizing a non-ideal oscillator. It is aimed to use the non-linearity and quasi-zero stiffness of absorber (snap-through truss absorber) to obtain a significantly attenuation the jump phenomenon. There is also an interest to exhibit the reduction of Sommerfeld effect, to confirm the saturation phenomenon occurrence and show the power transfer in a non-linear structure, evidencing the pumping energy. As shown by simulations in this work, this absorber allows the energy pumping before and during the jump phenomenon, decreasing the higher amplitudes of considered system. Additionally, the occurrence of saturation phenomenon due use of snap-through truss absorber is verified. The analysis of parameter uncertainties was introduced. Sensitivity of system with parametric errors demonstrated a trustable system. © IMechE 2012.

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Calcium copper titanate, CaCu3Ti4O12, CCTO, thin films with polycrystalline nature have been deposited by RF sputtering on Pt/Ti/SiO2/Si (100) substrates at a room temperature followed by annealing at 600 °C for 2 h in a conventional furnace. The CCTO thin film present a cubic structure with lattice parameter a = 7.379 ±0.001 Å free of secondary phases. The observed electrical features of CCTO thin films are highly dependent on the [CaO12], [CaO 4], [CuO11], [CuO11Vx 0] and [TiO5.VO] clusters. The CCTO film capacitor showed a dielectric loss of 0.40 and a dielectric permittivity of 70 at 1 kHz. The J-V behavior is completely symmetrical, regardless of whether the conduction is limited by interfacial barriers or by bulk-like mechanisms. © 2013 Elsevier B.V. All rights reserved.

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Several Lamb wave modes can be coupled to a particular structure, depending on its geometry and transducer used to generate the guided waves. Each Lamb mode interacts in a particular form with different types of defects, like notches, delamination, surface defects, resulting in different information which can be used to improve damage detection and characterization. An image compounding technique that uses the information obtained from different propagation modes of Lamb waves for non-destructive testing of plate-like structures is proposed. A linear array consisting of 16 piezoelectric elements is attached to a 1 mm thickness aluminum plate, coupling the fundamental A0 and S0 modes at the frequencies of 100 kHz and 360 kHz, respectively. For each mode two images are obtained from amplitude and phase information: one image using the Total Focusing Method (TFM) and one phase image obtained from the Sign Coherence Factor (SCF). Each TFM image is multiplied by the SCF image of the respective mode to improve contrast and reduce side and grating lobes effects. The high dispersive characteristic of the A0 mode is compensated for adequate defect detection. The information in the SCF images is used to select one of the TFM mode images, at each pixel, to obtain the compounded image. As a result, dead zone is reduced, resolution and contrast are improved, enhancing damage detection when compared to the use of only one mode. © 2013 Elsevier Ltd.

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The aim of this study was to evaluate the transdentinal cytotoxicity of experimental adhesive systems (EASs) with different hydrophilicity and dentin saturation solutions on odontoblast-like cells. One hundred 0.4-mm-thick dentin discs were mounted in in vitro pulp chambers and assigned to 10 groups. MDPC-23 cells were seeded onto the pulpal side of the discs, incubated for 48 h. The EASs with increasing hydrophilicity (R1, R2, R3 and R4) were applied to the occlusal side after etching and saturation of etched dentin with water or ethanol. R0 (no adhesive) served as controls. R1 is a non-solvated hydrophobic blend, R2 is similar to a simplified etch-and-rinse adhesive system and R3 and R4 are similar to self-etching adhesives. After 24 h, cell metabolism was evaluated by MTT assay (n = 8 discs) and cell morphology was examined by SEM (n = 2 discs). Type of cell death was identified by flow cytometry and the degree of monomer conversion (%DC) was determined by infrared spectroscopy (FTIR) after 10 s or 20 s of photoactivation. Data were analyzed by the Kruskal-Wallis and Mann-Whitney tests (α = 0.05). Dentin saturation with ethanol resulted in higher necrotic cell death ratios for R2, R3 and R4 compared with water saturation, although R2 and R3 induced higher SDH production. Photoactivation for 20 s significantly improved the %DC of all EASs compared with 10 s. A significant positive correlation was observed between the degree of hydrophilicity and %DC. In conclusion, except for R1, dentin saturation with ethanol increased the cytotoxicity of EASs, as expressed by the induction of necrotic cell death. © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Pós-graduação em Matemática Universitária - IGCE