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On the dominance of roots of characteristic equations for neutral functional differential equations

FRASSON, Miguel V. S.
Fonte: ELSEVIER SCIENCE INC Publicador: ELSEVIER SCIENCE INC
Tipo: Artigo de Revista Científica
Português
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We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.; FAPESP[2006/50943-5]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Zeros de polinômios característicos e estabilidade de métodos numéricos; Zeros of characteristic polynomials and stability of numerical methods

Botta, Vanessa Avansini
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 07/04/2008 Português
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A Teoria das equações diferenciais faz parte de uma área da Matemática muito rica em aplicações. Os métodos numéricos para a solução de equações diferenciais ordinárias são, da mesma forma que as próprias equações, fontes importantes de problemas a serem pesquisados. Como destaque tem-se os métodos multiderivadas de passo múltiplo, que são importantes na solução de problemas stiff. Os métodos numéricos mais conhecidos para a solução desses problemas são os BDF, que compõem, para L = 1, a família dos métodos (K, L) de Brown. Algumas questões relacionadas à estabilidade dos métodos (K, L) ainda não foram solucionadas como, por exemplo, uma conjectura de Jeltsch. Para analisá-la, é necessário estudar o comportamento dos zeros dos polinômios característicos associados aos métodos (K, L). Neste trabalho é apresentado um estudo sobre zeros de polinômios com o objetivo de demonstrar a validade da conjectura de Jeltsch para K '< OU =' 'K IND; L' . As regiões de estabilidade para alguns valores de K e L fixos são apresentadas e também é utilizada a teoria das order stars para mostrar algumas propriedades dos métodos (K, L). Portanto, este trabalho apresenta um estudo sobre os métodos (K, L) de Brown e usa uma ferramenta pouco utilizada na literatura...

Solução numérica de equações diferenciais parciais implícitas de primeira ordem; Numerial solution of partial equations implicit first order

Escobedo, Sergio Moises Aquise
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 05/12/2014 Português
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As equações diferencias parciais tem origem na modelagem do problemas nas ciências e engenharia, tais como a equação do calor, equação da onda, equação de Poisson, entre outras. Para muitas destas equações não é tão simples obter uma técnica analítica para achar sua solução e nestes casos é necessário uso de soluções aproximadas obtidas pelo computador. Existem técnicas tradicionais para solução numérica de uma grande classe de equações diferenciais, mas quando esta equação está na forma implícita, muitas destas técnicas já não podem ser aplicadas. Frequentemente as equações diferenciais parciais de segunda ordem tem maior estudo que as equações de primeira ordem sendo uma das razões que os modelos envolvem derivadas de segunda ordem. No caso das equações diferenciais parciais de primeira ordem implícitas a não linearidade em alguns casos não permite determinar uma solução de forma simples. O trabalho desenvolvido faz uma revisão do método das características para estabelecer as condições necessárias e suficientes, que permitam encontrar uma solução, ao mesmo tempo evidencia a complexidade de determinar uma solução clássica. Dentro das aplicações existentes relacionadas com as Equações Diferenciais Parciais Implícitas de Primeira Ordem...

A simplified method for determining the high frequency induction motor equivalent electrical circuit parameters to be used in EMI effect

Riehl, Rudolf Ribeiro; Ruppert Filho, Ernesto
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 1244-1248
Português
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The aim of this paper is to present a simple method for determining the high frequency parameters of a three-phase induction motor to be used in studies involving variable speed drives with PWM three-phase inverters, in which it is necessary to check the effects caused to the motor by the electromagnetic interference, (EMI) in the differential mode, as well as in the common mode. The motor parameters determination is generally performed in adequate laboratories using accurate instruments, such as very expensive RLC bridges. The method proposed here consists in the identification of the motor equivalent electrical circuit parameters in rated frequency and in high frequency through characteristic tests in the laboratory, together with the use of characteristic equations and curves, shown in the references to be mentioned for determining the motor high frequency parasite capacitances and also through system simulations using dedicated software, like Pspice, determining the characteristic waveforms involved in the differential and common mode phenomena, comparing and validating the procedure through published papers [01].

Application of Generalized Linear Models and Generalized Estimation Equations to model at-haulback mortality of blue sharks captured in a pelagic longline fishery in the Atlantic Ocean

Coelho, Rui; Infante, Paulo; Santos, Miguel N.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Português
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At-haulback mortality of blue shark (Prionace glauca) captured by the Portuguese pelagic longline fish- ery targeting swordfish in the Atlantic was modeled. Data was collected by onboard fishery observers that monitored 762 fishing sets (1 005 486 hooks) and recorded information on 26 383 blue sharks. The sample size distribution ranged from 40 to 305 cm fork length, with 13.3% of the specimens captured dead at-haulback. Data modeling was carried out with Generalized Linear Models (GLM) and Gener- alized Estimation Equations (GEE), given the fishery-dependent source of the data. The explanatory variables influencing blue shark mortality rates were year, specimen size, fishing location, sex, season and branch line material. Model diagnostics and validation were performed with residual analysis, the Hosmer–Lemeshow test, a receiver operating characteristic (ROC) curve, and a 10-fold cross validation procedure. One important conclusion of this study was that blue shark sizes are important predictors for estimating at-haulback mortality rates, with the probabilities of dying at-haulback decreasing with increasing specimen sizes. The effect in terms of odds-ratios are non-linear, with the changing odds- ratios of surviving higher for the smaller sharks (as sharks grow in size) and then stabilizing as sharks reach larger sizes. The models presented in this study seem valid for predicting blue shark at-haulback mortality in this fishery...

Tangency quantum cohomology and characteristic numbers

KOCK,JOACHIM
Fonte: Academia Brasileira de Ciências Publicador: Academia Brasileira de Ciências
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/09/2001 Português
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This work establishes a connection between gravitational quantum cohomology and enumerative geometry of rational curves (in a projective homogeneous variety) subject to conditions of infinitesimal nature like, for example, tangency. The key concept is that of modified psi classes, which are well suited for enumerative purposes and substitute the tautological psi classes of 2D gravity. The main results are two systems of differential equations for the generating function of certain top products of such classes. One is topological recursion while the other is Witten-Dijkgraaf-Verlinde-Verlinde. In both cases, however, the background metric is not the usual Poincaré metric but a certain deformation of it, which surprisingly encodes all the combinatorics of the peculiar way modified psi classes restrict to the boundary. This machinery is applied to various enumerative problems, among which characteristic numbers in any projective homogeneous variety, characteristic numbers for curves with cusp, prescribed triple contact, or double points.

Elastodynamic Equations: Characteristics, Wavefronts And Rays

Bos, Len; Slawinski, Michael A.
Fonte: Oxford University Press Publicador: Oxford University Press
Tipo: Artigo de Revista Científica Formato: text/html
Português
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We derive the characteristic equations, and the so-called Christoffel equation, for the vector elastodynamic equations in terms of both hypersurfaces of nonuniqueness and as wavefronts based on a physical definition. We follow Courant and Hilbert in defining a wavefront as a surface for which a solution may be zero on one side but nonzero on the other. We show that wavefronts defined in this way must be characteristics. Moreover, we give a partial converse showing that in the case of analytic coefficients, characteristics must (locally) be wavefronts. Furthermore, we show how the equations defining wavefronts, which are characteristics, can be obtained by letting frequency tend to infinity in a certain trial solution expressed in the frequency domain. The last approach might suggest that ray theory, which results from the Christoffel equation, is an asymptotic theory. Taking the limit, however, is just a technicality and is unnecessary to obtain the Christoffel equation, which is contained in the elastodynamic equations and their characteristic equations.

On an infinite integral arising in the numerical integration of stochastic differential equations

Stump, D.; Hill, J.
Fonte: Royal Soc London Publicador: Royal Soc London
Tipo: Artigo de Revista Científica
Publicado em //2005 Português
Relevância na Pesquisa
35.83%
We study a stochastic integral that arises during the implementation of the Milstein method for the numerical integration of systems of stochastic differential equations. The distribution of the integral can be written as the inverse Fourier transform of a characteristic function with essential singularities. This leads to a generalized integral that can be expressed as an infinite series involving the derivatives of Meixner polynomials. The generating function of the polynomials in combination with the Mittag–Leffler expansion theorem is used to obtain a novel series representation for the integral and the motivating problem in particular. This new form is rapidly convergent and, therefore, well suited to numerical work.; David M. Stump and James M. Hill

Entwicklung und Untersuchung von Moving Least Square Verfahren zur numerischen Simulation hydrodynamischer Gleichungen; Development and Analysis of Moving Least Square Procedures for the Numerical Simulation of the Hydrodynamic Equations

Kunle, Matthias
Fonte: Universidade de Tubinga Publicador: Universidade de Tubinga
Tipo: Dissertação
Português
Relevância na Pesquisa
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Ziel dieser Arbeit ist die Entwicklung und Erprobung neuer Verfahren zur numerischen Lösung der hydrodynamischen Gleichungen. Der generelle Ansatz der untersuchten Verfahren basiert auf einer funktionellen Approximation, welcher die Moving Least Square Methode zugrunde liegt. Mit diesen Approximationen werden nun diskrete Gleichungen aufgestellt, sowohl in Eulerscher als auch Lagrangescher Beschreibungsweise einer Strömung. Die praktische Umsetzung und Erprobung der gefundenen Diskretisierungen erfolgt anhand einfacher Testbeispiele. Im ersten Teil der Arbeit werden die durch die Moving Least Square Methode erhaltenen Approximationen auf wichtige Eigenschaften untersucht. Die wohl wichtigste Eigenschaft betrifft die Basisfunktionen bezüglich derer eine Funktion entwickelt wird. Es stellt sich heraus, daß die Basisfunktionen exakt approximiert werden. Diese Tatsache begründet die Konsistenz der folgenden Verfahren. Im zweiten Teil der Arbeit wird die Moving Least Square Methode und die daraus folgenden Diskretisierungen in drei unterschiedlichen Verfahren vorgestellt. Bei diesen handelt es sich um ein Kollokationsverfahren, ein Galerkin-Verfahren und ein Lagrangesches Verfahren. Im Kollokationsverfahren werden die Moving Least Square Approximationen direkt auf die Funktionen in den vorliegenden Differentialgleichungen angewandt. Die Ergebnisse entsprechen dem eines Verfahrens mit Finiten Differenzen. Im Galerkin-Verfahren findet die schwache Formulierung einer Differentialgleichung Verwendung. Bei den gefundenen Diskretisierungen der hydrodynamischen Gleichungen ergeben sich Erhaltungssätze für Gesamtmasse...

Asymptotic analysis of the Navier-Stokes equations in a curved domain with a non-characteristic boundary

Gie, G.-M.; Makram, H.; Tema,, R.
Fonte: American Institute of Mathematical Sciences Publicador: American Institute of Mathematical Sciences
Tipo: Artigo de Revista Científica
Português
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We consider the Navier-Stokes equations of an incompressible fluid in a three dimensional curved domain with permeable walls in the limit of small viscosity. Using a curvilinear coordinate system, adapted to the boundary, we construct a corrector function at order $varepsilon^{j}$, $j = 0, 1$, where $varepsilon$ is the (small) viscosity parameter. This allows us to obtain an asymptotic expansion of the Navier-Stokes solution at order $varepsilon^{j}$, $j = 0, 1$, for $varepsilon$ small . Using the asymptotic expansion, we prove that the Navier-Stokes solutions converge, as the viscosity parameter tends to zero, to the corresponding Euler solution in the natural energy norm. This work generalizes earlier results in [14] or [26], which discussed the case of a channel domain, while here the domain is curved.

Mitigating the Curse of Dimensionality: Sparse Grid Characteristics Method for Optimal Feeback Control and HJB Equations

Kang, Wei; Wilcox, Lucas C.
Fonte: Escola de Pós-Graduação Naval Publicador: Escola de Pós-Graduação Naval
Tipo: Artigo de Revista Científica
Português
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We address finding the semi-global solutions to optimal feedback con- trol and the Hamilton–Jacobi–Bellman (HJB) equation. Using the solu- tion of an HJB equation, a feedback optimal control law can be imple- mented in real-time with minimum computational load. However, except for systems with two or three state variables, using traditional techniques for numerically finding a semi-global solution to an HJB equation for general nonlinear systems is infeasible due to the curse of dimensionality. Here we present a new computational method for finding feedback optimal control and solving HJB equations which is able to mitigate the curse of dimensionality. We do not discretize the HJB equation directly, instead we introduce a sparse grid in the state space and use the Pontryagin’s maximum principle to derive a set of necessary conditions in the form of a boundary value problem, also known as the characteristic equations, for each grid point. Using this approach, the method is spatially causality free, which enjoys the advantage of perfect parallelism on a sparse grid. Compared with dense grids, a sparse grid has a significantly reduced size which is feasible for systems with relatively high dimensions, such as the 6-D system shown in the examples. Once the solution obtained at each grid point...

Equações diferenciais ordinárias lineares com coeficientes constantes e derivação da equação característica; Linear ordinary differential equations with coefficients and constant equation derivation feature

Santos, Ricardo da Silva
Fonte: Universidade Federal de Goiás; Brasil; UFG; Programa de Pós-graduação em PROFMAT (RG); Instituto de Matemática e Estatística - IME (RG) Publicador: Universidade Federal de Goiás; Brasil; UFG; Programa de Pós-graduação em PROFMAT (RG); Instituto de Matemática e Estatística - IME (RG)
Tipo: Dissertação Formato: application/pdf
Português
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This work was divided into three chapters , the rst we have some basic de nitions for the study of di erential equations, and basic results as Euler's formula and Wronskian . In the second chapter, we talked about Di erential Equations of First Order Linear, and commenting on PVI, and the Theorem of Existence and Uniqueness for ODEs. In the third and main chapter, we work with resolution methods Di erential Equations. In particular, we present a unnusual in mathematics literature to solve Linear Di erential Equations, which is by Equation Characteristic.; Este trabalho foi dividido em 3 capítulos. No primeiro temos algumas de finições básicas para o estudo de Equações Diferenciais, e resultados básicos como a fórmula de Euler e Wronskiano. No segundo capítulo, falamos sobre Equações Diferenciais Lineares de Primeira Ordem, além de comentarmos sobre o que vem a ser Problema do Valor Inicial (PVI), e o Teorema da Existência e Unicidade para EDO's. No terceiro e principal capítulo, trabalhamos com métodos de resolução de uma Equação Diferencial Ordinária Com Coe ficentes Constantes. Em especial, apresenta-mos um método não tão usual na literatura Matemática pra resolver EDOs Lineares, que é através da Derivação da Equação Caraterística.

Solution of the Navier - Stokes equation using the method of characteristic curves

Villegas Jim??nez, Jos?? David
Fonte: Universidad EAFIT; Maestr??a en Ingenier??a; Escuela de Ingenier??a Publicador: Universidad EAFIT; Maestr??a en Ingenier??a; Escuela de Ingenier??a
Tipo: masterThesis; Tesis de Maestr??a; acceptedVersion
Português
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This project deals about the solution of the Navier Stokes Equations by the Method of Characteristics -- This method is used to eliminate the convective part of equations of the convection-diffusion type, conducting the material derivative in a Lagrangian manner along the characteristic curves of each node in a fixed grid -- Following this approach, the method is able to solve the incompressible Navier Stokes Equations with the advantage of using large timesteps -- In the present case, the solution of the well known Lid Driven Cavity Flow problem is obtained for several Reynolds numbers, showing good agreement when compared to solutions obtained by other methods

On characteristic equations, trace identities and Casimir operators of simple Lie algebras

Macfarlane, A. J.; Pfeiffer, H.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/07/1999 Português
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Two approaches are developed to exploit, for simple complex or compact real Lie algebras g, the information that stems from the characteristic equations of representation matrices and Casimir operators. These approaches are selected so as to be viable not only for `small' Lie algebras and suitable for treatment by computer algebra. A very large body of new results emerges in the forms, a) of identities of a tensorial nature, involving structure constants etc. of g, b) of trace identities for powers of matrices of the adjoint and defining representations of g, c) of expressions of non-primitive Casimir operators of g in terms of primitive ones. The methods are sufficiently tractable to allow not only explicit proof by hand of the non-primitive nature of the quartic Casimir of g2, f4, e6, but also e.g. of that of the tenth order Casimir of f4.; Comment: 39 pages, 8 tables, latex

Asymptotic properties of the spectrum of neutral delay differential equations

Kyrychko, Y. N.; Blyuss, K. B.; Hoevel, P.; Schoell, E.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/01/2012 Português
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Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived exact stability boundary. The approximate and exact stability borders agree quite well for the large time delay, and the inclusion of a time-delayed velocity feedback improves this agreement for small delays. Theoretical results are complemented by a numerically computed spectrum of the corresponding characteristic equations.; Comment: 14 pages, 6 figures

Spectral curves and discrete Painlev\'e equations

Ormerod, Christopher M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/12/2014 Português
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It is well known that isomonodromic deformations admit a Hamiltonian description. These Hamiltonians appear as coefficients of the characteristic equations of their Lax matrices, which define spectral curves for linear systems of differential and difference systems. The characteristic equations in the case of the associated linear problems for various discrete Painlev\'e equations is biquadratic in the Painlev\'e variables. We show that the discrete isomonodromic deformations that define the discrete Painlev\'e equations may be succinctly described in terms of the characteristic equation of their Lax matrices.; Comment: 21 pages

Theory of orthogonality of eigenfunctions of the characteristic equations as a method of solution boundary problems for model kinetic equations

Latyshev, A. V.; Kurilov, A. D.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/07/2014 Português
Relevância na Pesquisa
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We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous Riemann boundary value problem with a coefficient equal to the ratio of the boundary values dispersion function, develops the theory of the half-space orthogonality of generalized singular eigenfunctions corresponding characteristic equations, which leads separation of variables. And in this two boundary value problems of the kinetic theory (diffusion light component of a binary gas and Kramers problem about isothermal slip) shows the application of the theory orthogonality eigenfunctions for analytical solutions these tasks.; Comment: 17 pages, 0 figures

Asymptotic properties of solutions to linear nonautonomous delay differential equations through generalized characteristic equations

Cuevas, Claudio; Frasson, Miguel V. S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We study some properties concerning the asymptotic behavior of solutions to nonautonomous retarded functional differential equations, depending on the knowledge of certain solutions of the associated generalized characteristic equation.; Comment: 5 pages

Geometric order parameter equations

Holm, Darryl D.; Putkaradze, Vakhtang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/08/2006 Português
Relevância na Pesquisa
35.89%
Aggregation of particles whose interaction potential depends on their mutual orientation is considered. The aggregation dynamics is derived using a version of Darcy's law and a variational principle depending on the geometric nature of the physical quantities. The evolution equations that result separate into two classes: either characteristic equations, or gradient flow equations. We derive analytical solutions of both types of equations which are collapsed (clumped) states and show their dynamical emergence from smooth initial conditions in numerical simuations.; Comment: 10 pages, 3 figures. Submitted to Physical Review Letters

Exponential Spline Interpolation in Characteristic Based Scheme for Solving the Advective-Diffusion Equation

Zoppou, Christopher; Roberts, Stephen; Renka, R J
Fonte: John Wiley & Sons Inc Publicador: John Wiley & Sons Inc
Tipo: Artigo de Revista Científica
Português
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This paper demonstrates the use of shape-preserving exponential spline interpolation in a characteristic based numerical scheme for the solution of the linear advective-diffusion equation. The results from this scheme are compared with results from a number of numerical schemes in current use using test problems in one and two dimensions. These test cases are used to assess the merits of using shape-preserving interpolation in a characteristic based scheme. The evaluation of the schemes is based on accuracy, efficiency, and complexity. The use of the shape-preserving interpolation in a characteristic based scheme is accurate, captures discontinuities, does not introduce spurious oscillations, and preserves the monotonicity and positivity properties of the exact solution. However, fitting exponential spline interpolants to the nodal concentrations is computationally expensive. Exponential spline interpolants were also fitted to the integral of the concentration profile. The integral of the concentration profile is a smoother function than the concentration profile. It requires less computational effort to fit an exponential spline interpolant to the integral than the nodal concentrations. By differentiating the interpolant, the nodal concentrations are obtained. This results in a more efficient and more accurate numerical scheme.