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Lagrange-Chebyshev Based Single Step Methods for Solving Differential EquationsStoffel, Joshua David 07 May 2012 (has links)
No description available.
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Optimization of linear time-invariant dynamic systems without lagrange multipliersVeeraklaew, Tawiwat January 1995 (has links)
No description available.
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The application of Buckingham π theorem to Lattice-Boltzmann modelling of sewage sludge digestionDapelo, Davide, Trunk, R., Krause, M.J., Cassidy, N., Bridgeman, John 25 November 2020 (has links)
Yes / For the first time, a set of Lattice-Boltzmann two-way coupling pointwise Euler-Lagrange models is applied to gas mixing of sludge for anaerobic digestion. The set comprises a local model, a “first-neighbour” (viz., back-coupling occurs to the voxel where a particle sits, plus its first neighbours) and a “smoothing-kernel” (forward- and back-coupling occur through a smoothed-kernel averaging procedure). Laboratory-scale tests display grid-independence problems due to bubble diameter being larger than voxel size, thereby breaking the pointwise Euler-Lagrange assumption of negligible particle size. To tackle this problem and thereby have grid-independent results, a novel data-scaling approach to pointwise Euler-Lagrange grid independence evaluation, based on an application of the Buckingham π theorem, is proposed. Evaluation of laboratory-scale flow patterns and comparison to experimental data show only marginal differences in between the models, and between numerical modelling and experimental data. Pilot-scale simulations show that all the models produce grid-independent, coherent data if the Euler-Lagrange assumption of negligible (or at least, small) particle size is recovered. In both cases, a second-order convergence was achieved. A discussion follows on the opportunity of applying the proposed data-scaling approach rather than the smoothing-kernel model.
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Étude numérique de la réduction de traînée par injection de bulles en écoulement de Taylor-Couette / Numerical study of bubbly drag reduction in Taylor-Couette flowChouippe, Agathe 12 July 2012 (has links)
La thèse porte sur l'étude de la réduction de traînée par injection de bulles. La réduction de traînée présente un intérêt pour les applications navales puisqu'elle est issue d'une modification des structures cohérentes qui contribuent le plus à la résistance à l'avancement. Le but de cette étude est d'analyser les mécanismes à l'origine de cette diminution du frottement pariétal. L'approche utilisée dans le cadre de cette étude est numérique, elle emploie le code JADIM par une approche Euler-Lagrange : la phase continue est simulée par Simulation Numérique Directe et la phase dispersée est simulée en suivant individuellement chaque bulle. La configuration retenue dans le cadre de cette étude est celle de l'écoulement de Taylor-Couette (écoulement compris entre deux cylindres en rotation). La première partie de la thèse vise à adapter l'outil numérique employé, afin de pouvoir prendre en compte le retour de la phase dispersée via des termes de forçage dans les équations bilan de matière et de quantité de mouvement. La deuxième partie de la thèse vise à étudier l'écoulement porteur en configuration monophasique, afin de disposer d'une référence sur l'écoulement non perturbé. La troisième partie de la thèse a pour objectif d'étudier la dispersion passive des bulles dans le système, afin d'analyser les mécanismes de migrations mis en jeu. Enfin la dernière partie de la thèse vise à étudier l'influence des bulles sur l'écoulement porteur en analysant l'effet de certains paramètres, notamment le taux de vide et la flottabilité. / The study deals with drag reduction induced by bubble injection, its application concerns naval transport. The aim of the study is to shed more light on mechanisms that are involved in this wall friction reduction. The study is based on a numerical approach, and use the JADIM code with an Euler-Lagrange approach: the continuous phase is solved by Direct Numerical Simulation, and the disperse phase by a tracking of each bubble. Within the framework of this study we consider the Taylor-Couette flow configuration (flow between two concentric cylinders in rotation). The first part of the study deals with the modification of the numerical tool, in order to take into account the influence of the disperse phase on the continuous one through forcing terms in the mass and momentum balance equations. The aim of the second part is to study de Taylor-Couette flow in its monophasic configuration, for the purpose of providing a reference of the undisturbed flow. The third part deals with the passive dispersion of bubble in Taylor-Couette flow, in order to analyze the migration mechanisms involved. And the aim of the last part is to study the effects of the disperse phase on the continuous one, by analyzing the influence of bubbly phase parameters (like void fraction and buoyancy).
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[en] A SMOOTH TRANSITION PERIODIC AUTO REGRESSIVE MODEL FOR SHORT TERM ELECTRICITY LOAD FORECAST / [pt] UM MODELO DE MÚLTIPLOS REGIMES AUTO REGRESSIVO PERIÓDICO COM TRANSIÇÃO SUAVE APLICADO A PREVISÃO DE CURTO PRAZO DE CARGA DE ENERGIA ELÉTRICALUIZ FELIPE MOREIRA DO AMARAL 16 May 2007 (has links)
[pt] Essa tese considera um modelo não linear para se obter
previsões de curto
prazo de carga de energia elétrica. O modelo combina um
modelo de múltiplos
regimes auto-regressivo com transição suave com um
periódico auto-regressivo
criando o modelo de múltiplos regimes periódico com
transição suave (STPAR).
Um método de construção do modelo é desenvolvido com
métodos estatísticos
simples e um teste de linearidade contra a hipótese de
modelo periódico autoregressivo
com transição suave. Outros dois destes foram elaborados
para se
avaliar o modelo estimado: um teste de Multiplicador de
Lagrange (LM) para a
hipótese de auto-correlação serial dos resíduos e outro
teste LM para a hipótese de
não linearidade remanescente. Um experimento de Monte
Carlo foi implementado
para avaliar a performance dos testes propostos. Estimação
por mínimos
quadrados não lineares é considerado. Finalmente, dados de
carga de energia
elétrica do estado de New South Wales na Austrália são
apresentados e foram
usados como exemplo real. Outros modelos foram utilizados
para comparar a
performance do modelo. / [en] This thesis considers a non linear approach to obtain
short term forecast for
electricity load. The model combines a smooth transition
autoregressive process
with a periodic autoregressive time series model, creating
the Smooth Transition
Periodic Autoregressive (STPAR) model. A model-building
procedure is
developed and a linearity test against smooth transition
periodic auto-regressive is
proposed. Other two tests were created to evaluate the
model: a Lagrange
multiplier (LM) test for the hypothesis of no error
autocorrelation and LM-type
test for the hypothesis of no remaining non-linearity. A
Monte Carlo experiment
was implemented to evaluate the performance of the
proposed tests. Estimation by
nonlinear least squares is considered. Finally, load data
from New South Wales
State in Australia`s electricity retail market is
presented and will be used as a real
example. Other models were used to compare the performance
of the proposes
model.
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Estabilidade de Liapunov e derivada radial / Liapunov stability and radial derivativeAlva Morales, Gerard John 31 October 2014 (has links)
Apresentaremos uma classe de energias potenciais $\\Pi \\in C^{\\infty}(\\Omega,R)$ que são s-decidíveis e que admitem funções auxiliares de Cetaev da forma $\\langle abla j^s\\Pi(q),q angle$, $q\\in \\Omega \\subset R^n$ que são s-resistentes. / We will present a class of potential energies $\\Pi \\in C^{\\infty}(\\Omega,R)$ that are s-decidable and that admit auxiliary functions of Cetaev of the form $\\langle abla j^s\\Pi(q),q angle$, $q \\in \\Omega \\subset R^n$ which are s-resistant.
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[en] BIDIMENSIONAL ANALYSIS OF FLEXIBLE LINE DYNAMICS INCLUDING THE CONTACT EFFECTS WITH SEABED / [pt] ANÁLISE BIDIMENSIONAL DA DINÂMICA DE LINHAS FLEXÍVEIS INCLUINDO OS EFEITOS DO CONTATO COM O FUNDO MARINHOABEL TORRES ANDREWS 26 October 2004 (has links)
[pt] Neste trabalho apresenta-se uma metodologia pelo método dos
elementos
finitos para a análise estática-dinâmica bi-dimensional de
linhas marítimas
considerando-se o contato com o leito marinho. Para o cabo
considera-se o
elemento de dois nós do modelo de viga de Euler-Bernoulli
com as grandezas
estáticas e dinâmicas referidas a um sistema co-
rotacionado. Considera-se a nãolinearidade
geométrica associada ao movimento de corpo rígido da
estrutura,
supondo pequenas deformações. No movimento da linha, são
consideradas as
influências do peso próprio, empuxo, carregamentos
hidrodinâmicos das correntes
marinhas, deslocamentos prescritos no ponto superior da
linha, forças de inercia e
ação de flutuadores. Os efeitos sobre a linha associados ao
contato com o fundo
marinho são considerados empregando-se a técnica dos
multiplicadores de
Lagrange. Estes representam o carregamento (forças e
momentos) requerido para
garantir as restrições geométricas. No modelo não são
considerados os efeitos das
forças de atrito com o fundo marinho, cuja rigidez é
considerada muito superior à
do cabo. A matriz de rigidez usual do modelo de vigas é
aumentada de forma a
acomodar as novas incógnitas resultantes da imposição das
condições de contato.
Desta forma, condições de contato, separação repetidos
(contato variável) e
grandes movimentos relativos do cabo com o leito são
contemplados pelo modelo.
A solução das equações algébricas não-lineares, resultantes
da integração
temporal passo-a-passo de Newmark, é obtida com a técnica
iterativa de Newton
Raphson. A metodologia numérica foi implementada e
resultados de alguns testes
para situações da engenharia offshore são mostrados e
comparados com os
apresentados por outros autores independentes. / [en] In this work a finite element methodology for two-
dimensional static and/or
dynamic analysis of maritime risers including contact with
the seabed is
considered. The line is modeled by a two node beam element
based on the Euler-
Bernoulli theory with a co-rotational coordinate system,
defined from the structure
space coordinate nodes, to refer the element equilibrium
and motion equations.
Geometric non-linear effects are considered, all associated
with rigid body
motions from the structure, under small strain hypothesis.
In the riser motion, the
influences of its own weight, buoyancy forces, hydrodynamic
loadings due to the
maritime currents, the prescribed displacements at the top
point line, the inertia
forces and the floating action are considered. Effects on
the line associated to the
seabed contact are considered using Lagrange multipliers.
They represent, the
required loading (forces and moments) to ensure the cable
geometric restrictions.
In the model, friction forces effects on the seabed are not
considered and the
seabed stiffness is taken much greater than the riser s.
The beam model stiffness
matrix results into an increased matrix to accommodate the
new model unknowns
reactions, which are represented by the contact forces and
moments. Similarly,
conditions for variable contact and/or separation, as well
as large relative motions
between the flexible line and the seabed, are contemplated
by the model.
Solutions of the resulting nonlinear motion equations are
obtained using
Newmark s step-by-step time integration procedure with the
Newton-Raphson
iterative technique, for the numerical solution
convergence. The methodology has
been implemented and some representative offshore
engineering testing analysis
results are presented compared to other independently
published solutions.
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Kontaktprobleme in der nichtlinearen ElastizitätstheorieHabeck, Daniel 29 July 2008 (has links) (PDF)
Es werden Kontaktprobleme im Rahmen der nichtlinearen Elastizitätstheorie mit Mitteln der Variationsrechnung behandelt. Dabei liegt das Hauptaugenmerk auf der Untersuchung des Selbstkontakts eines nichtlinear elastischen Körpers. Unter Verwendung einer geeigneten Lagrangeschen Multiplikatorenregel wird eine notwendige Bedingung für Minimierer hergeleitet. Weiterhin werden Ergebnisse für den Kontakt zweier elastischer Körper formuliert.
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On Economic Interpretation of Lagrange MultipliersMeznik, Ivan 19 March 2012 (has links) (PDF)
No description available.
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Um estudo sobre fun??es de v?rias vari?veisGuimar?es, Bruce Franca 17 October 2017 (has links)
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Previous issue date: 2017 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / O foco do presente trabalho ? apresentar um estudo sobre fun??es reais de v?rias vari?veis reais, bem como, estudar as principais t?cnicas envolvendo esse tipo de fun??o. Conv?m destacar os conceitos de limites, derivadas parciais, m?ximos e m?nimos multiplicadores de Lagrange. Na parte final da disserta??o, apresentamos uma aplica??o na Engenharia. / Disserta??o (Mestrado Profissional) ? Programa de P?s-Gradua??o Matem?tica, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2017. / The focus of the present work is to present a study on the real functions of several real variables, as well as to study the main techniques involving this type of function. It is worth mentioning the concepts of limits, partial derivatives, maximum and minimum and Lagrange multipliers. In the final part of the dissertation, we present an application in Engineering.
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