Dissertations / Theses: 'Algebraic Modeling'

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Wintz, Julien. "Algebraic methods for geometric modeling." Nice, 2008. http://www.theses.fr/2008NICE4005.

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The two fields of algebraic geometry and algorithmic geometry, though closely related, are traditionally represented by almost disjoint communities. Both fields deal with curves and surfaces but objects are represented in different ways. While algebraic geometry defines objects by the mean of equations, algorithmic geometry use to work with linear models. The current trend is to apply algorithmic geometry algorithms to non linear models such as those found in algebraic geometry. Such algorithms play an important role in many practical fields such as Computer Aided Geometric Design. Their use raises important questions when it comes to developing software featuring such models. First, the manipulation of their representation implies the use of symbolic numeric computations which still represent one major research interest. Second, their visualization and manipulation is not straightforward because of their abstract nature. The first part of this thesis covers the use of algebraic methods in geometric modeling, with an emphasis on topology, intersection and self-intersection for arrangement computation of semi-algebraic sets with either implicit or parametric representation. Special care is given to the genericity of the algorithms which can be specified whatever the context, and then specialized to meet specific representation requirements. The second part of this thesis presents a prototype of an algebraic geometric modeling environment which aim is to provide a generic yet efficient way to model with algebraic geometric objects such as implicit or parametric curves or surfaces, both from a user and developer point of view, by using symbolic numeric computational libraries as a backend for the manipulation of the polynomials defining the geometric objects
Les domaines de géométrie algébrique et de géométrie algorithmique, bien qu'étroitement liés, sont traditionnellement représentés par des communautés de recherche disjointes. Chacune d'entre elles utilisent des courbes et surfaces, mais représentent les objets de différentes manières. Alors que la géométrie algébrique définit les objets par le biais d'équations polynomiales, la géométrie algorithmique a pour habitude de manipuler des modèles linéaires. La tendance actuelle est d'appliquer les algorithmes traditionnels de géométrie algorithmique sur des modèles non linéaires tels que ceux trouvés en géométrie algébrique. De tels algorithmes jouent un rôle important dans de nombreux champs d'application tels que la Conception Assistée par Ordinateur. Leur utilisation soulève d'importantes questions en matière de développement logiciel. Tout d'abord, la manipulation de leur représentation implique l'utilisation de calculs symboliques numériques qui représentent toujours un domaine de recherche majeur. Deuxièmement, leur visualisation et leur manipulation n'est pas évidente, en raison de leur caractère abstrait. La première partie de cette thèse porte sur l'utilisation de méthodes algébriques en modélisation géométrique, l'accent étant mis sur la topologie, l'intersection et l'auto-intersection dans le cadre du calcul d'arrangement d'ensembles semi-algébriques comme les courbes et surfaces Ã représentation implicite ou paramétrique. Une attention particulière est portée à la généricité des algorithmes qui peuvent être spécifiés quel que soit le contexte, puis spécialisés pour répondre aux exigences d'une certaine représentation. La seconde partie de cette thèse présente le prototypage d'un environnement de modélisation géométrique dont le but est de fournir un moyen générique et efficace pour modéliser des solides à partir d'objets géométriques à représentation algébrique tels que les courbes et surfaces implicites ou paramétriques, à la fois d'un point de vue utilisateur et d'un point de vue de développeur, par l'utilisation de librairies de calcul symbolique numérique pour la manipulation des polynômes définissant les objets géométriques

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Murrugarra, Tomairo David M. "Algebraic Methods for Modeling Gene Regulatory Networks." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/28388.

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So called discrete models have been successfully used in engineering and computational systems biology. This thesis discusses algebraic methods for modeling and analysis of gene regulatory networks within the discrete modeling context. The first chapter gives a background for discrete models and put in context some of the main research problems that have been pursued in this field for the last fifty years. It also outlines the content of each subsequent chapter. The second chapter focuses on the problem of inferring dynamics from the structure (topology) of the network. It also discusses the characterization of the attractor structure of a network when a particular class of functions control the nodes of the network. Chapters~3 and 4 focus on the study of multi-state nested canalyzing functions as biologically inspired functions and the characterization of their dynamics. Chapter 5 focuses on stochastic methods, specifically on the development of a stochastic modeling framework for discrete models. Stochastic discrete modeling is an alternative approach from the well-known mathematical formalizations such as stochastic differential equations and Gillespie algorithm simulations. Within the discrete setting, a framework that incorporates propensity probabilities for activation and degradation is presented. This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations. Finally, Chapter 6 discusses future research directions inspired by the work presented here.
Ph. D.

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Bose, Jyoti Sankar. "Modeling turbulence anisotropy using algebraic Reynolds stress models." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq22277.pdf.

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4

YODER, DENNIS ALLEN. "ALGEBRAIC REYNOLDS STRESS MODELING OF PLANAR MIXING LAYER FLOWS." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1115637717.

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5

Borchert, Katja. "Disassociation between arithmetic and algebraic knowledge in mathematical modeling /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/9141.

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Lorenzetti, David Michael. "Numerical solution of nonlinear algebraic systems in building energy modeling." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/10752.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture and Planning, 1997.
Includes bibliographical references (p. 249-251).
When solving a system of nonlinear equations by Newton-Raphson's method, a common means of avoiding divergence requires each step to reduce some vector norm of the residual errors, usually the convenient and tractable sum of squares. Unfortunately, the descent requirement subjects the solver to difficulties typically associated with function minimization-- stagnation, and convergence to local minima. The descent requirement also can disrupt a successful Newton-Raphson sequence. To explore these problems, the thesis reformulates the theory of function minimization in terms of the familiar Jacobian matrix, which linearizes the equations, and a vector which relates first-order changes in the norm to first-order changes in the residuals. The resulting expressions give the norm's gradient, and approximate its Hessian, as functions of the key variables defining the underlying equations. Therefore when Newton- raphson diverges, the solver can choose a reasonable alternate search strategy directly from the Jacobian model, and subsequently construct an appropriate norm for evaluating the search. Applying these results, the thesis modifies a standard equation-solving algorithm, the double dogleg method. Replacing the published algorithm's r-square norm with a general family of weighted r-square norms, it develops and tests a variety of rules for choosing the particular weighting factors. Selecting new weights at each iteration avoids local minima; in tests on a standard suite of nonlinear systems, the resulting algorithms prove more robust to stagnation, and often converge faster, than the double dogleg. In separate investigations, the thesis specializes to equation-solving a double dogleg variation which minimizes the norm model in the plane of its steepest descent and Newton-Raphson directions, and develops a scalar measure of divergence which, unlike a residual norm, does not depend on results from function minimization.
by David Michael Lorenzetti.
Ph.D.

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Kwong, Gordon Houng. "Approximations for Nonlinear Differential Algebraic Equations to Increase Real-time Simulation Efficiency." Thesis, Virginia Tech, 2010. http://hdl.handle.net/10919/42753.

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Full-motion driving simulators require efficient real-time high fidelity vehicle models in order to provide a more realistic vehicle response. Typically, multi-body models are used to represent the vehicle dynamics, but these have the unfortunate drawback of requiring the solution of a set of coupled differential algebraic equations (DAE). DAE's are not conducive to real-time implementation such as in a driving simulator, without a very expensive processing capability. The primary objective of this thesis is to show that multi-body models constructed from DAE's can be reasonably approximated with linear models using suspension elements that have nonlinear constitutive relationships. Three models were compared in this research, an experimental quarter-car test rig, a multi-body dynamics differential algebraic equation model, and a linear model with nonlinear suspension elements. Models constructed from differential algebraic equations are computationally expensive to compute and are difficult to realize for real-time simulations. Instead, a linear model with nonlinear elements was proposed for a more computationally efficient solution that would retain the nonlinearities of the suspension. Simplifications were made to the linear model with nonlinear elements to further reduce computation time for real-time simulation. The development process of each model is fully described in this thesis. Each model was excited with the same input and their outputs were compared. It was found that the linear model with nonlinear elements provides a reasonably good approximation of actual model with the differential algebraic equations.
Master of Science

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Gordon, Brandon W. (Brandon William). "State space modeling of differential-algebraic systems using singularly perturbed sliding manifolds." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/9340.

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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999.
Includes bibliographical references (p. 126-128).
This thesis introduces a new approach for modeling and control of algebraically constrained dynamic systems. The formulation of dynamic systems in terms of differential equations ·and algebraic constraints provides a systematic framework that is well suited for object oriented modeling of thermo-fluid systems. In this approach, differential equations are used to describe the evolution of subsystem states and algebraic equations are used to define the interconnections between the subsystems (boundary conditions). Algebraic constraints also commonly occur as a result of modeling simplifications such as steady state approximation of fast dynamics and rigid body assumptions that result in kinematic constraints. Important examples of algebraically constrained dynamic systems include multi-body problems, chemical processes, and two phase thermo-fluid systems. Differential-algebraic equation (DAE) systems often referred to as descriptor, implicit, or singular systems present a number of difficult problems in simulation and control. One of the key difficulties is that DAEs are not expressed in an explicit state space form required by many simulation and control design methods. This is particularly true in control of nonlinear DAE systems for which there are few known results. Existing control methods for nonlinear DAEs have so far relied on deriving state space models for limited classes of problems. A new approach for state space modeling of DAEs is developed by formulating an equivalent nonlinear control problem. The zero dynamics of the control system represent the dynamics of the original DAE. This new connection between DAE model representation and nonlinear control is used to obtain state space representations for a general class of differential-algebraic systems. By relating nonlinear control concepts to DAE structural properties a sliding manifold is constructed that asymptotically satisfies the constraint equations. Sliding control techniques are combined with elements of singular perturbation theory to develop an efficient state space model with properties necessary for controller synthesis. This leads to the singularly perturbed sliding manifold (SPSM) approach for state space realization. The new approach is demonstrated by formulating a state space model of vapor compression cycles. This allows verification of the method and provides more insight into the problems associated with modeling differential algebraic systems.
by Brandon W. Gordon.
Ph.D.

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Song, Xuefeng. "Dynamic modeling issues for power system applications." Texas A&M University, 2003. http://hdl.handle.net/1969.1/1591.

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Power system dynamics are commonly modeled by parameter dependent nonlinear differential-algebraic equations (DAE) x p y x f ) and 0 = p y x g ) . Due to (,, (,, the algebraic constraints, we cannot directly perform integration based on the DAE. Traditionally, we use implicit function theorem to solve for fast variables y to get a reduced model in terms of slow dynamics locally around x or we compute y numerically at each x . However, it is well known that solving nonlinear algebraic equations analytically is quite difficult and numerical solution methods also face many uncertainties since nonlinear algebraic equations may have many solutions, especially around bifurcation points. In this thesis, we apply the singular perturbation method to model power system dynamics in a singularly perturbed ODE (ordinary-differential equation) form, which makes it easier to observe time responses and trace bifurcations without reduction process. The requirements of introducing the fast dynamics are investigated and the complexities in the procedures are explored. Finally, we propose PTE (Perturb and Taylors expansion) technique to carry out our goal to convert a DAE to an explicit state space form of ODE. A simplified unreduced Jacobian matrix is also introduced. A dynamic voltage stability case shows that the proposed method works well without complicating the applications.

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Gabrielson, Donald D. "Battle group stationing algebraic modeling system : an anti-air warfare tactical decision aid methodology /." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1995. http://handle.dtic.mil/100.2/ADA296246.

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Rasam, Amin. "Explicit algebraic subgrid-scale stress and passive scalar flux modeling in large eddy simulation." Licentiate thesis, KTH, Linné Flow Center, FLOW, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-34453.

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The present thesis deals with a number of challenges in the field of large eddy simulation (LES). These include the performance of subgrid-scale (SGS) models at fairly high Reynolds numbers and coarse resolutions, passive scalar and stochastic modeling in LES. The fully-developed turbulent channel flow is used as the test case for these investigations. The advantage of this particular test case is that highly accurate pseudo-spectral methods can be used for the discretization of the governing equations. In the absence of discretization errors, a better understanding of the subgrid-scale model performance can be achieved. Moreover, the turbulent channel flow is a challenging test case for LES, since it shares some of the common important features of all wall-bounded turbulent flows. Most commonly used eddy-viscosity-type models are suitable for moderately to highly-resolved LES cases, where the unresolved scales are approximately isotropic. However, this makes simulations of high Reynolds number wall-bounded flows computationally expensive. In contrast, explicit algebraic (EA) model takes into account the anisotropy of SGS motions and performs well in predicting the flow statistics in coarse-grid LES cases. Therefore, LES of high Reynolds number wall-bounded flows can be performed at much lower number of grid points in comparison with other models. A demonstration of the resolution requirements for the EA model in comparison with the dynamic Smagorinsky and its high-pass filtered version for a fairly high Reynolds number is given in this thesis. One of the shortcomings of the commonly used eddy diffusivity model arises from its assumption of alignment of the SGS scalar flux vector with the resolved scalar gradients. However, better SGS scalar flux models that overcome this issue are very few. Using the same methodology that led to the EA SGS stress model, a new explicit algebraic SGS scalar flux model is developed, which allows the SGS scalar fluxes to be partially independent of the resolved scalar gradient. The model predictions are verified and found to improve the scalar statistics in comparison with the eddy diffusivity model. The intermittent nature of energy transfer between the large and small scales of turbulence is often not fully taken into account in the formulation of SGS models both for velocity and scalar. Using the Langevin stochastic differential equation, the EA models are extended to incorporate random variations in their predictions which lead to a reasonable amount of backscatter of energy from the SGS to the resolved scales. The stochastic EA models improve the predictions of the SGS dissipation by decreasing its length scale and improving the shape of its probability density function.
QC 20110615

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Ciochetto, David S. "Analysis of Three Dimensional Turbulent Shear Flow Experiments with Respect to Algebraic Modeling Parameters." Thesis, Virginia Tech, 1997. http://hdl.handle.net/10919/36808.

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The extension of the theory for two dimensional turbulent boundary layers into three dimensional flows has met with limited success. The failure of the extended models is attributed to the anisotropy of the turbulence. This is seen by the turbulent shear stress angle lagging the flow gradient angle and by the behavior of the Reynolds shear stresses lagging that of the mean flow. Transport equations for the turbulent shear stresses were proposed to be included in a modeling effort capable of accounting for the lags seen in the flow. This study is aimed at developing algebraic relationships between the various Reynolds-averaged terms in these modeling equations. Particular emphasis was placed on the triple products that appear in the transport equations. Eleven existing experimental data sets were acquired from the original authors and re-examined with respect to developed and existing parameters. A variety of flow geometries were collected for comparison. Emphasis was placed on experiments that included all six components of the Reynolds stress tensor and triple products. Parameters involving the triple products are presented that appear to maintain a relatively constant value across regions of the boundary layer. The variation of these parameters from station to station and from flow to flow is discussed. Part of this study was dedicated to parameters that were previously introduced, but never examined with respect to the data that was collected. Results of these parameters are presented and discussed with respect to agreement or disagreement with the previous results. The parameters presented will aid in the modeling of three dimensional turbulent boundary layers especially with models that employ the transport equations for the Reynolds stresses.
Master of Science

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Ramanathan, Krishnan Adithya. "Explicit algebraic subfilter scale modeling for DES-like methods and extension to variable density flows." Thesis, Aix-Marseille, 2019. http://www.theses.fr/2019AIXM0117.

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Dans cette thèse, l’objectif est d’améliorer les capacités prédictives des méthodes hybrides RANS/LES par le développement d’un modèle à l’échelle de sous-filtre qui prend en compte une relation algébrique explicite pour les stresses turbulents de sous-filtre non-isotropes et les flux scalaires turbulents. Tout d'abord, un modèle explicite algébrique (EARSM) est développé et calibré avec le modèle BSL de Menter pour les écoulements incompressibles dans un contexte RANS. Deuxièmement, le modèle EARSM est étendu dans le cadre hybrides RANS/LES. Méthodes hybrides RANS/LES spécifiquement dans le cadre de l'Equivalent-Detached Eddy Simulation, aboutissant au modèle hybride explicite algébrique EAHSM. Le travail de validation est réalisé pour l'écoulement entièrement développé du canal à un nombre de Reynolds de frottement à 550 et l'écoulement dans un tuyau carré à un nombre de Reynolds de frottement de 600. Enfin, en supposant que l'approximation de Boussinesq soit valide, les modèles EARSM et EAHSM sont étendus à des écoulements à densité légèrement variable. Suite à la solution directe des relations algébriques implicites, le modèle algébrique explicite pour les contraintes de Reynolds et les flux scalaires est obtenu dans un cadre RANS amené au modèle explicite algébrique de flux scalaire (EASFM). Une méthode itérative est utilisée pour traiter la non-linéarité des expressions couplées pour les relations algébriques. Ensuite, l’EASFM est étendu au cadre des méthodes hybrides RANS/LES. Le comportement des modèles est évalué sur l'écoulement homogène, en stratification stable
The aim of this work is to improve the predictive capabilities of hybrid RANS/LES methods HRLM through the development of a subfilter scale model which considers an explicit algebraic relation for the non-isotropic turbulent subfilter stress and turbulent scalar fluxes, contributing to the improvement of the safety analysis concerning hydrogen hazards. Firstly, an Explicit Algebraic Reynolds Stress Model EARSM is developed using the direct solution method and calibrated with Menter's BSL model for incompressible flows in a RANS framework. Secondly, the EARSM model is extended to seamless HRLM specifically in the framework of Equivalent-Detached Eddy Simulation, arriving at the Explicit Algebraic Hybrid Stress Model EAHSM. The calibration of the model constant is performed on the decay of isotropic turbulence. The validation is performed against the DNS data available in the literature for the fully developed Channel flow at a moderate friction Reynolds number of 550 and flow in a square pipe at a friction Reynolds number of 600. Finally, assuming the Boussinesq approximation to be valid, the developed EARSM and the EAHSM models are extended to slightly variable density flows. Following the direct solution of the implicit algebraic relationships, the explicit algebraic model for both the Reynolds stresses and the scalar flux is obtained in a RANS framework which leads to the Explicit Algebraic Scalar Flux Model(EASFM). An effective iterative solution method is used to treat the nonlinearity of the coupled expressions for the algebraic relations. The EASFM is extended to the framework of seamless HRLM. The behaviour of the models is assessed for stably stratified flows

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Stigler, Brandilyn Suzanne. "An Algebraic Approach to Reverse Engineering with an Application to Biochemical Networks." Diss., Virginia Tech, 2005. http://hdl.handle.net/10919/28791.

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One goal of systems biology is to predict and modify the behavior of biological networks by accurately monitoring and modeling their responses to certain types of perturbations. The construction of mathematical models based on observation of these responses, referred to as reverse engineering, is an important step in elucidating the structure and dynamics of such networks. Continuous models, described by systems of differential equations, have been used to reverse engineer biochemical networks. Of increasing interest is the use of discrete models, which may provide a conceptual description of the network. In this dissertation we introduce a discrete modeling approach, rooted in computational algebra, to reverse-engineer networks from experimental time series data. The algebraic method uses algorithmic tools, including Groebner-basis techniques, to build the set of all discrete models that fit time series data and to select minimal models from this set. The models used in this work are discrete-time finite dynamical systems, which, when defined over a finite field, are described by systems of polynomial functions. We present novel reverse-engineering algorithms for discrete models, where each algorithm is suitable for different amounts and types of data. We demonstrate the effectiveness of the algorithms on simulated networks and conclude with a description of an ongoing project to reverse-engineer a real gene regulatory network in yeast.
Ph. D.

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Mathai, Pramod P. "Application of reduced order modeling techniques to problems in heat conduction, isoelectric focusing and differential algebraic equations." College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8997.

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Thesis (Ph.D.) -- University of Maryland, College Park, 2008.
Thesis research directed by: Dept. of Aerospace Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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Szydlarski, Mikolaj. "Algebraic Domain Decomposition Methods for Darcy flow in heterogeneous media." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2010. http://tel.archives-ouvertes.fr/tel-00550728.

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Afin de répondre aux besoins de l'industrie pétrolière d'une description plus fine de la géométrie et des propriétés pétrophysiques des bassins et des réservoirs, la simulation numérique des écoulements en milieux poreux doit évoluer vers des algorithmes plus performants et plus robustes vis à vis de la taille des simulations, de la complexité des maillages et des hétérogénéités du milieu poreux. Les méthodes de décomposition de domaine constituent une alternative aux méthodes multigrilles et pourraient permettre de lever les difficultés précédentes en terme de robustesse et d'efficacité sur architectures parallèles. Elles sont par nature plus adaptées au calcul parallèle et sont plus robustes en particulier lorsque les sous domaines sont résolus par des méthodes directes. Elles permettent aussi de traiter dans un cadre unique les couplages de modèles comme les puits ou les failles conductrices et s'étendent au cas des systèmes couplés. Le travail de thèse traite plus particulièrement de méthodes définies au niveau algébrique. On ne suppose pas avoir une connaissance préalable du problème continu dont la matrice provient. On n'a pas non plus accés aux matrices avant assemblage. Ce manque d'informations a priori rend plus difficile la construction de méthodes efficaces. On propose deux nouvelles méthodes de construction de méthodes de décomposition de domaine au niveau algébrique: la construction de conditions d'interface optimisées et d'une grille grossière. Ce dernier point est particulièrement important pour avoir des méthodes robustes vis à vis du nombre des sous-domaines. Les méthodes sont adaptatives et basées sur l'analyse de l'espace de Krylov généré durant les premières itérations de la méthode de Schwarz classique. A partir des vecteurs de Ritz correspondant aux plus basses valeurs propres, on construit des conditions d'interface et des grilles grossières qui annihilent l'erreur sur ces composantes. Les méthodes ont été testées sur des calculateurs parallèles pour des matrices issues de la simulation de milieux poreux.

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Kipps, Mark Rew. "A modular approach to modeling an isolated power system on a finite voltage bus using a differential algebraic equation solving routine." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1994. http://handle.dtic.mil/100.2/ADA281036.

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Bernardos, Barreda Luis Francisco. "Modélisation de la transition vers la turbulence d'une couche limite décollée Algebraic Nonlocal Transition Modeling of Laminar Separation Bubbles Using k−ω Turbulence Models Prediction of Separation-Induced Transition on the SD7003 Airfoil Using Algebraic Transition Triggering." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS184.

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Le but de cette thèse est de proposer des modèles qui améliorent la précision des prévisions RANS des bulbes de décollement laminaire. Dans un premier temps, des données de simulations numériques "haute-fidélité'' sur une configuration de référence ont été exploitées afin de comprendre les défauts des modèles existants. À partir de cette analyse, deux problèmes majeurs ont été mis en évidence : les modèles existants ne produisent pas de turbulence à un rythme suffisamment élevé dans la région transitionnelle décollée, et en général ils manquent de diffusivité dans la région située juste en aval du bulbe. Dans un deuxième temps, un ensemble de modèles ont été proposés qui corrigent les défauts observés. Ces modèles, nommés LSTT (Laminar Separation Transition Triggering), permettent à plusieurs modèles RANS existants de produire de la turbulence à un taux adéquat dans la région transitionnelle, améliorant ainsi notablement la précision de la prévision du bulbe de décollement et de la couche limite en aval de ce dernier. Enfin, une évaluation complète des modèles LSTT a été effectuée en les appliquant à différentes géométries de profils aérodynamiques de type drone, éolienne, turbine et hélicoptère. En général, on observe que les modèles LSTT améliorent la précision des prévisions RANS des bulbes de décollement laminaire et servent à capturer l'influence de l'angle d'incidence, du nombre de Reynolds et du taux de turbulence en amont
The objective of this thesis was to propose new models that improve the precision of RANS predictions of LSB. Firstly, high-fidelity numerical data was analyzed in order to understand the precision defects of existing models. From this analysis, two main defects were identified: existing models do not produce turbulence at a sufficient rate in the transitional region, and they generally lack diffusion right downstream of the LSB. Secondly, a set of models were proposed that correct the defects. The new approach, named laminar separation transition triggering (LSTT), allow several existing RANS models for enhanced production of turbulence in the transitional region, which improves the precision of the prediction of the LSB topology and the overall flowfield. Lastly, a large assessment of LSTT models was undertaken using different airfoils of drones, wind turbines, tubojet engines and helicopters. In general, it was found that LSTT models improve the precision of the RANS predictions of LSB and can be used to predict the influence on angle-of-attack, Reynolds number and turbulence intensity

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Moberg, Stig. "On Modeling and Control of Flexible Manipulators." Licentiate thesis, Linköping University, Linköping University, Automatic Control, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-10463.

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Industrial robot manipulators are general-purpose machines used for industrial automation in order to increase productivity, flexibility, and quality. Other reasons for using industrial robots are cost saving, and elimination of heavy and health-hazardous work. Robot motion control is a key competence for robot manufacturers, and the current development is focused on increasing the robot performance, reducing the robot cost, improving safety, and introducing new functionalities. Therefore, there is a need to continuously improve the models and control methods in order to fulfil all conflicting requirements, such as increased performance for a robot with lower weight, and thus lower mechanical stiffness and more complicated vibration modes. One reason for this development of the robot mechanical structure is of course cost-reduction, but other benefits are lower power consumption, improved dexterity, safety issues, and low environmental impact.

This thesis deals with three different aspects of modeling and control of flexible, i.e., elastic, manipulators. For an accurate description of a modern industrial manipulator, the traditional flexible joint model, described in literature, is not sufficient. An improved model where the elasticity is described by a number of localized multidimensional spring-damper pairs is therefore proposed. This model is called the extended flexible joint model. This work describes identification, feedforward control, and feedback control, using this model.

The proposed identification method is a frequency-domain non-linear gray-box method, which is evaluated by the identification of a modern six-axes robot manipulator. The identified model gives a good description of the global behavior of this robot.

The inverse dynamics control problem is discussed, and a solution methodology is proposed. This methodology is based on a differential algebraic equation (DAE) formulation of the problem. Feedforward control of a two-axes manipulator is then studied using this DAE approach.

Finally, a benchmark problem for robust feedback control of a single-axis extended flexible joint model is presented and some proposed solutions are analyzed.

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Singh, Manjeet. "Mathematical Models, Heuristics and Algorithms for Efficient Analysis and Performance Evaluation of Job Shop Scheduling Systems Using Max-Plus Algebraic Techniques." Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1386087325.

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Mahmood, Imran. "A Verification Framework for Component Based Modeling and Simulation : “Putting the pieces together”." Doctoral thesis, KTH, Programvaruteknik och Datorsystem, SCS, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-116678.

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The discipline of component-based modeling and simulation offers promising gains including reduction in development cost, time, and system complexity. This paradigm is very profitable as it promotes the use and reuse of modular components and is auspicious for effective development of complex simulations. It however is confronted by a series of research challenges when it comes to actually practice this methodology. One of such important issue is Composability verification. In modeling and simulation (M&S), composability is the capability to select and assemble components in various combinations to satisfy specific user requirements. Therefore to ensure the correctness of a composed model, it is verified with respect to its requirements specifications.There are different approaches and existing component modeling frameworks that support composability however in our observation most of the component modeling frameworks possess none or weak built-in support for the composability verification. One such framework is Base Object Model (BOM) which fundamentally poses a satisfactory potential for effective model composability and reuse. However it falls short of required semantics, necessary modeling characteristics and built-in evaluation techniques, which are essential for modeling complex system behavior and reasoning about the validity of the composability at different levels.In this thesis a comprehensive verification framework is proposed to contend with some important issues in composability verification and a verification process is suggested to verify composability of different kinds of systems models, such as reactive, real-time and probabilistic systems. With an assumption that all these systems are concurrent in nature in which different composed components interact with each other simultaneously, the requirements for the extensive techniques for the structural and behavioral analysis becomes increasingly challenging. The proposed verification framework provides methods, techniques and tool support for verifying composability at its different levels. These levels are defined as foundations of a consistent model composability. Each level is discussed in detail and an approach is presented to verify composability at that level. In particular we focus on theDynamic-Semantic Composability level due to its significance in the overallcomposability correctness and also due to the level of difficulty it poses in theprocess. In order to verify composability at this level we investigate the application ofthree different approaches namely (i) Petri Nets based Algebraic Analysis (ii) ColoredPetri Nets (CPN) based State-space Analysis and (iii) Communicating SequentialProcesses based Model Checking. All the three approaches attack the problem ofverifying dynamic-semantic composability in different ways however they all sharethe same aim i.e., to confirm the correctness of a composed model with respect to itsrequirement specifications. Beside the operative integration of these approaches inour framework, we also contributed in the improvement of each approach foreffective applicability in the composability verification. Such as applying algorithmsfor automating Petri Net algebraic computations, introducing a state-space reductiontechnique in CPN based state-space analysis, and introducing function libraries toperform verification tasks and help the molder with ease of use during thecomposability verification. We also provide detailed examples of using each approachwith different models to explain the verification process and their functionality.Lastly we provide a comparison of these approaches and suggest guidelines forchoosing the right one based on the nature of the model and the availableinformation. With a right choice of an approach and following the guidelines of ourcomponent-based M&S life-cycle a modeler can easily construct and verify BOMbased composed models with respect to its requirement specifications.

Overseas Scholarship for PHD in selected Studies Phase II Batch I

Higher Education Commision of Pakistan.

QC 20130224

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Uliana, Murilo. "Soluções de equação de balanço populacional pelo método de classes com aplicação a processo de polimerização em suspensão." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/3/3137/tde-09082007-181813/.

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Neste trabalho estudou-se a modelagem matemática de processo de polimerização em suspensão de estireno, envolvendo a equação de balanço populacional para a previsão da distribuição de tamanhos de partículas. Neste problema os termos referentes aos processos de quebra e coalescência de partículas são importantes. Foram estudados métodos de solução da equação de balanço populacional e a solução desta equação, para o problema de polimerização em suspensão, foi obtida pelo método discretização do domínio em classes, usando a técnica dos pivôs fixos. Foram investigados os efeitos no número de elementos de discretização (número de classes) e o modo de modelar a distribuição inicial de tamanhos de gotas de monômero, quando esta não é medida experimentalmente. Neste caso, adotou-se uma distribuição normal com média elevada e variância pequena, arbitrárias, e simulou-se o processo de agitação com ocorrência de quebra e coalescência, até que se atingisse uma distribuição que não variasse com o tempo. Esta distribuição era usada então como condição inicial para a simulação do processo. Os resultados da simulação foram validados por comparação com dados experimentais referentes à evolução da distribuição de tamanhos das partículas, obtidos da literatura. O primeiro conjunto de dados foi referente ao processo de dispersão de gotas de estireno em água (sem ocorrência de polimerização). O segundo conjunto de dados foi referente ao processo de polimerização em suspensão de estireno em reator de batelada de escala de laboratório, nas quais os efeitos da velocidade de agitação, quantidade de agente estabilizante e fração de fase dispersa foram estudados. Em ambos os casos, o modelo representou corretamente o comportamento dos dados experimentais.
The mathematical modeling of suspension polymerization of styrene accounting for the population balance equation to predict the dynamic behavior of particle size distribution was studied. In this process, the population balance is determined by the rates of breakage and coalescence. Different methods for solving population balance (BP) equations were studied and, for the case of suspension polymerization, the numerical solution was obtained using the discretized BP by the method of classes and the fixed pivot technique. The effect of the number of discretization elements (number of classes) was investigated. In order to model the initial particle size distribution (PSD), which was not measured experimentally, an initial normal distribution with high average and low variance was assumed and the agitation process with breakage and coalescence was simulated until a constant PSD is reached. This PSD is then used as the initial condition for the process simulation. Simulation results were validated by comparison with experimental data taken from the literature. The first data set involves the dispersion process of styrene droplets in water, without polymerization. The second data set refers to the process of suspension polymerization of styrene carried out in a laboratory-scale batch reactor, in which the effects of agitation speed, amount of stabilizer (surface-active agent) and disperse phase holdup were studied. In both cases, the model was able to represent correctly the trends of the experimental data.

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Renker, Gerrit. "An algebraic framework for constraint problem modelling." Thesis, Robert Gordon University, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.423325.

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Garcia-Puente, Luis David. "Algebraic Geometry of Bayesian Networks." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11133.

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We develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry--statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification, in terms of primary decomposition of polynomial ideals, is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties. Moreover, a complete algebraic classification, in terms of generating sets of polynomial ideals, is given for Bayesian networks on at most three random variables and one hidden variable. The relevance of these results for model selection is discussed.
Ph. D.

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Lazeroms, Werner. "Explicit algebraic turbulence modelling in buoyancy-affected shear flows." Licentiate thesis, KTH, Turbulens, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-122468.

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Turbulent flows affected by buoyancy forces occur in a large amount of applica-tions, from heat transfer in industrial settings to the effects of stratification inEarth’s atmosphere. The two-way coupling between the Reynolds stresses andthe turbulent heat flux present in these flows poses a challenge in the searchfor an appropriate turbulence model. The present thesis addresses this issueusing the class of explicit algebraic models. Starting from the transport equations for the Reynolds stresses and the tur-bulent heat flux, an explicit algebraic framework is derived for two-dimensionalmean flows under the influence of buoyancy forces. This framework consistsof a system of 18 linear equations, the solution of which leads to explicit ex-pressions for the Reynolds-stress anisotropy and a scaled heat flux. The modelis complemented by a sixth-order polynomial equation for a quantity relatedto the total production-to-dissipation ratio of turbulent kinetic energy. Sinceno exact solution to such an equation can be found, various approximationmethods are presented in order to obtain a fully explicit algebraic model. Several test cases are considered in this work. Special attention is given tothe case of stably stratified parallel shear flows, which is also used to calibratethe model parameters. As a result of this calibration, we find a critical Richard-son number of 0.25 in the case of stably stratified homogeneous shear flow,which agrees with theoretical results. Furthermore, a comparison with directnumerical simulations (DNS) for stably stratified channel flow shows an excel-lent agreement between the DNS data and the model. Other test cases includeunstably stratified channel flow and vertical channel flow with either mixed con-vection or natural convection, and a reasonably good agreement between themodel and the scarcely available, low-Reynolds-number DNS is found. Com-pared to standard eddy-viscosity/eddy-diffusivity models, an improvement inthe predictions is observed in all cases. For each of the aforementioned test cases, model coefficients and additionalcorrections are derived separately, and a general formulation has yet to be given.Nevertheless, the results presented in this thesis have the potential of improvingthe prediction of buoyancy-affected turbulence in various application areas.

QC 20130530

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Ball, J. K. "An algebraic approach to the theory of phase transitions." Thesis, University of Nottingham, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330162.

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Scott, Erin G. "Process algebra with layers : a language for multi-scale integration modelling." Thesis, University of Stirling, 2016. http://hdl.handle.net/1893/23516.

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Multi-scale modelling and analysis is becoming increasingly important and relevant. Analysis of the emergent properties from the interactions between scales of multi-scale systems is important to aid in solutions. There is no universally adopted theoretical/computational framework or language for the construction of multi-scale models. Most modelling approaches are specific to the problem that they are addressing and use a hybrid combination of modelling languages to model specific scales. This thesis addresses if process algebra can offer a unique opportunity in the definition and analysis of multi-scale models. In this thesis the generic Process Algebra with Layers (PAL) is defined: a language for multi-scale integration modelling. This work highlights the potential of process algebra to model multi-scale systems. PAL was designed based on features and challenges found from modelling a multi-scale system in an existing process algebra. The unique features of PAL are the layers: Population and Organism. The novel language modularises the spatial scales of the system into layers, therefore, modularising the detail of each scale. An Organism can represent a molecule, organelle, cell, tissue, organ or any organism. An Organism is described by internal species. An internal species, dependent on the scale of the Organism, can also represent a molecule, organelle, cell, tissue, organ or any organism. Populations hold specific types of Organism, for example, life stages, cell phases, infectious states and many more. The Population and Organism layers are integrated through mirrored actions. This novel language allows the clear definition of scales and interactions within and between these scales in one model. PAL can be applied to define a variety of multi-scale systems. PAL has been applied to two unrelated multi-scale system case studies to highlight the advantages of the generic novel language. Firstly the effects of ocean acidification on the life stages of the Pacific oyster. Secondly the effects of DNA damage from cancer treatment on the length of a cell cycle and cell population growth.

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Richardson, G. A. "Algebraic stress modelling for shock-wave/turbulent boundary-layer interactions." Thesis, Cranfield University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267213.

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Aleem, Hosam Abdel. "An algebraic approach to modelling the regulation of gene expression." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/an-algebraic-approach-to-modelling-the-regulation-of-gene-expression(d5d400b5-690e-4f32-9fd6-c80e4db455f3).html.

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Biotechnology is witnessing a remarkable growth evident both in the types of new products and in the innovative new processes developed. More efficient process design, optimisation and troubleshooting can be achieved through a better understanding of the underlying biological processes inside the cell; a key one of which is the regulation of gene expression. For engineers such understanding is attained through mathematical modelling, and the most commonly used models of gene expression regulation are those based on differential equations, as they give quantitative results. However, those results are undermined by several difficulties including the large number of parameters some of which, such as kinetic constants, are difficult to determine. This prompted the development of qualitative models, most notably Boolean models, based on the assumption that biological variables are binary in nature, e.g. a gene can be on or off and a chemical species present or absent. There are situations however, where different actions take place in the cell at different threshold values of the biological variables, and hence the binary assumption no longer holds.The purpose of this study was to develop a method for modelling gene regulatory functions where the variables can be thought of as taking more than two discrete values. A method was developed, where, with the appropriate assumptions the biological variables can be regarded as elements of an algebraic structure known as a finite field, in which case the regulatory function can be considered as a function on such a field.The formulation was adopted from electronic engineering, and leads to a polynomial known as the Reed-Muller expansion of the discrete function.The model was first developed for the more familiar binary case. It was given three different algebraic interpretations each enabling the study of a different biological problem, albeit related to gene regulation. The first interpretation is as a function on a Boolean algebra, but using the Exclusive OR (XOR) operation instead of the OR operation. The discriminating superiority of the XOR allows a more efficient determination of the gene regulatory function from the data, a problem known as reverse engineering.The second interpretation is as a polynomial on a finite field, where analogy with the Taylor series expansion of a real valued function allowed the coefficients of the expansion to be thought of as conveying sensitivity information. Furthermore a method was devised to detect mutation in the cell by regarding the problem as detecting a fault in a digital circuit.The third interpretation is as a transform on a discrete function space, which was demonstrated to be useful in synthetic biology design. The method was then extended to the multiple-valued case and demonstrated with modelling the gene regulation of a well known example system, the bacteriophage lambda.

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Hadj, Said Yanis. "Prise en compte de la complexité de modélisation dans la gestion énergétique des bâtiments." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAT121/document.

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Du fait de son impact énergétique, la gestion énergétique dans le bâtiment est devenu un enjeu majeur ses dernières années, qu'il s'agisse d'encourager la sobriété énergétique ou de s'adapter aux besoins des réseaux énergétiques. Différents travaux de recherche ont conduit à des gestionnaires énergétiques souvent dotés de capacités d'anticipation. Les premiers résultats, bien qu'encourageants, n'envisagent pas la complexité tant du fait nombre d'éléments que de la diversité des applications de gestion énergétique.Cette thèse propose d'apporter des éléments de solution à la problématique de complexité. Les travaux ont démarré par l'analyse du gestionnaire énergétique GHomeTech et son adaptation au prototype de bâtiment complexe CANOPEA. Les problématiques de composition sont explorées. Une solution favorisant la réutilisabilité d'éléments de modèles, l'agrégation et la transformation vers des modèles d'optimisation de type programmation linéaire en nombres entiers (PLNE), est proposée. L'outil résultant a été validé sur le projet CANOPEA.La gestion énergétique ne se limite pas à l'optimisation PLNE. Différentes natures d'applications permettent d'offrir d'autres services : l'estimation paramétrique de modèles pour simplifier la configuration des gestionnaires énergétiques, la simulation pour la validation et la prédiction fonction de scénarios définis par exemple. Cette autre dimension de la complexité est abordée dans un second volet du manuscrit. Des solutions de réécriture automatique de modèles sont proposées grâce à des manipulations symboliques permettant différents types de transformation. Plusieurs exemples de génération automatique de modèles applicatifs sont présentés
Energy management for building has become a major issue this last decade because of its energy impact. Building energy management reduces energy wastes and enable a better matching between energy needs and grid capabilities. Different types of energy management systems are proposed in scientific literature, most of them with anticipation capacities.The first results do not really consider the complexity issue coming from the number of modeling elements and also coming from the diversity of energy management applications.This thesis proposes elements of solution to the complexity problem. The work started by analyzing the energy management system 'GHomeTech' and its adaptation to the complex building prototype CANOPEA. The issue of composition from elementary models is explored. A solution is proposed; it enables the reusability of elementary models. Aggregation and transformation into mixed integer linear programming optimization models is presented. The resulting tool has been validated on the CANOPEA project.Energy management is not limited to MILP optimization. Different types of applications are also used to provide other services: parametric estimation models to simplify the configuration of energy management systems, simulation for validation and prediction depending on pre-defined scenarios for example. This other dimension of complexity is discussed in a second part of the manuscript. Solutions for automatic rewriting of models are detailed. It relies on symbolic manipulations in different types of processing. Several examples of applications illustrating the automatic generation of models are presented

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Minárik, Michal. "Modelování elektrických obvodů s využitím diferenciálního počtu." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2010. http://www.nusl.cz/ntk/nusl-237269.

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This master's thesis deals with modeling of linear electrical circuits through the differential algebraical equation systems. It describes methods of numerical solving, discusses the need of algebraical conversions and possibility of minimalization through the use of parasitic components. In addition, it involves the design and implementation of extension of available simulation tool.

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Bittencourt, Olga Regina Fradico de Oliveira. "Algebraic modelling of spatiotemporal objects: understanding change in the Brazilian Amazon." Instituto Nacional de Pesquisas Espaciais, 2009. http://urlib.net/sid.inpe.br/mtc-m18@80/2009/07.28.13.46.

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Essa tese propõe uma álgebra, a Álgebra GeoEspacial, para descrever a evolução de objetos espaço-temporais. Ela é composta de um conjunto de operações, axiomas e regras definidas para cada aplicação. Especificamente, nós trabalhamos com objetos evolutivos, que são objetos que evoluem alterando suas bordas e seus atributos. Eles ocorrem, por exemplo, em casos de mudança de uso e cobertura do solo em áreas urbanas e rurais. Nós também propomos operadores para tratar histórias de evolução de um conjunto de objetos evolutivos, assim como tratar as histórias individuais de cada objeto no conjunto. Nós aplicamos a álgebra para analisar séries temporais de áreas que sofreram mudança de uso e cobertura do solo Amazônia. Nossos resultados mostram que acompanhando a evolução dos objetos, somos capazes de descobrir e quantificar relevantes informações a respeito dos padrões de desflorestamento.
This thesis proposes an algebra to describe how spatiotemporal objects evolve, named geospatial algebra, and a model to apply it. This algebra is composed of a set of operations, axioms and rules defined by the application. Specifically, we handle evolving objects, which are objects that evolve by changing their boundaries and attributes. These objects appear in cases of land change in rural and urban areas. We also propose operators to track the history of a set of evolving objects as well as the individual history of each object in the set. In addition, we developed a system to use the algebra and analyze time series of deforestation objects in three case studies of land use and land cover in the Brazilian Amazon. Our results show that, by tracking the object evolution, we can discover and quantify important issues related to the patterns of deforestation in the Brazilian Amazon.

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Rewitzky, Ingrid Moira. "Modelling the algebra of weakest preconditions." Master's thesis, University of Cape Town, 1991. http://hdl.handle.net/11427/23363.

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In expounding the notions of pre- and postconditions, of termination and nontermination, of correctness and of predicate transformers I found that the same trivalent distinction played a major role in all contexts. Namely: Initialisation properties: An execution of a program always, sometimes or never starts from an initial state. Termination/nontermination properties: If it starts, the execution always, sometimes or never terminates. Clean-/messy termination properties: A terminating execution always, sometimes or never terminates cleanly. Final state properties: All, some or no final states of α from s have a given property.

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Bradley, Jeremy Thomas. "Towards reliable modelling with stochastic process algebras." Thesis, University of Bristol, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302166.

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Mitic, Peter. "Computer algebra techniques in object-oriented mathematical modelling." Thesis, Open University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.286921.

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Rasam, Amin. "Anisotropy-resolving subgrid-scale modelling using explicit algebraic closures for large eddy simulation." Doctoral thesis, KTH, Turbulens, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-142401.

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The present thesis deals with the development and performance analysis ofanisotropy-resolving models for the small, unresolved scales (”sub-grid scales”,SGS) in large eddy simulation (LES). The models are characterised by a descriptionof anisotropy by use of explicit algebraic models for both the subgridscale(SGS) stress tensor (EASSM) and SGS scalar flux vector (EASSFM). Extensiveanalysis of the performance of the explicit algebraic SGS stress model(EASSM) has been performed and comparisons made with the conventionalisotropic dynamic eddy viscosity model (DEVM). The studies include LES ofplane channel flow at relatively high Reynolds numbers and a wide range ofresolutions and LES of separated flow in a channel with streamwise periodichill-shaped constrictions (periodic hill flow) at coarse resolutions. The formersimulations were carried out with a pseudo-spectral Navier–Stokes solver, whilethe latter simulations were computed with a second-order, finite-volume basedsolver for unstructured grids. The LESs of channel flow demonstrate that theEASSM gives a good description of the SGS anisotropy, which in turn gives ahigh degree of resolution independence, contrary to the behaviour of LES predictionsusing the DEVM. LESs of periodic hill flow showed that the EASSMalso for this case gives significantly better flow predictions than the DEVM.In particular, the reattachment point was much better predicted with the EASSMand reasonably well predicted even at very coarse resolutions, where theDEVM is unable to predict a proper flow separation.The explicit algebraic SGS scalar flux model (EASSFM) is developed toimprove LES predictions of complex anisotropic flows with turbulent heat ormass transfer, and can be described as a nonlinear tensor eddy diffusivity model.It was tested in combination with the EASSM for the SGS stresses, and itsperformance was compared to the conventional dynamic eddy diffusivity model(DEDM) in channel flow with and without system rotation in the wall-normaldirection. EASSM and EASSFM gave predictions of high accuracy for meanvelocity and mean scalar fields, as well as stresses and scalar flux components.An extension of the EASSM and EASSFM, based on stochastic differentialequations of Langevin type, gave further improvements. In contrast to conventionalmodels, these extended models are able to describe intermittent transferof energy from the small, unresolved scales, to the resolved large ones.The present study shows that the EASSM/EASSFM gives a clear improvementof LES of wall-bounded flows in simple, as well as in complex geometriesin comparison with simpler SGS models. This is also shown to hold for a widerange of resolutions and is particularly accentuated for coarse resolution. The advantages are also demonstrated both for high-order numerical schemes andfor solvers using low-order finite volume methods. The models therefore havea clear potential for more applied computational fluid mechanics.

QC 20140304

Explicit algebraic sub-grid scale modelling for large-eddy simulations

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Imaev, Aleksey A. "Hierarchical Modeling of Manufacturing Systems Using Max-Plus Algebra." Ohio University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1257871858.

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Gerdin, Markus. "Identification and Estimation for Models Described by Differential-Algebraic Equations." Doctoral thesis, Linköping : Department of Electrical Engineering, Linköpings universitet, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7600.

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Viana, Filho João Pereira. "Ensino e aprendizagem de função: uma metanálise de dissertações brasileiras sobre modelagem matemática produzidas entre 1987 e 2010." Pontifícia Universidade Católica de São Paulo, 2012. https://tede2.pucsp.br/handle/handle/10919.

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Made available in DSpace on 2016-04-27T16:57:17Z (GMT). No. of bitstreams: 1 Joao Pereira Viana Filho.pdf: 1271947 bytes, checksum: 208d347d897241981c97d9a49aefc09d (MD5) Previous issue date: 2012-06-20
This has been written to investigate possible contributions of Mathematical modeling to teaching functions on Basic Education. In order to do this, investigations were aimed on answering the main question in the research: what are the contributions from researches which use Mathematical modeling, and what possibilities and difficulties come from this teaching and learning methodology or strategy to introduce or teach functions on both Ensino Fundamental (in Brazil it is from 1st grade to 9th grade) and Médio (10th to 12th grade)? A meta-analysis has been developed for this, and, in this case, we understand it according to Fiorentini and Lorenzato s (2009) proposal: a systematic review of other researches aiming to make a critical evaluation about them, with the intention of making a documental study, to summarize ideas, investigate contributions, classify and find research categories, find similarities and point possible differences or peculiarities between research results. The analysis has been done by following Severino s (2002) guidelines to reading, analyzing and interpreting texts, and it was conducted on seven Master s Degrees produced in Brazil, which have approached the theme learning and teaching functions with Mathematical modeling. Five of those are Professionalizing Masters (Mestrado Profissionalizante) and two of them are Academic Masters (Mestrado Acadêmico). Three of them are focused on Ensino Fundamental and four of them are focused on Ensino Médio. Those researches were found in and selected from the CAPES abstracts database. On research results, we present our identification and classifying criteria: eight categories for conception of Mathematical modeling, eight ways this can contribute to function teaching, six types of possibilities and five types of difficulties found on implementation and development activities and actions in the classroom, and six types of possible contributions that Mathematical modeling, when adopted as a function teaching and learning methodology or strategy in Ensino Fundamental and Médio, can bring. The results from the search and analysis of the theses have also pointed to the necessity of more research on themes related to the approach of functions in Basic Education (Educação Básica, from Preschool to 9th grade), using Mathematical modeling; specially Doctoral degrees (Doutorados)
Este trabalho teve como objetivo investigar possíveis contribuições da modelagem matemática para o ensino de função na Educação Básica. Para atender tal objetivo, as investigações foram delineadas de forma a responder a questão de pesquisa: o que as pesquisas que utilizam a modelagem matemática em sala de aula, trazem como contribuição, e apontam como possibilidades e dificuldades do uso dessa metodologia ou estratégia de ensino e aprendizagem para introduzir ou ensinar função no Ensino Fundamental e Médio? Foi desenvolvida, para isso, uma metanálise que aqui é entendida, segundo propõem Fiorentini e Lorenzato (2009), como sendo uma revisão sistemática de outras pesquisas, visando realizar uma avaliação crítica sobre elas, quando se intenciona realizar um estudo de caráter documental, com o objetivo de sintetizar ideias, investigar contribuições, classificar e encontrar categorias de pesquisa, encontrar similaridades e apontar possíveis divergências ou particularidades entre resultados de pesquisas. A análise seguiu as diretrizes para a leitura, análise e interpretação de textos, propostas por Severino (2002) e foi feita sobre sete dissertações de mestrado produzidas no Brasil, as quais abordaram o tema ensino e aprendizagem de função com modelagem matemática. Dessas, cinco são de Mestrado Profissionalizante e duas de Mestrado Acadêmico, em que três delas dedicaram suas investigações ao Ensino Fundamental e quatro as dedicaram ao Ensino Médio. As pesquisas foram levantadas e selecionadas a partir do Banco de resumos da CAPES. Nos resultados de pesquisa, apresentamos, segundo nossos critérios de identificação e classificação: oito categorias de concepções de modelagem matemática, oito maneiras pelas quais pode contribuir para o ensino de função, seis tipos de possibilidades e cinco tipos de dificuldades encontradas na implementação e no desenvolvimento das atividades e das ações em sala de aula, além de seis tipos de possíveis contribuições que a modelagem matemática, quando adotada como uma metodologia ou estratégia de ensino e aprendizagem de função no Ensino Fundamental e Médio pode trazer. Os resultados da busca e análise dos trabalhos, apontaram, também, para a necessidade de mais pesquisas sobre temas relacionados à abordagem das funções na Educação Básica, por meio da modelagem matemática, em especial, de pesquisas de doutorado

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Whitbrook, Amanda Marie. "The efficient numerical solution of differential/algebraic boundary value problems arising in detonation modelling." Thesis, Nottingham Trent University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.388868.

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Pua, Chai Seng. "Process algebra approach to parallel DBMS performance modelling." Thesis, Heriot-Watt University, 1999. http://hdl.handle.net/10399/1262.

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Voiculescu, Irina Dana. "Implicit function algebra in set-theoretic geometric modelling." Thesis, University of Bath, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.392056.

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Iakymchuk, Roman [Verfasser]. "Performance modeling and prediction for linear algebra algorithms / Roman Iakymchuk." Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2012. http://d-nb.info/1026308690/34.

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Deddi, Hafsa. "Dualité géométrique et relations de correspondance entre courbes primales et duales." Phd thesis, Université Joseph Fourier (Grenoble), 1997. http://tel.archives-ouvertes.fr/tel-00004935.

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Cette thèse est une étude de base qui traite de la transformation de la dualité géométrique entre un point et un hyperplan d'un espace affine. Une étape indispensable est alors d'établir une définition rigoureuse de la dualité géométrique ainsi que ses propriétés et caractéristiques. Cette notion de dualité peut se généraliser pour toute forme géométrique décrite à l'aide d'une famille de points ou d'hyperplans. Ainsi une courbe duale d'une courbe paramétrique plane est définie comme enveloppe d'une famille de droites. Ces courbes duales sont ensuite analysées pour trouver des relations de correspondances entre une courbe paramétrique et son image duale. En effet, des correspondances d'interpolation et de convexité sont établies et des exemples de courbes de Bézier duales sont illustrés. On fait ensuite une étude complète des correspondances de singularités entre courbes primales et duales. Enfin, une généralisation de la dualité géométrique à l'aide d'une matrice symétrique inversible a permis d'associer à une courbe paramétrique quelconque une famille de courbes duales dépendant de la matrice symétrique considérée.

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Wang, Xuyan. "Landscape dynamic modelling with vector map algebra in GIS /." [St. Lucia, Qld.], 2004. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe18161.pdf.

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Degasperi, Andrea. "Multi-scale modelling of biological systems in process algebra." Thesis, University of Glasgow, 2011. http://theses.gla.ac.uk/2946/.

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There is a growing interest in combining different levels of detail of biological phenomena into unique multi-scale models that represent both biochemical details and higher order structures such as cells, tissues or organs. The state of the art of multi-scale models presents a variety of approaches often tailored around specific problems and composed of a combination of mathematical techniques. As a result, these models are difficult to build, compose, compare and analyse. In this thesis we identify process algebra as an ideal formalism to multi-scale modelling of biological systems. Building on an investigation of existing process algebras, we define process algebra with hooks (PAH), designed to be a middle-out approach to multi-scale modelling. The distinctive features of PAH are: the presence of two synchronisation operators, distinguishing interactions within and between scales, and composed actions, representing events that occur at multiple scales. A stochastic semantics is provided, based on functional rates derived from kinetic laws. A parametric version of the algebra ensures that a model description is compact. This new formalism allows for: unambiguous definition of scales as processes and interactions within and between scales as actions, compositionality between scales using a novel vertical cooperation operator and compositionality within scales using a traditional cooperation operator, and relating models and their behaviour using equivalence relations that can focus on specified scales. Finally, we apply PAH to define, compose and relate models of pattern formation and tissue growth, highlighting the benefits of the approach.

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Lacoursière, Claude. "Ghosts and machines : regularized variational methods for interactive simulations of multibodies with dry frictional contacts." Doctoral thesis, Umeå University, Computing Science, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1143.

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A time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low order integration methods. These are applied to mechanical systems subject to mixed constraints and dry frictional contacts and impacts---machines. The framework includes physics motivated constraint regularization and stabilization schemes. This is done by adding potential energy and Rayleigh dissipation terms in the Lagrangian formulation used throughout. These terms explicitly depend on the value of the Lagrange multipliers enforcing constraints. Having finite energy, the multipliers are thus massless ghost particles. The main numerical stepping method produced with the framework is called SPOOK.

Variational integrators preserve physical invariants globally, exactly in some cases, approximately but within fixed global bounds for others. This allows to product realistic physical trajectories even with the low order methods. These are needed in the solution of nonsmooth problems such as dry frictional contacts and in addition, they are computationally inexpensive. The combination of strong stability, low order, and the global preservation of invariants allows for large integration time steps, but without loosing accuracy on the important and visible physical quantities. SPOOK is thus well-suited for interactive simulations, such as those commonly used in virtual environment applications, because it is fast, stable, and faithful to the physics.

New results include a stable discretization of highly oscillatory terms of constraint regularization; a linearly stable constraint stabilization scheme based on ghost potential and Rayleigh dissipation terms; a single-step, strictly dissipative, approximate impact model; a quasi-linear complementarity formulation of dry friction that is isotropic and solvable for any nonnegative value of friction coefficients; an analysis of a splitting scheme to solve frictional contact complementarity problems; a stable, quaternion-based rigid body stepping scheme and a stable linear approximation thereof. SPOOK includes all these elements. It is linearly implicit and linearly stable, it requires the solution of either one linear system of equations of one mixed linear complementarity problem per regular time step, and two of the same when an impact condition is detected. The changes in energy caused by constraints, impacts, and dry friction, are all shown to be strictly dissipative in comparison with the free system. Since all regularization and stabilization parameters are introduced in the physics, they map directly onto physical properties and thus allow modeling of a variety of phenomena, such as constraint compliance, for instance.

Tutorial material is included for continuous and discrete-time analytic mechanics, quaternion algebra, complementarity problems, rigid body dynamics, constraint kinematics, and special topics in numerical linear algebra needed in the solution of the stepping equations of SPOOK.

The qualitative and quantitative aspects of SPOOK are demonstrated by comparison with a variety of standard techniques on well known test cases which are analyzed in details. SPOOK compares favorably for all these examples. In particular, it handles ill-posed and degenerate problems seamlessly and systematically. An implementation suitable for large scale performance and accuracy testing is left for future work.

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Moench, Megan Elaine. "Modeling literacy strategies for English language learners in mathematics class." Laramie, Wyo. : University of Wyoming, 2009. http://proquest.umi.com/pqdweb?did=1939263631&sid=1&Fmt=2&clientId=18949&RQT=309&VName=PQD.

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Tian, Xijin. "Modeling of planar elastically coupled rigid bodies: Geometric algebra methods and applications." Diss., The University of Arizona, 2002. http://hdl.handle.net/10150/280214.

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This study presents two new, generic methods to modeling planar elastically coupled rigid body systems using Geometric Algebra. The two methods are twist-based potential energy function method and twistor-based potential energy function method. In this research, the rigid body motion in the plane is modeled as a twist or twistor motion in which the rotational motion and translational motion happen simultaneously. The twist is denoted as a bivector using Geometric Algebra which facilitates the notation and computation. A twistor is defined in an intermediate frame half way between two displacement frames. The twistor parameters intuitively represent the relative displacement between two frames. Both twist-based and twistor-based potential energy functions are shown to be frame-independent and body-independent. The kinematics is studied using twist and twistor parameters. The constitutive equations are derived in which the wrench exerted by a pair of elastic bodies is computable given twist or twistor displacements. To analyze large displacements, this study also provides two higher order polynomial potential energy functions of twist parameters and twistor parameters. The polynomial potential energy functions are also shown to be frame-independent and body-independent. They are generally applicable to analyze large displacements of elastically coupled rigid body systems. Several case studies are provided in this research to demonstrate the utility of the presented modeling methods. A micropositioning stage device is modeled as a flexural mechanism with 6 rigid bodies and 7 flexural joints. Simulation is performed using Scilab software. The simulation results show good agreement with actual experimental data. The methods are also applied to simulate the displacement of flexural four-bar linkages with various geometry and various flexural hinges. This case study shows that the presented methods in this research are generic and case-independent. In another case study, the higher order polynomial function method is applied to fit some randomly generated data which demonstrates the generality of the method and the applicability of the method in cases when only experimental data is available without knowing the geometry parameters of a mechanism. The case study of modeling electrostatic potential energy between liquid water molecules using polynomial function of twistor shows the potential utility of the method in the analysis of large displacement. The methods presented in this research have been shown to be generic, easily applicable, and easily computable.

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Yang, Hong. "Modeling and Querying Graph Data." Digital Archive @ GSU, 2009. http://digitalarchive.gsu.edu/cs_diss/34.

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Databases are used in many applications, spanning virtually the entire range of data processing services industry. The data in many database applications can be most naturally represented in the form of a graph structure consisting of various types of nodes and edges with several properties. These graph data can be classified into four categories: social networks describing the relationships between individual person and/or groups of people (e.g. genealogy, network of coauthorship among academics, etc); information networks in which the structure of the network reflects the structure of the information stored in the nodes (e.g. citation network among academic papers, etc); geographic networks, providing geographic information about public transport systems, airline routes, etc; and biological networks (e.g. biochemical networks, neuron network, etc). In order to analyze such networks and obtain desired information that users are interested in, some typical queries must be conducted. It can be seen that many of the query patterns are across multiple categories described above, such as finding nodes with certain properties in a path or graph, finding the distance between nodes, finding sub-graphs, paths enumeration, etc. However, the classical query languages like SQL, OQL are inept dealing with these types of queries needed to be performed in the above applications. Therefore, a data model that can effectively represent the graph objects and their properties, and a query language which empowers users to answer queries across multiple categories are needed. In this research work, a graph data model and a query language are proposed to resolve the issues existing in the current database applications. The proposed graph data model is an object-oriented graph data model which aims to represent the graph objects and their properties for various applications. The graph query language empowers users to query graph objects and their properties in a graph with specified conditions. The capability to specify the relationships among the entities composing the queried sub-graph makes the language more flexible than others.

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Dissertations / Theses on the topic 'Algebraic Modeling'

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