Yes / Large amount of sediment deposits in the reservoir area can cause dam break, which not only leads to an immeasurable loss to the society, but also the sediments from the reservoir can be transported to generate further problems in the downstream catchment. This study aims to investigate the short-to-long term sediment transport and channel meandering process under such a situation. A coupled explicit-implicit technique based on the Euler-Lagrangian method (ELM) is used to solve the hydrodynamic equations, in which both the small and large time steps are used separately for the fluid and sediment marching. The main feature of the model is the use of the Characteristic-Based Split (CBS) method for the local time step iteration to correct the ELM traced lines. Based on the solved flow field, a standard Total Variation Diminishing (TVD) finite volume scheme is applied to solve the sediment transportation equation. The proposed model is first validated by a benchmark dambreak water flow experiment to validate the efficiency and accuracy of ELM modelling capability. Then an idealized engineering dambreak flow is used to investigate the long-term downstream channel meandering process with nonuniform sediment transport. The results showed that both the hydrodynamic and morphologic features have been well predicted by the proposed coupled model. / This research work is supported by Sichuan Science and Technology Support Plan (2014SZ0163), Start-up Grant for the Young Teachers of Sichuan University (2014SCU11056), and Open Research Fund of the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University (SKLH 1409; 1512).

This research effort focuses on large-scale linear programming problems that arise in the context of solving various problems such as discrete linear or polynomial, and continuous nonlinear, nonconvex programming problems, using linearization and branch-and-cut algorithms for the discrete case, and using polyhedral outer-approximation methods for the continuous case. These problems arise in various applications in production planning, location-allocation, game theory, economics, and many engineering and systems design problems. During the solution process of discrete or continuous nonconvex problems using polyhedral approaches, one has to contend with repeatedly solving large-scale linear programming(LP) relaxations. Thus, it becomes imperative to employ an efficient method in solving these problems. It has been amply demonstrated that solving LP relaxations using a simplex-based algorithm, or even an interior-point type of procedure, can be inadequately slow ( especially in the presence of complicating constraints, dense coefficient matrices, and ill-conditioning ) in comparison with a Lagrangian Relaxation approach. With this motivation, we present a practical primal-dual subgradient algorithm that incorporates a dual ascent, a primal recovery, and a penalty function approach to recover a near optimal and feasible pair of primal and dual solutions. The proposed primal-dual approach is comprised of three stages. Stage I deals with solving the Lagrangian dual problem by using various subgradient deflection strategies such as the Modified Gradient Technique (MGT), the Average Direction Strategy (ADS), and a new direction strategy called the Modified Average Direction Strategy (M-ADS). In the latter, the deflection parameter is determined based on the process of projecting the unknown optimal direction onto the space spanned by the current subgradient direction and the previous direction. This projected direction approximates the desired optimal direction as closely as possible using the conjugate subgradient concept. The step-length rules implemented in this regard are the Quadratic Fit Line Search Method and a new line search method called the Directional Derivative Line Search Method in which we start with a prescribed step-length and then ascertain whether to increase or decrease the step-length value based on the right-hand and left-hand derivative information available at each iteration. In the second stage of the algorithm (Stage II), a sequence of updated primal solutions is generated using some convex combinations of the Lagrangian subproblem solutions. Alternatively, a starting primal optimal solution can be obtained using the complementary slackness conditions. Depending on the extent of feasibility and optimality attained, Stage III applies a penalty function method to improve the obtained primal solution toward a near feasible and optimal solution. We present computational experience using a set of randomly generated, structured, linear programming problems of the type that might typically arise in the context of discrete optimization. / Master of Science

Although ships have been used for thousands of years, modeling the dynamics of marine craft has historically been restricted by the complex nature of the hydrodynamics. The principal challenge is that the vehicle motion is coupled to the ambient fluid motion, effectively requiring one to solve an infinite dimensional set of equations to predict the hydrodynamic forces and moments acting on a marine vehicle. Additional challenges arise in parametric modeling, where one approximates the fluid behavior using reduced-order ordinary differential equations. Parametric models are typically required for model-based state estimation and feedback control design, while also supporting other applications including vehicle design and submarine operator training. In this dissertation, Lagrangian mechanics is used to derive nonlinear, parametric motion models for marine craft operating in the presence of a free surface. In Lagrangian mechanics, one constructs the equations of motion for a dynamic system using a system Lagrangian, a scalar energy-like function canonically defined as the system kinetic energy minus the system potential energies. The Lagrangian functions are identified under ideal flow assumptions and are used to derive two sets of equations. The first set of equations neglects hydrodynamic forces due to exogenous fluid motions and may be interpreted as a nonlinear calm water maneuvering model. The second set of equations incorporates effects due to exogenous fluid motion, and may be interpreted as a nonlinear, unified maneuvering and seakeeping model. Having identified the state- and time-dependent model parameters, one may use these models to rapidly simulate surface-affected marine craft maneuvers, enabling model-based control design and state estimation algorithms. / Ph. D.

Ocean surface transport plays a critical role in marine ecosystems, influencing the complex spatiotemporal patterns of both marine species and pollutants. The theory of Lagrangian coherent structures (LCSs) aims to identify fundamental patterns within time-dependent, nonlinear fluid flows. LCSs are material surfaces that act as dividing lines which fluid does not cross for a relevant period of time. LCS theory is still under active development, and there are multiple proposed ways to mathematically determine an LCS. Each proposed mathematical definition aims to capture the same physical properties, and some capture those properties more successfully and consistently than others. Here we examine two proposed definitions from the founder of the LCS field: finite time Lyapunov exponents (FTLEs) and geodesic detection. While geodesic detection was developed as an improvement on FTLEs, FTLEs remain the most popular method for using LCSs as an analytical tool. We apply both methods to a novel application. We analyze ocean surface current data in an area off the coast of central California slated for wind energy development, comparing their relative strengths and weaknesses both in theory and in practice.

In this Thesis, we study some of the classical properties of an extension of the Skyrme model defined by adding a sixth order derivative term to the Lagrangian. In chapter 1, we review the physical as well as the mathematical motivation behind the study of the Skyrme model and in chapter 2, we give a brief summary of various extended Skyrme models that have been proposed over the last few years. We then define a new sixth order Skyrme model by introducing a dimensionless parameter λ that denotes the mixing between the two higher order terms, the Skyrme term and the sixth order term. In chapter 3 we compute numerically the multi-skyrmion solutions of this extended model and show that they have the same symmetries with the usual skyrmion solutions. In addition, we analyse the dependence of the energy and radius of these classical solutions with respect to the coupling constant λ. We compare our results with experimental data and determine whether this modified model can provide us with better theoretical predictions than the original one. In chapter 4, we use the rational map ansatz, introduced by Houghton, Manton and Sutcliffe, to approximate minimum energy multi-skyrmion solutions with B ≤ 9 of the SU(2) model and with B ≤ 6 of the SU(3) model. We compare our results with the ones obtained numerically and show that the rational map ansatz works just as well for the generalised model as for the pure Skyrme model, at least for B ≤ 5. In chapter 5, we use a generalisation of the rational map ansatz, introduced by loannidou, Piette and Zakrzewski, to construct analytically some topologically non-trivial solutions of the extended model in SU(3). These solutions are spherically symmetric and some of them can be interpreted as bound states of skyrmions. Finally, we use the same ansatz to construct low energy configurations of the SU(N) sixth order Skyrme model.

Made available in DSpace on 2014-06-11T19:27:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-03-23Bitstream added on 2014-06-13T19:15:35Z : No. of bitstreams: 1 silva_fm_me_sjrp.pdf: 817059 bytes, checksum: eb6c0e0e69f3687d3831dbbbc3cf6e09 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho consiste numa extensão do estudo de um problema de dimensionamento de lotes com custo de transporte feito por Norden e Velde [53], onde a produção dos itens é transportada, em paletes, para um armazém. O transporte é feito por uma empresa terceirizada sob um contrato com os seguintes custos pré-estabelecidos: um custo fixo de contrato, um custo para o transporte de um determinado volume de paletes e um custo adicional para paletes extras. O problema foi estendido, no presente trabalho, considerando restrições de capacidade e a possibilidade de atrasos no atendimento a demanda. Nosso objetivo é propor um modelo matemático para o problema estendido e desenvolver dois métodos heurísticos de resolução. Tais métodos são baseados em dois tipos de relaxação: relaxação Lagrangiana e relaxação Lagrangiana/Surrogate. Os resultados obtidos pelas heurísticas são comparados com os resultados obtidos pelo pacote de otimização CPLEX 10.0. Além disso, é feita uma comparação entre os métodos heurísticos. / This work consist of an extension of a study of the capacitated lot-sizing problems with transportation cost by Norden and Velde [53], where the production of itens is transported into pallets to an warehouse. The transportation is executed by another company, under a contract with the following transportation cost established: a fixed contract cost, a transportation cost for determined quantity of pallets and an additional cost for extra pallets. The problem was extended, in this work, considering capacity constraint and backlogging. Our objective is to propose a mathematical model for the extended problem and to develop two heuristics methods of resolution. The methods are based on two types of relaxation: Lagrangian relaxation and Lagrangian/Surrogate relaxation. The results obtained by heuristics are compared with the results obtained by CPLEX 10.0. Furthermore, a comparison between the heuristics is made.

Orientadores: Carlos Eduardo Durán Fernandez, Marcos Benevenutto Jardim / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-16T11:28:16Z (GMT). No. of bitstreams: 1 Vitorio_HenriquedeBarrosCorreia_D.pdf: 1074812 bytes, checksum: e23ca71f5e87d6990c05425cdcb87bee (MD5) Previous issue date: 2010 / Resumo: A presente tese dá continuidade ao recente trabalho de J.C . Álvarez e C.E. Durán acerca dos invariantes geométricos de uma classe genérica de curvas em variedades de Grassmann, ditas "curvas fanning". Mais precisamente, considera-se como tais curvas de planos lagrangeanos comportam-se mediante uma redução simplética, e conclui-se a existência de dois novos invariantes que desempenham um papel fundamental neste contexto, mais notavelmente a maneira pela qual eles generalizam as bem conhecidas fórmulas de O'Neill para submersões isométricas / Abstract: The present thesis gives continuity to the recent work of J.C. Álvarez e C.E. Durán about the geometric invariants of a generic class of curves in the Grassmann manifolds, called "fanning curves". More precisely, we look at how such curves of lagrangean planes behave under a symplectic reduction, and establish the existence of two new invariants which play a fundamental role in that context, more notably the way they generalize the well known O'Neill's formulas for isometric submersions / Doutorado / Matematica / Doutor em Matemática

Le premier objectif de cette thèse est de générer et d'analyser une base de données pour l'écoulement intracardiaque dans des géométries réalistes. Dans ce but, une stratégie couplant simulation numérique et imagerie médicale est appliquée à un cœur gauche pathologique et à un cœur gauche sain. Le second objectif est d'illustrer comment cette base de données peut être analysée afin de mieux comprendre l'écoulement intracardiaque, en portant une attention particulière aux caractéristiques instationnaires de l'écoulement et à sa nature turbulente. Une chaîne numérique pour simuler l'écoulement dans des géométries spécifiques au patient est tout d'abord présentée. La cavité cardiaque et ses mouvements sont extraits à partir d'images médicales à l'aide d'un algorithme de recalage d'image afin d'obtenir le domaine de calcul. Les équations qui régissent l'écoulement sont écrites dans le cadre d'un maillage se déformant au cours du temps (approche arbitrairement Lagrangienne ou Eulérienne). Les valves cardiaques sont modélisées à l'aide de frontières immergées. L'application de cette chaîne numérique à deux cœurs gauches, l'un pathologique, l'autre sain est ensuite détaillée. L'écoulement sanguin est caractérisé par sa nature transitoire, donnant un écoulement complexe et cyclique. Il est montré que l'écoulement n'est ni laminaire, ni pleinement turbulent, justifiant a posteriori l'utilisation de simulation aux grandes échelles. Le développement instationnaire de la turbulence est analysé à l'aide de l'écoulement moyenné sur un nombre suffisant de cycles cardiaques. Les statistiques de l'écoulement, l'énergie turbulente, la production de turbulence et une analyse spectrale sont notamment présentées. Une étude Lagrangienne est aussi effectuée en utilisant des statistiques calculées à l'aide de particules ensemencées dans l'écoulement. En plus des caractéristiques habituellement rapportées, ce travail met en évidence le caractère perturbé et transitoire de l'écoulement, tout en identifiant les mécanismes de production de la turbulence. / The first objective of this thesis is to generate and analyse CFD-based databases for the intracardiac flow in realistic geometries. To this aim, an image-based CFD strategy is applied to both a pathological and a healthy human left hearts. The second objective is to illustrate how the numerical database can be analysed in order to gain insight about the intracardiac flow, mainly focusing on the unsteady and turbulent features. A numerical framework allowing insight in fluid dynamics inside patient-specific human hearts is first presented. The heart cavities and their wall dynamics are extracted from medical images, with the help of an image registration algorithm, in order to obtain a patient-specific moving numerical domain. Flow equations are written on a conformal moving computational domain, using an Arbitrary Lagrangian-Eulerian framework. Valves are modelled using immersed boundaries.Application of this framework to compute flow and turbulence statistics in both a realistic pathological and a realistic healthy human left hearts is presented. The blood flow is characterized by its transitional nature, resulting in a complex cyclic flow. Flow dynamics is analysed in order to reveal the main fluid phenomena and to obtain insights into the physiological patterns commonly detected. It is demonstrated that the flow is neither laminar nor fully turbulent, thus justifying a posteriori the use of Large Eddy Simulation.The unsteady development of turbulence is analysed from the phase averaged flow, flow statistics, the turbulent stresses, the turbulent kinetic energy, its production and through spectral analysis. A Lagrangian analysis is also presented using Lagrangian particles to gather statistical flow data. In addition to a number of classically reported features on the left heart flow, this work reveals how disturbed and transitional the flow is and describes the mechanisms of turbulence production.

Fuel sprays play a major role in order to achieve the required combustion characteristics and pollutant emissions reduction on internal combustion engines, and thus, an accurate prediction of its behavior is required to perform reliable engine combustion and pollutant simulations. A great effort both on experimental and theoretical studies of spray atomization and dispersion has been performed in the latest years. As a result, Computational Fluid Dynamics (CFD) calculations have become a standard tool not only for spray physics understanding but also for design and optimization of engine spray systems. However, spray modeling in its different uses in the Internal Combustion Engine (ICE) context is still nowadays a challenging task due to the complex interrelated phenomena taking place, some of them still not fully understood. Primary atomization and secondary breakup, droplet collision, coalescence and vaporization, turbulent interactions between phases have to be solved under high Reynolds (so they are turbulent) and Weber numbers conditions due to the high speed (~500 m/s) and small nozzle diameter (~100 µm) imposed by current engine injection systems technologies. Moreover, Taylor numbers cover a wide range, according to the composition of the injected liquid. Those conditions make experimental observations quite challenging and probably insufficient, especially in the very near nozzle region, where primary atomization takes place. Most of the CFD spray models are currently based on the Discrete Droplet Method. The continuous liquid jet is discretized into 'blobs' or 'parcels', which consists in a number of droplets with the same characteristics. A Lagrangian method is applied to track the liquid phase parcels, which are subject to breakup according to atomization models mainly based on the linear instability theory proposed by Reitz and later extended by Huh and Gosman for liquid turbulence effects to be considered. This approach has been successfully applied b / Khuong ., AD. (2012). The Eulerian-Lagrangian Spray Atomization (ELSA) Model of the Jet Atomization in CFD Simulations: Evaluation and Validation [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/17237 / Palancia

Finite element(FE) method has been used to model cutting process since 1970s. However, it requires special techniques to cope with the difficulties in simulating extremely large strain when compare to static or small deformation problems. With the advancement of FE techniques, researchers can now have a deeper insight of the mechanism of material flow and chip formation of metal cutting process. Even the stagnation effect of the workpiece material in front of the cutting edge radius can be captured by using FE techniques such as Remeshing and Arbitrary Lagrangian Eulerian(ALE) formulation. However most of this models are limited to plane strain assumption which means they are 2-dimensional. Although 3D models are existing in the literatures, most of them employ Remeshing technique which is very computationally intensive and has many critics regarding its accuracy due to its frequent remeshing and mapping process. The rest of the 3D models employ Lagrangian formulation. The 3D models by Lagrangian formulation have the same limitations and drawbacks as in 2D models, as it requires failure criteria and in most of the cases predefined partition surfaces are also required. ALE technique on the other hand resolves all the drawbacks of the other formulations, it not only inherits the advantages of the other techniques but also has its own unique advantages such as it can simulate a longer time span up to couple seconds more economically by fixing the number of elements used. Although it's commonly accepted that ALE formulation is superior to other formulations of techniques in modeling metal cutting process, its usage is only limited to 2D models. Limited 3D ALE metal cutting models is available in the literature. Thus the main objective of this research is to explore the possibility of building a 3D metal cutting model with ALE formulation. The reliability and limitations will also be studied. Furthermore, Couple Eulerian-Lagrangian(CEL) formulation is a recent developed formulation that has a lot of potential in modeling metal cutting process in 3D. It will be compared with ALE models to study its potential and limitations in modeling metal cutting process. A new frictional model will also be proposed, which suggests that the frictional phenomenon in metal cutting is a consolidated effect of both friction between material interface and shear yield of the workpiece material. This idea provide a brand new perspective of viewing the friction phenomenon of metal cutting compared to those existed models. / Thesis / Master of Science (MSc)