Dissertations / Theses on the topic 'Computational stability analysis'

Thesis (Ph. D.)--George Mason University, 2007.
Title from PDF t.p. (viewed Jan. 22, 2008). Thesis director: Iosif I. Vaisman. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Bioinformatics. Vita: p. 140. Includes bibliographical references (p. 133-139). Also available in print.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
O presente trabalho apresenta aplicações das técnicas de Relaxação Dinâmica e Análise Limite ao estudo da estabilidade de maciços rochosos fraturados. O maciço é modelado como um meio descontínuo formado por blocos rígidos com deformação concentrada nas juntas. A técnica de Relaxação Dinâmica é usada para a solução do problema de equilíbrio resultante, através do programa BLOCO. As expressões desenvolvidas para a matriz de rigidez tangente, usando o modelo de Barton & Bandis, foram implementadas no programa BLOCO. Exemplos para a validação do algoritmo são apresentados. A partir do trabalho de Faria (1992), foi implementado um procedimento automatizado e otimizado para a solução do problema de Análise Limite em um meio formado por blocos rígidos. O procedimento desenvolvido permitiu a solução de problemas de porte relatados na literatura.
This work presents some applications of the Dynamic Relaxation and Limit Analysis techniques, to the study of the stability of fractured rock masses. Rock mass is modeled as a discontinuum formed by rigid blocks with deformable joints. Dynamic Relaxation was applied to solve the resulting equilibrium problem, using the program BLOCO. Expressions obtained for tangent stiffness matrix, derived from Barton & Bandis model, were implemented into the BLOCO program. In order to extend Faria`s (1992) work, an automatic and optimized procedure, to solve the Limit Analysis problem of a media formed by rigid blocks was implemented. The developed procedure was applied to the study of relatively large dimensions problems, reported in the literature.
Este trabajo presenta aplicaciones de las técnicas de Relajación Dinámica y Análisis Límite al estudio de la estabilidad de macizos rocosos fracturados. EL macizo es modelado como un medio discontinuo formado por bloques rígidos con deformación concentrada en las juntas. La técnica de Relajación Dinámica se utiliza para resolver el problema de equilíbrio resultante, a través del programa BLOQUE. Las expresiones desarrolladas para la matriz de rígidez tangente, usando el modelo de Barton & Bandis, se implementaron en el programa BLOQUE. Se presentan algunos ejemplos para la evaluación del algoritmo. A partir del trabajo de Faria (1992), fue implementado un procedimiento automatizado y optimizado para la solución del problema de Análisis Límite en un medio formado por bloques rígidos. El procedimiento desarrollado permitió resolver problemas de porte relatados en la literatura.

Thanks to the increasing slenderness and lightness allowed by new construction techniques and materials, the effects of wind on structures became in the last decades a research field of great importance in Civil Engineering. Thanks to the advances in computers power, the numerical simulation of wind tunnel tests has became a valid complementary activity and an attractive alternative for the future. Due to its flexibility, during the last years, the computational approach gained importance with respect to the traditional experimental investigation. However, still today, the computational approach to fluid-structure interaction problems is not as widely adopted as it could be expected. The main reason for this lies in the difficulties encountered in the numerical simulation of the turbulent, unsteady flow conditions generally encountered around bluff bodies. This thesis aims at providing a guide to the numerical simulation of bridge deck aerodynamic and aeroelastic behaviour describing in detail the simulation strategies and setting guidelines useful for the interpretation of the results.

The search for robust, low-noise modelocked comb sources has attracted significant attention during the last two decades. Passively modelocked fiber lasers are among the most attractive comb sources. The most important design problems for a passively modelocked laser include: (1) finding a region in the laser’s adjustable parameter space where it operates stably, (2) optimizing the pulse profile within that region, and (3) lowering the noise level. Adjustable parameters will typically include the cavity length, the pump power, and the amplifier gain, which may be a function of the pump power, the pump wavelength, and both the material and geometry of the gain medium.

There are two basic computational approaches for modeling passively modelocked laser systems: the evolutionary approach and the dynamical approach. In the evolutionary approach, which replicates the physical behavior of the laser, one launches light into the simulated laser and follows it for many round trips in the laser. If one obtains a stationary or periodically-stationary modelocked pulse, the laser is deemed stable and, if no such pulse is found, the laser is deemed unstable. The effect of noise can be studied by using a random number generator to add computational noise. In the dynamical approach, one first obtains a single modelocked pulse solution either analytically or by using the evolutionary approach. Next, one finds the pulse parameters as the laser parameters vary by solving a root-finding algorithm. One then linearizes the evolution equations about the steady-state solution and determines the eigenvalues of the linearized equation, which we refer to as the equation’s dynamical spectrum. If any eigenvalue has a positive real part, then the modelocked pulse is unstable. The effect of noise can be determined by calculating the noise that enters each of the modes in the dynamical spectrum, whose amplitudes are described by either a Langevin process or a random walk process.

The evolutionary approach is intuitive and straightforward to program, and it is widely used. However, it is computationally time-consuming to determine the stable operating regions and can give ambiguous results near a stability boundary. When evaluating the noise levels, Monte Carlo simulations, which are based upon the evolutionary approach, are often prohibitively expensive computationally. By comparison, the dynamical approach is more difficult to program, but it is computationally rapid, yields unambiguous results for the stability, and avoids computationally expensive Monte Carlo simulations. The two approaches are complementary to each other. However, the dynamical approach can be a powerful tool for system design and optimization and has historically been undertilized.

In this dissertation, we discuss the dynamical approach that we have developed for design and optimization of passively modelocked laser systems. This approach provides deep insights into the instability mechanisms of the laser that impact or limit modelocking, and makes it possible to rapidly and unambiguously map out the regions of stable operation in a large parameter space. For a given system setup, we can calculate the noise level in the laser cavity within minutes on a desktop computer.

Compared to Monte Carlo simulations, we will show that the dynamical approach improves the computational efficiency by more than three orders of magnitude. We will apply the dynamical approach to a laser with a fast saturable absorber and to a laser with a slow saturable absorber. We apply our model of a laser with a slow saturable absorber to a fiber comb laser with a semiconductor absorbing mirror (SESAM) that was developed at National Institute of Standards and Technology (NIST), Boulder, CO. We optimize its parameters and show that it is possible to increase its output power and bandwidth while lowering the pump power that is needed.

The objective of this thesis is to develop and validate a computational framework based on mathematical models for the motion prediction and dynamic stability quantification of human walking, which can differentiate the dynamic stability of human walking with different mechanical properties of the leg. Firstly, a large measurement database of human walking motion was created. It contains walking measurement data of 8 subjects on 3 self-selected walking speeds, which 10 trials were recorded at each walking speed. The motion of whole-body centre of mass and the leg were calculated from the kinetic-kinematic measurement data. The fundamentals of leg property have been presented, and the parameters of leg property were extracted from the measurement data of human walking where the effects of walking speed and condition of foot-ground contact were investigated. Three different leg property definitions comprising linear axial elastic leg property, nonlinear axial elastic leg property and linear axial-tangential elastic leg property were used to extracted leg property parameters. The concept of posture-dependent leg property has been proposed, and the leg property parameters were extracted from the measurement data of human walking motion where the effects of walking speed and condition of foot-ground contact were also investigated. The compliant leg model with axial elastic property (CAE) was used for the dynamic stability analysis of human walking with linear and nonlinear axial elastic leg property. The compliant leg model with axial and tangential elastic property (CATE) was used for that with linear axial-tangential elastic leg property. The posture - dependent elastic leg model (PDE) was used for that with posture-dependent leg property. It was found that, with linear axial elastic leg property, the global stability of human walking improves with the bigger touchdown contact angle. The average leg property obtained from the measurement data of all participants allows the maximum global stability of human walking. With nonlinear axial elastic leg property, the global stability decreases with the stronger nonlinearity of leg stiffness. The incorporation of the tangential elasticity improves the global stability and shifts the stable walking velocity close to that of human walking at self-selected low speed (1.1-1.25 m/s).By the PDE model, the human walking motions were better predicted than by the CATE model. The effective range of walking prediction was enlarged to 1.12 – 1.8 m/s. However, represented by PDE model, only 1-2 walking steps can be achieved. In addition, the profiles of mechanical energies represented by the PDE model are different from that of the orbital stable walking represented by CATE model. Finally, the minimal requirements of the human walking measurements and the flexibility of simple walking models with deliberate leg property definitions allow the computational framework to be applicable in the dynamic stability analysis of the walking motion with a wide variety of mechanical property of the leg.

Philosophiae Doctor - PhD
Numerical approximations of multiscale problems of important applications in ecology are investigated. One of the class of models considered in this work are singularly perturbed (slow-fast) predator-prey systems which are characterized by the presence of a very small positive parameter representing the separation of time-scales between the fast and slow dynamics. Solution of such problems involve multiple scale phenomenon characterized by repeated switching of slow and fast motions, referred to as relaxationoscillations, which are typically challenging to approximate numerically. Granted with a priori knowledge, various time-stepping methods are developed within the framework of partitioning the full problem into fast and slow components, and then numerically treating each component differently according to their time-scales. Nonlinearities that arise as a result of the application of the implicit parts of such schemes are treated by using iterative algorithms, which are known for their superlinear convergence, such as the Jacobian-Free Newton-Krylov (JFNK) and the Anderson’s Acceleration (AA) fixed point methods.

In this work is presented development of computational model of real timber truss in collapse state. The model was solved linearly and geometrically non-linearly and the results were evaluated. The aim was to depict the real behavior of the structure.

Boundary-layer transition from a laminar to a turbulent regime is a critical driver in the design of high-speed vehicles. The aerothermodynamic loads associated with transitional or fully turbulent hypersonic boundary layers are several times higher than those associated with laminar flow. The presence of isolated roughness elements on the surface of a body can accelerate the growth of incoming disturbances and introduce additional instability mechanisms in the flow field, eventually leading to a premature occurrence of transition. This dissertation studies the instabilities induced by three-dimensional discrete roughness elements located inside a high-speed boundary layer developing on a flat plate. Two-dimensional local linear stability theory (2D-LST) is employed to identify the instabilities evolving in the three-dimensional flow field that characterizes the wake induced by the roughness elements and to investigate their evolution downstream. A formulation of the disturbance energy evolution equation available for base flows depending on a single spatial direction is generalized for the first time to base flows featuring two inhomogeneous directions and perturbations depending on three spatial directions. This generalization allows to obtain a decomposition of the temporal growth rate of 2D-LST instabilities into the different contributions that lead to the production and dissipation of the total disturbance energy. This novel extension of the formulation provides an additional layer of information for understanding the energy exchange mechanisms between a three-dimensional base flow and the perturbations resulting from 2D-LST. Stability computations for a calorically perfect gas illustrate that the wake induced by the roughness elements supports the growth of different sinuous and varicose instabilities which coexist together with the Mack-mode perturbations that evolve in the flat-plate boundary layer, and which become modulated by the roughness-element wake. A single pair of sinuous and varicose disturbances is found to dominate the wake instability in the vicinity of the obstacles. The application of the newly developed decomposition of the temporal growth rate reveals that the roughness-induced wake modes extract most of their potential energy from the transport of entropy fluctuations across the base-flow temperature gradients and most of their kinetic energy from the work of the disturbance Reynolds stresses against the base-flow velocity gradients. Further downstream, the growth rate of the wake instabilities is found to be influenced by the presence of Mack-mode disturbances developing on the flat plate. Strong evidence is observed of a continuous synchronization mechanism between the wake instabilities and the Mack-mode perturbations. This phenomenon leads to an enhancement of the amplification rate of the wake modes far downstream of the roughness element, ultimately increasing the associated integrated amplification factors for some of the investigated conditions. The effects of vibrational molecular excitation and chemical non-equilibrium on the instabilities induced by a roughness element are studied for the case of a high-temperature boundary layer developing on a sharp wedge configuration. For this purpose, a 2D-LST solver for chemical non-equilibrium flows is developed for the first time, featuring a fully consistent implementation of the thermal and transport models employed for the base flow and the perturbation fields. This is achieved thanks to the automatic derivation and implementation tool (ADIT) available within the von Karman Institute extensible stability and transition analysis (VESTA) tool-kit, which enables an automatic derivation and implementation of the 2D-LST governing equations for different thermodynamic flow assumptions and models. The stability computations for this configuration show that sinuous and varicose disturbances also dominate the wake instability in the presence of vibrational molecular energy mode excitation and chemical reactions. The resulting base-flow cooling associated with the modeling of such high-temperature phenomena is found to have opposite stabilizing and destabilizing effects on the streamwise evolution of the sinuous and varicose instabilities. The modeling of vibrational excitation and chemical non-equilibrium acting exclusively on the perturbations is found to have a stabilizing influence in all cases.
Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished

Chování laminátových desek namáhaných na tlak či na smyk může být výrazně ovlivněno přítomností delaminací, tedy oblastí, kde je porušena vazba mezi sousedními vrstvami. Cílem této práce je rozšířit znalosti o chování delaminovaných desek, a to především o chování desek s větším počtem delaminací a desek s delaminacemi libovolného tvaru, neboť taková podoba porušení laminátu více odpovídá poškození vznikajícího v důsledku nízkorychlostního dopadu cizího tělesa na laminátovou desku. Disertační práce se skládá ze tří hlavních částí. V první části jsou stručně nastíněny postupy využívané při analýze boulení delaminovaných desek a jsou diskutována omezení těchto analýz. Dále jsou v této části shrnuty hlavní poznatky o boulení delaminovaných desek. V druhé části práce je popsán výpočtový model použitý v rámci disertační práce pro analýzu boulení delaminovaných desek. Schopnost modelu předpovědět chování delaminovaných desek je pak dokumentována na několika ověřovacích úlohách. Třetí část disertační práce se skládá ze tří samostatných studií chování desek s několika delaminacemi eliptického či kruhového tvaru a jedné studie zabývající se možností náhrady obecného tvaru delaminace kruhem či elipsou. Je probírán vliv řady parametrů na chování delaminovaných desek, konkrétně vliv orientace vrstev laminátu a dále vliv počtu, tvaru, orientace a umístění delaminací. Na základě těchto studií jsou pak zformulována doporučení ohledně postupu při posuzování únosnosti delaminovaných konstrukcí.

Master thesis deals with a computing simulation of two props turbines lines. The thesis output is gaining maximum possible load, at which a commencement of deformation stability critical state for various geometrical imperfections has not arisen yet. The calculation has been done by FEM in two different ways: linear solution (using a calculation conversion into eigenbuckling) and nonlinear solution (using a FEM deformation option). Result analysis compares both methods outcomes. Safety factor for the props operation has been proposed taking into consideration known influences on operating state.

Modeling and prediction of gene-expression patterns has an important place in computational biology and bioinformatics. The measure of gene expression is determined from the genomic analysis at the mRNA level by means of microarray technologies. Thus, mRNA analysis informs us not only about genetic viewpoints of an organism but also about the dynamic changes in environment of that organism. Different mathematical methods have been developed for analyzing experimental data. In this study, we discuss the modeling approaches and the reasons why we concentrate on models derived from differential equations and improve the pioneering works in this field by including affine terms on the right-hand side of the nonlinear differential equations and by using Runge- Kutta instead of Euler discretization, especially, with Heun&rsquo
s method. Herewith, for stability analysis we apply modified Brayton and Tong algorithm to time-discrete dynamics in an extended space.

This diploma thesis deals with the subject of slenderness bars’ stability assessment, especially in the steel structures. Before the assessment of bars in the frame constructions, we search for the influence of the computational model’s settings on the final result. The initial geometrical imperfections are examined on the model of Euler’s bar. The influence of the rigidity of girders on the poles’ buckling length is examined on the basic frame construction. The buckling lengths are assessed in the comparison with the figures we got from the statistical tables and the computational software. The influence of construction’s initial tilt and its replacement by the system of outer forces is examined on the frame structure. Three-hinged frame structure with variable cross-section member is designed then and the influence of non-linear calculations on the inner forces is studied. In the complex frame assessment, the influence of the number of parts of variable cross-section member on the bars’ buckling length is examined.

Landslides cause significant damage to property and human lives throughout the world. Rainfall is the most common triggering factor for the occurrence of landslides. This dissertation presents two novel methodologies for assessment of rainfall-triggered shallow landslide hazard. The first method focuses on using remotely sensed soil moisture and soil surface properties in developing a framework for real-time regional scale landslide hazard assessment while the second method is a deterministic approach to landslide hazard assessment of the specific sites identified during first assessment. In the latter approach, landslide inducing transient seepage in soil during rainfall and its effect on slope stability are modeled using numerical analysis. Traditionally, the prediction of rainfall-triggered landslides has been performed using pre-determined rainfall intensity-duration thresholds. However, it is the infiltration of rainwater into soil slopes which leads to an increase of porewater pressure and destruction of matric suction that causes a reduction in soil shear strength and slope instability. Hence, soil moisture, pore pressure and infiltration properties of soil must be direct inputs to reliable landslide hazard assessment methods. In-situ measurement of pore pressure for real-time landslide hazard assessment is an expensive endeavor and thus, the use of more practical remote sensing of soil moisture is constantly sought. In past studies, a statistical framework for regional scale landslide hazard assessment using remotely sensed soil moisture has not been developed. Thus, the first major objective of this study is to develop a framework for using downscaled remotely sensed soil moisture available on a daily basis to monitor locations that are highly susceptible to rainfall- triggered shallow landslides, using a well-structured assessment procedure. Downscaled soil moisture, the relevant geotechnical properties of saturated hydraulic conductivity and soil type, and the conditioning factors of elevation, slope, and distance to roads are used to develop an improved logistic regression model to predict the soil slide hazard of soil slopes using data from two geographically different regions. A soil moisture downscaling model with a proven superior prediction accuracy than the downscaling models that have been used in previous landslide studies is employed in this study. Furthermore, this model provides satisfactory classification accuracy and performs better than the alternative water drainage-based indices that are conventionally used to quantify the effect that elevated soil moisture has upon the soil sliding. Furthermore, the downscaling of soil moisture content is shown to improve the prediction accuracy. Finally, a technique that can determine the threshold probability for identifying locations with a high soil slide hazard is proposed. On the other hand, many deterministic methods based on analytical and numerical methodologies have been developed in the past to model the effects of infiltration and subsequent transient seepage during rainfall on the stability of natural and manmade slopes. However, the effects of continuous interplay between surface and subsurface water flows on slope stability is seldom considered in the above-mentioned numerical and analytical models. Furthermore, the existing seepage models are based on the Richards equation, which is derived using Darcy’s law, under a pseudo-steady state assumption. Thus, the inertial components of flow have not been incorporated typically in modeling the flow of water through the subsurface. Hence, the second objective of this study is to develop a numerical model which has the capability to model surface, subsurface and infiltration water flows based on a unified approach, employing fundamental fluid dynamics, to assess slope stability during rainfall-induced transient seepage conditions. The developed model is based on the Navier-Stokes equations, which possess the capability to model surface, subsurface and infiltration water flows in a unified manner. The extended Mohr-Coulomb criterion is used in evaluating the shear strength reduction due to infiltration. Finally, the effect of soil hydraulic conductivity on slope stability is examined. The interplay between surface and subsurface water flows is observed to have a significant impact on slope stability, especially at low hydraulic conductivity values. The developed numerical model facilitates site-specific calibration with respect to saturated hydraulic conductivity, remotely sensed soil moisture content and rainfall intensity to predict landslide inducing subsurface pore pressure variations in real time.

Wave propagation problems can be modeled by partial differential equations. In this thesis, we study wave propagation in fluids and in solids, modeled by the acoustic wave equation and the elastic wave equation, respectively. In real-world applications, waves often propagate in heterogeneous media with complex geometries, which makes it impossible to derive exact solutions to the governing equations. Alternatively, we seek approximated solutions by constructing numerical methods and implementing on modern computers. An efficient numerical method produces accurate approximations at low computational cost. There are many choices of numerical methods for solving partial differential equations. Which method is more efficient than the others depends on the particular problem we consider. In this thesis, we study two numerical methods: the finite difference method and the discontinuous Galerkin method. The finite difference method is conceptually simple and easy to implement, but has difficulties in handling complex geometries of the computational domain. We construct high order finite difference methods for wave propagation in heterogeneous media with complex geometries. In addition, we derive error estimates to a class of finite difference operators applied to the acoustic wave equation. The discontinuous Galerkin method is flexible with complex geometries. Moreover, the discontinuous nature between elements makes the method suitable for multiphysics problems. We use an energy based discontinuous Galerkin method to solve a coupled acoustic-elastic problem.

This dissertation presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, for triangular meshes, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree. Finally, for rectangular meshes, the test space is reduced, yet the convergence is recovered regardless of parity.

Downstream regulatory element antagonist modulator (DREAM) is involved in various interactions with targets both inside and outside of the nucleus. In the cytoplasm, DREAM interacts with the C-terminal fragments of presenilins to facilitate the production of β-amyloid plaques in Alzheimer’s disease. In the nucleus, Ca2+ free DREAM directly binds to specific downstream regulatory elements of prodynorphin/c-fos gene to repress the gene transcription in pain modulation. These interactions are regulated by Ca2+ and/or Mg2+ association at the EF-hands in DREAM. Therefore, understanding the conformational dynamics and stability associated with Ca2+ and/or Mg2+ binding to DREAM is crucial for elucidating the mechanisms of interactions of DREAM with DNA or presenilins. The critical barrier for envisioning the mechanisms of these interactions lies in the lack of NMR/crystal structures of Apo and Mg2+DREAM. Using a combination of fluorescence spectroscopy, circular dichroism, isothermal titration calorimetry, photothermal spectroscopy, and computational approaches, I showed that Mg2+ association at the EF-hand 2 structurally stabilizes the N-terminal alpha-helices 1, 2, and 5, facilitating the interaction with DNA. Binding of Ca2+ at the EF-hand 3 induces significant structural changes in DREAM, mediated by several hydrophobic residues in both the N- and C-domains. These findings illustrate the critical role of EF-hand 3 for Ca2+ signal transduction from the C- to N-terminus in DREAM. The Ca2+ association at the EF-hand 4 stabilizes the C-terminus by forming a cluster consisting of several hydrophobic residues in C-terminal domain. I also demonstrated that association of presenilin-1 carboxyl peptide with DREAM is Ca2+ dependent and the complex is stabilized by aromatic residues F462 and F465 from presenilin-1 and F252 from DREAM. Stabilization is also provided by residues R200 and R207 in the loop connecting a7 and a8 in DREAM and the residues D450 and D458 in presenilin-1. These findings provide a structural basis for the development of new drugs for chronic pain and Alzheimer’s disease treatments.

Abstract : Recently, there is a great interest to study the flow characteristics of suspensions in different environmental and industrial applications, such as snow avalanches, debris flows, hydrotransport systems, and material casting processes. Regarding rheological aspects, the majority of these suspensions, such as fresh concrete, behave mostly as non-Newtonian fluids. Concrete is the most widely used construction material in the world. Due to the limitations that exist in terms of workability and formwork filling abilities of normal concrete, a new class of concrete that is able to flow under its own weight, especially through narrow gaps in the congested areas of the formwork was developed. Accordingly, self-consolidating concrete (SCC) is a novel construction material that is gaining market acceptance in various applications. Higher fluidity characteristics of SCC enable it to be used in a number of special applications, such as densely reinforced sections. However, higher flowability of SCC makes it more sensitive to segregation of coarse particles during flow (i.e., dynamic segregation) and thereafter at rest (i.e., static segregation). Dynamic segregation can increase when SCC flows over a long distance or in the presence of obstacles. Therefore, there is always a need to establish a trade-off between the flowability, passing ability, and stability properties of SCC suspensions. This should be taken into consideration to design the casting process and the mixture proportioning of SCC. This is called “workability design” of SCC. An efficient and non-expensive workability design approach consists of the prediction and optimization of the workability of the concrete mixtures for the selected construction processes, such as transportation, pumping, casting, compaction, and finishing. Indeed, the mixture proportioning of SCC should ensure the construction quality demands, such as demanded levels of flowability, passing ability, filling ability, and stability (dynamic and static). This is necessary to develop some theoretical tools to assess under what conditions the construction quality demands are satisfied. Accordingly, this thesis is dedicated to carry out analytical and numerical simulations to predict flow performance of SCC under different casting processes, such as pumping and tremie applications, or casting using buckets. The L-Box and T-Box set-ups can evaluate flow performance properties of SCC (e.g., flowability, passing ability, filling ability, shear-induced and gravitational dynamic segregation) in casting process of wall and beam elements. The specific objective of the study consists of relating numerical results of flow simulation of SCC in L-Box and T-Box test set-ups, reported in this thesis, to the flow performance properties of SCC during casting. Accordingly, the SCC is modeled as a heterogeneous material. Furthermore, an analytical model is proposed to predict flow performance of SCC in L-Box set-up using the Dam Break Theory. On the other hand, results of the numerical simulation of SCC casting in a reinforced beam are verified by experimental free surface profiles. The results of numerical simulations of SCC casting (modeled as a single homogeneous fluid), are used to determine the critical zones corresponding to the higher risks of segregation and blocking. The effects of rheological parameters, density, particle contents, distribution of reinforcing bars, and particle-bar interactions on flow performance of SCC are evaluated using CFD simulations of SCC flow in L-Box and T-box test set-ups (modeled as a heterogeneous material). Two new approaches are proposed to classify the SCC mixtures based on filling ability and performability properties, as a contribution of flowability, passing ability, and dynamic stability of SCC.
Résumé : Récemment, il y a un grand intérêt à étudier les caractéristiques d'écoulement des suspensions dans différentes applications environnementales et industrielles, telles que les avalanches des neiges, les coulées de débris, les systèmes de transport et les processus d’écoulement des matériaux. En ce qui concerne les aspects rhéologiques, la plupart des suspensions, comme le béton frais, se comportent comme un fluide non-Newtonien. Le béton est le matériau de construction le plus largement utilisé dans le monde. En raison de limites qui caractérisent le béton normal en termes de maniabilité et de capacité de remplissage de coffrage, il était nécessaire de développer une nouvelle classe de béton qui peut couler sous son propre poids, en particulier à travers les zones congestionnées du coffrage. Par conséquent, le béton autoplaçant (BAP) est un nouveau matériau de construction qui est de plus en plus utilisé dans les différentes applications. Étant donné sa fluidité élevée de BAP peut être utilisé dans certaines applications particulières, notamment dans la section densément renforcée. Cependant, la fluidité élevée rend le béton plus sensible à la ségrégation des gros granulats pendant l'écoulement (la ségrégation dynamique) et ensuite au repos (ségrégation statique). La ségrégation dynamique peut augmenter lorsque le BAP est coulé sur une longue distance ou en présence d'obstacles. Par conséquent, il est toujours nécessaire d'établir un compromis entre la fluidité, la capacité de passage, et la stabilité du BAP. Ceci doit être pris en considération afin de concevoir le processus de coulée et dosage des mélanges du BAP. Ceci est appelé la conception d'ouvrabilité du BAP. Une conception de maniabilité efficace et non coûteuse peut être achevée à travers la e prévision et l'optimisation de l'ouvrabilité des mélanges de béton pour les procédés de construction sélectionnés, notamment le transport, le pompage, la mise en place, le compactage, la finition, etc. En effet, les formulations de mélange doivent se confirmer à la qualité de la construction demandée, par exemple les niveaux exigés de fluidité, la capacité de passage, la capacité de remplissage, et la stabilité (statique et dynamique). Celui est nécessaire pour développer des outils théoriques afin d’évaluer dans quelles conditions les exigences de qualité de la construction sont satisfaites. Cette thèse est consacrée à la réaliser des simulations analytiques et numériques pour prédire la performance d'écoulement du BAP dans différents procédés de la mise en place du béton. L'objectif spécifique de cette étude consiste à simuler l'écoulement du BAP dans essais empiriques, notamment la boite en L et la boite en T pour évaluer la performance du BAP pendent la mise en place (la fluidité, la capacité de passage, la capacité de remplissage, et la ségrégation dynamique induite par cisaillement ou par gravité). Par conséquent, le BAP est modélisé comme matériau hétérogène. En outre, un modèle analytique est proposé pour prédire la performance à l'écoulement du BAP dans la boite en L en utilisant la théorie de Dam Break. D'autre part, les résultats des simulations numériques de l’écoulement du BAP dans une poutre renforcée sont comparés aux résultats expérimentaux par des profils de surface libres. Les résultats des simulations numériques de BAP coulée (modélisée comme un fluide homogène unique), sont utilisés pour déterminer les zones critiques correspondant à des risques plus élevés de ségrégation et de blocage. Les effets des paramètres rhéologiques, la masse volumique, le contenu des particules, la distribution de barres d'armature, et les interactions particule-barres sur les performances d'écoulement du BAP sont évaluées à l'aide de simulations MFN d’écoulement du BAP par les essais des L-Box et T-box (modélisée comme une matériau hétérogène). Deux nouvelles approches sont proposées pour classifier les mélanges du BAP sur la base de la capacité de remplissage, et les propriétés de performabilité, en fonction de la fluidité, la capacité de passage et de la stabilité dynamique du BAP.

Swarms are groups of agents, which we model as point particles, whose collective behavior emerges from individual interactions. We study a first-order swarming model in a periodic coordinate system with pairwise social forces, investigating its stable configurations for differing numbers of agents relative to the periodic width. Two states emerge from numerical simulations in one dimension: even spacing throughout the period, or clumping within a certain portion of the period. A mathematical analysis of the energy of the system allows us to determine stability of these configurations. We also perform numerical simulations for evolution to equilibrium over time, and find results in agreement with our mathematical analysis. For certain values of the periodic width relative to the number of agents, our numerical simulations show that either clumping or even spacing can be stable equilibria, and which equilibrium is reached depends on on starting conditions, indicating hysteresis.

In this thesis we will investigate how the SBP-SAT finite difference method behave with and without an interface. As model problem, we consider the heat equation with piecewise constant coefficients. The thesis is split in two main parts. In the first part we look at the heat equation in one-dimension, and in the second part we expand the problem to a two-dimensional domain. We show how the SAT-parameters are chosen such that the scheme is dual consistent and stable. Then, we perform numerical experiments, now looking at the static case. In the one-dimensional case we see that the second order SBP-SAT method with an interface converge with an order of two, while the second order SBP-SAT method without an interface converge with an order of one.

This work presents an alternative approach to power system computations, Graph Trace Analysis (GTA), and applies GTA to the power flow problem. A novel power flow algorithm is presented, where GTA traces are used to implement a modified Gauss-Seidel algorithm coupled with a continuation method. GTA is derived from the Generic Programming Paradigm of computer science. It uses topology iterators to move through components in a model and perform calculations. Two advantages that GTA brings are the separation of system equations from component equations and the ability to distribute calculations across processors. The implementation of KVL and KCL in GTA is described. The GTA based power flow algorithm is shown to solve IEEE standard transmission models, IEEE standard distribution models, and integrated transmission and distribution models (hybrid models) constructed from modifying IEEE standard models. The GTA power flow is shown to solve a set of robustness testing circuits, and solutions are compared with other power flow algorithms. This comparison illustrates convergence characteristics of different power flow algorithms in the presence of voltage stability concerns. It is also demonstrated that the GTA power flow solves integrated transmission and distribution system models. Advantages that GTA power flow bring are the ability to solve realistic, complex circuit models that pose problems to many traditional algorithms; the ability to solve circuits that are operating far from nominal conditions; and the ability to solve transmission and distribution networks together in the same model.
PHD

Un logiciel critique est un logiciel dont le mauvais fonctionnement peut avoir un impact important sur la sécurité ou la vie des personnes, des entreprises ou des biens.L'ingénierie logicielle pour les systèmes critiques est particulièrement difficile et combine différentes méthodes pour garantir la qualité des logiciels produits.Parmi celles-ci, les méthodes formelles peuvent être utilisées pour prouver qu'un logiciel respecte ses spécifications.Le travail décrit dans cette thèse s'inscrit dans le contexte de la validation de propriétés de sûreté de programmes critiques, et plus particulièrement des propriétés numériques de logiciels embarqués dans des systèmes de contrôle-commande.La première partie de cette thèse est consacrée aux preuves de stabilité au sens de Lyapunov.Ces preuves s'appuient sur des calculs en nombres réels, et ne sont pas valables pour décrire le comportement d'un programme exécuté sur une plateforme à arithmétique machine.Nous présentons un cadre théorique générique pour adapter les arguments des preuves de stabilité de Lyapunov aux arithmétiques machine.Un outil effectue automatiquement la traduction de la preuve en nombres réels vers une preuve en nombres a virgule flottante.La seconde partie de la thèse porte sur l'analyse des relations affines, en utilisant une interprétation abstraite basée sur l'approximation des valuations associées aux points de contrôle d'un programme par des polyèdres convexes.Nous présentons ALICe, un framework permettant de comparer différentes techniques de génération d'invariants.Il s'accompagne d'une collection de cas de tests tirés de publications sur l'analyse de programmes, et s'interface avec trois outils utilisant différents algorithmes de calcul d'invariants: Aspic, iscc et PIPS.Afin d'affiner les résultats de PIPS, deux techniques de restructuration de code sont introduites, et plusieurs améliorations sont apportées aux algorithmes de génération d'invariants et évaluées à l'aide d'ALICe
A critical software is a software whose malfunction may result in death or serious injury to people, loss or severe damage to equipment or environmental harm.Software engineering for critical systems is particularly difficult, and combines different methods to ensure the quality of produced software.Among them, formal methods can be used to prove that a software obeys its specifications.This thesis falls within the context of the validation of safety properties for critical software, and more specifically, of numerical properties for embedded software in control-command systems.The first part of this thesis deals with Lyapunov stability proofs.These proofs rely on computations with real numbers, and do not accurately describe the behavior of a program run on a platform with machine arithmetic.We introduce a generic, theoretical framework to adapt the arguments of Lyapunov stability proofs to machine arithmetic.A tool automatically translates the proof on real numbers to a proof with floating-point numbers.The second part of the thesis focuses on linear relation analysis, using an abstract interpretation based on the approximation by convex polyhedrons of valuations associated with each control point in a program.We present ALICe, a framework to compare different invariant generation techniques.It comes with a collection of test cases taken from the program analysis literature, and interfaces with three tools, that rely on different algorithms to compute invariants: Aspic, iscc and PIPS.To refine PIPS results, two code restructuring techniques are introduced, and several improvements are made to the invariant generation algorithms and evaluated using ALICe

Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order. In this thesis both computational and theoretical discussion of the application of numerical methods on differential equations takes place. The thesis consists of an investigation of various categories of numerical methods for the solution of ordinary differential equations including the numerical solution of ordinary differential equations from a number of practical fields such as equations arising in population dynamics and astrophysics. It includes discussion what are the advantages and disadvantages of implicit methods over explicit methods, the accuracy and stability of methods and how the order of various methods can be approximated numerically. Also, semidiscretization of some partial differential equations and stiff systems which may arise from these semidiscretizations are examined.

It is well-known that, increasing the flow rate in polymer extrusion, the flow becomes unstable and the smooth extrudate surface becomes wavy and disordered to an increasing degree. In order to investigate the mechanisms responsible for these instabilities we perform a linear stability analysis of the steady extrusion of a viscoelastic fluid flowing through a planar die under creeping flow conditions. We consider the Phan-Thien-Tanner (PTT) model to account for the viscoelasticity of the material. We employ the mixed finite element method combined with an elliptic grid generator to account for the deformable shape of the interface. The generalized eigenvalue problem is solved using Arnoldi’s algorithm. We perform a thorough parametric study in order to determine the effects of all material properties and rheological parameters. We investigate in detail the effect of interfacial tension and the presence of a deformable interface. It is found that the presence of a finite surface tension destabilizes the flow as compared to the case of the stick-slip flow. We recognize two modes which are found to become unstable beyond a critical value of the Weissenberg number and perform an energy analysis to examine the mechanisms responsible for the destabilization of the flow and compare against the mechanisms that have been suggested in the literature.
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In metal powder compaction, density non-uniformity due to friction can be a source of flaws. Currently in industry, uniform density distribution is achieved by the optimization of punch motions through trial and error. This method is both costly and time consuming. Over the last decade, the finite element (FE) method has received significant attention as an alternative to the trial and error method; however, there is still lack of an accurate and robust material model for the simulation of metal powder compaction. In this study, Cam-clay and Drucker-Prager cap (DPC) material models were implemented into the commercial FE software ABAQUS/Explicit using the user-subroutine VUMAT. The Cam-clay model was shown to be appropriate for simple geometries. The DPC model is a pressure-dependent, non-smooth, multi-yield surface material model with a high curvature in the cap yield surface. This high curvature tends to result in instability issues; a sub-increment technique was implemented to address this instability problem. The DPC model also shows instability problems at the intersection of the yield surfaces; this problem was solved using the corner region in DPC material models for soils. The computational efficiency of the DPC material model was improved using a novel technique to solve the constitutive equations. In a case study it was shown that the numerical technique leads to a 30% decrease in computational cost, while degrading the accuracy of the analysis by only 0.4%. The forward Euler method was shown to be accurate in the integration of the constitutive equations using an error control scheme. Experimental tests were conducted where cylindrical-shaped parts were compacted from Distaloy AE iron based powder to a final density of 7.0 g/cm3. To measure local density, metallography and image processing was used. The FE results were compared to experimental results and it was shown that the FE analysis predicted local relative density within 2% of the actual experimental density.
Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2010-09-23 12:15:27.371

abstract: What causes social systems to resist change? Studies of the emergence of social complexity in archaeology have focused primarily on drivers of change with much less emphasis on drivers of stability. Social stability, or the persistence of social systems, is an essential feature without which human society is not possible. By combining quantitative modeling (Exponential Random Graph Modeling) and the comparative archaeological record where the social system is represented by networks of relations between settlements, this research tests several hypotheses about social and geographic drivers of social stability with an explicit focus on a better understanding of contexts and processes that resist change. The Valencian Bronze Age in eastern Spain along the Mediterranean, where prior research appears to indicate little, regional social change for 700 years, serves as a case study. The results suggest that social stability depends on a society’s ability to integrate change and promote interdependency. In part, this ability is constrained or promoted by social structure and the different, relationship dependencies among individuals that lead to a particular social structure. Four elements are important to constraining or promoting social stability—structural cohesion, transitivity and social dependency, geographic isolation, and types of exchange. Through the framework provided in this research, an archaeologist can recognize patterns in the archaeological data that reflect and promote social stability, or lead to collapse. Results based on comparisons between the social networks of the Northern and Southern regions of the Valencian Bronze Age show that the Southern Region’s social structure was less stable through time. The Southern Region’s social structure consisted of competing cores of exchange. This type of competition often leads to power imbalances, conflict, and instability. Strong dependencies on the neighboring Argaric during the Early and Middle Bronze Ages and contributed to the Southern Region’s inability to maintain social stability after the Argaric collapsed. Furthermore, the Southern Region participated in the exchange of more complex technology—bronze. Complex technologies produce networks with hub and spoke structures highly vulnerable to collapse after the destruction of a hub. The Northern Region’s social structure remained structurally cohesive through time, promoting social stability.
Dissertation/Thesis
Webpage with data tables and R code
Doctoral Dissertation Anthropology 2020

Thesis (Ph. D.)--University of Notre Dame, 2005.
Thesis directed by Mark A. Stadtherr for the Department of Chemical and Biomolecular Engineering. "July 2005." Includes bibliographical references (leaves 113-120).

碩士
大同大學
電機工程研究所
88
In this thesis, an approach for analyzing the performances of the realization of a state regulator system running on a digital machine is proposed. This approach permits that equivalent stable state space structures when regarding their input-output characteristics with infinite precision can also perform stably when they are operating on a digital machine with finite word length(FWL) limitations. Both the rounding errors occurred by the coefficients-quantization and computation errors by additions and multiplications were studied in this thesis. It is shown from the Bellman-Grownwall Lemma and the pole sensitivity that the minimal mantissa-length is achieved and the optimal digital state-space structures is obtained. Finally, numerical simulation results are performed to illustrate the effectiveness of the proposed scheme.

This dissertation studies the theory and applications of a new and nonstandard class of dynamical system, called projected dynamical systems. We focus on three subjects: (1) the proposal of dynamical models, for social and economic systems that are subject to certain constraints, (2) the establishment of the stability analysis for such models, and (3) the development of discrete time algorithms for the computation of equilibria. The applications that this thesis is devoted to include: elastic and fixed demand transportation network problems, spatial price market problems, and oligopoly problems. The theoretical foundation is laid down through rigorous mathematics. (1) Projected dynamical system models. In each application chapter, a projected dynamical system model is proposed to describe the underlying competitive system of the equilibrium problem. These models extend the static variational inequality formulations of the equilibrium problems to an additional dimension of time so as to allow the study of the disequilibrium behavior that leads to the equilibrium states. (2) Stability analysis. An important achievement of this thesis is the establishment of the stability theory of projected dynamical systems, which is then utilized to provide stability analysis for the application models. The local and global stability results presented here address the following questions: Will the competitive system eventually approach an equilibrium and at what rate? If a competitive behavior starts near an equilibrium, will it stay close to it forever? Is a certain equilibrium state stable to some local perturbation and to what extent. In particular applications, these questions represent practical concerns of interest. (3) Discrete time algorithms. Another contribution is the development of efficient algorithms for the computation of equilibria that can be implemented on parallel computer architectures. These algorithms are derived through time discretization of the projected dynamical system models of the application problems, and hence, besides serving for computational purposes, they track the dynamic behavior of the competitive systems. We have established the convergence of these algorithms under reasonable conditions in the context of the specific applications.

We investigate the linear stability and perform the bifurcation analysis for Hopfield neural networks with a general distribution of delays, where the neurons are identical. We start by analyzing the scalar model and show what kind of information can be gained with only minimal information about the exact distribution of delays. We determine a mean delay and distribution independent stability region. We then illustrate a way of improving on this conservative result by approximating the true region of stability when the actual distribution is not known, but some moments or cumulants of the distribution are. We compare the approximate stability regions with the stability regions in the case of the uniform and gamma distributions. We show that, in general, the approximations improve as more moments or cumulants are used, and that the approximations using cumulants give better results than the ones using moments. Further, we extend these results to a network of n identical neurons, where we examine the stability of a symmetrical equilibrium point via the analysis of the characteristic equation both when the connection matrix is symmetric and when it is not. Finally, for the scalar model, we show under what conditions a Hopf bifurcation occurs and we use the centre manifold technique to determine the criticality of the bifurcation. When the kernel represents the gamma distribution with p=1 and p=2, we transform the delay differential equation into a system of ordinary differential equations and we compare the centre manifold computation to the one we obtain in the ordinary differential case.