Dissertations / Theses on the topic 'Structural stability Mathematical models'

Shear links are used as fuse elements in lateral load resisting systems to provide ductility and dissipate seismic energy. These links have traditionally been employed in eccentrically braced frames, but have more recently been suggested for use in the innovative linked column frame system (LCF). Current design specifications for shear links require intermediate web stiffeners to provide out-of-plane web stability so ductility requirements can be achieved. This research focused on moving from discrete transverse web stiffening to continuously stiffened webs in built up shear links. Built up links were designed to yield in shear when subjected to severe cyclic loading, however the webs of the links were designed using two metal sheets joined by an elastic core. These composite "sandwich" webs allowed for an increase in web thickness (and inherent flexural rigidity) without increasing the shear strength of the links. Numerical and experimental investigations were conducted to assess the performance of composite sandwich links subjected to severe loading. Numerical results showed improved web behavior in sandwich links in which the core material was assigned an elastic modulus greater than 5000psi. Due to fabrication limitations, experimental specimens were fabricated with a core material elastic modulus of 1000psi. These specimens did not perform as well as unstiffened base case links in terms global hysteretic behavior or ductility.

CSLIP2 (De Natale, 1987) is the only slope stability program that utilizes a "direction set" optimization routine in its search for the minimum safety factor. However, CSLIP2 which employs Powell's Conjugate Direction Method permits only the horizontal and vertical directions (x and y) to be used as the initial direction set. The efficiency of the existing search routine is improved by replacing the x-y coordinate directions with initial directions that are parallel to and perpendicular to the principal axis of the safety factor contours.

With a great amount of research currently being aimed towards dynamic analysis and control of very large, flexible structures, the need for accurate knowledge of the properties of a structure in terms of the mass, damping, and stiffness matrices is of extreme importance. Typical problems associated with existing structural model identification methods are: (i) non-unique solutions may be obtained when utilizing only free-response measurements (unless some parameters are fixed at their nominal values), (ii) convergence may be difficult to achieve if the initial estimate of the parameters is not "close" to the truth, (iii) physically unrealistic coupling in the system matrices may occur as a consequence of the identification process, (iv) large, highly redundant parameter sets may be required to characterize the system, and (v) large measurement sets may be required. To overcome these problems, a novel identification technique is developed in this dissertation to determine the mass, damping, and stiffness matrices of an undamped, lightly damped, or significantly damped structure from a small set of measurements of both free-response data (natural frequencies, damping factors) and forced-response data (frequency response functions). The identification method is first developed for undamped structures. Through use of the spectral decomposition of the frequency response matrix and the orthogonality properties of the mode shapes, a unique identification of the mass and stiffness matrices is obtained. The method is also shown to be easily incorporated into a substructure synthesis package for identifying high-order systems. The method is then extended to include viscous damped structures. A matrix perturbation approach is developed for lightly damped structures, in which the mass and stiffness matrices are identified using the imaginary components of the measured eigenvalues and, as a post-processor, the damping matrix is obtained from the real components of the measured eigenvalues. For significantly damped structures, the mass, dauping, and stiffness matrices are identified simultaneously. A simple, practical method is also developed for identification of the time-varying relaxation modulus associated with a viscoelastic structure. By assuming time-localized elastic behavior, the relaxation modulus is determined from a series of identification tests performed at various times throughout the response history. Many interesting examples are presented throughout the dissertation to illustrate the applicability and potential of the identification method. It is observed from the numerical results that the uniquely identified structure agrees with simulated measurements of both free and forced·response records.<br>Ph. D.

In many (social, economic, and political) strategic situations, conflict and cooperations coexist and group (or coalitional) behavior is as important as individual behavior. This dissertation studies several issues in such situations.<br>Chapter 1 provides an overview of the theoretical background and motivates the analysis undertaken.<br>Chapter 2 analyzes strategic situations with diverse coalitional interactions to ascertain the "stable" outcomes that will not be replaced by any rational (hence farsighted) coalition of individuals, and the coalitions that are likely to form. The analysis takes into full account the perfect foresight of rational individuals, which has been overlooked in the literature.<br>Chapter 3 defines "negotiation-proof Nash equilibrium", a notion that applies to environments where players can negotiate openly and directly prior to the play of a noncooperative game. The merit of the notion of negotiation-proof Nash equilibrium is twofold: (1) It resolves the nestedness and myopia embedded in the notion of coalition-proof Nash equilibrium. (2) The negotiation process, which is formalized by a "graph", serves as a natural alternative to the approach that models pre-play communication by an extensive form game.<br>Chapter 4 examines the notion of "renegotiation-proofness" in infinitely repeated games. It is shown that imposing renegotiation in all contingencies creates both conceptual and technical difficulties. A notion of self-enforcing agreements is offered: an agreement is self-enforcing if it is immune to any deviation by any coalition which cannot (confidently) count on renegotiation.

Autonomous deterministic epidemiological models are known to be asymptotically stable. Asymptotic stability of these models contradicts observations. In this thesis we consider some factors which were suggested as able to destabilise the system. We consider discrete-time and continuous-time autonomous epidemiological models. We try to keep our models as simple as possible and investigate the impact of different factors on the system behaviour. Global methods of dynamical systems theory, especially the theory of bifurcations and the direct Lyapunov method are the main tools of our analysis. Lyapunov functions for a range of classical epidemiological models are introduced. The direct Lyapunov method allows us to establish their boundedness and asymptotic stability. It also helps investigate the impact of such factors as susceptibles' mortality, horizontal and vertical transmission and immunity failure on the global behaviour of the system. The Lyapunov functions appear to be useful for more complicated epidemiological models as well. The impact of mass vaccination on the system is also considered. The discrete-time model introduced here enables us to solve a practical problem-to estimate the rate of immunity failure for pertussis in New Zealand. It has been suggested by a number of authors that a non-linear dependence of disease transmission on the numbers of infectives and susceptibles can reverse the stability of the system. However it is shown in this thesis that under biologically plausible constraints the non-linear transmission is unable to destabilise the system. The main constraint is a condition that disease transmission must be a concave function with respect to the number of infectives. This result is valid for both the discrete-time and the continuous-time models. We also consider the impact of mortality associated with a disease. This factor has never before been considered systematically. We indicate mechanisms through which the disease-induced mortality can affect the system and show that the disease-induced mortality is a destabilising factor and is able to reverse the system stability. However the critical level of mortality which is necessary to reverse the system stability exceeds the mortality expectation for the majority of human infections. Nevertheless the disease-induced mortality is an important factor for understanding animal diseases. It appears that in the case of autonomous systems there is no single factor able to cause the recurrent outbreaks of epidemics of such magnitudes as have been observed. It is most likely that in reality they are caused by a combination of factors.<br>Subscription resource available via Digital Dissertations

Most of the current optimization techniques for the design of light-weight structures are unable to generate structural alternatives at the concept stage of design. This research tackles the challenge of developing an optimization method for the early stage of design. The main goal is to propose a procedure to optimize material and shape of stiff shafts in torsion.<br>Recently introduced for bending stiffness design, shape transformers are presented in this thesis for optimizing the design of shafts in torsion. Shape transformers are geometric parameters defined to classify shapes and to model structural efficiency. The study of shape transformers are centered on concept selection in structural design. These factors are used to formulate indices of material and shape selection for minimum mass design. An advantage of the method of shape transformers is that the contribution of the shape can be decoupled from the contribution of the size of a cross-section. This feature gives the designer insight into the effects that scaling, shape, as well as material have on the overall structural performance.<br>Similar to the index for bending, the performance index for torsion stiffness design is a function of the relative scaling of two cross-sections. The thesis examines analytically and graphically the impact of scaling on the torsional efficiency of alternative cross-sections. The resulting maps assist the selection of the best material and shape for cross-sections subjected to dimensional constraints. It is shown that shape transformers for torsion, unlike those for bending, are generally function of the scaling direction.<br>The efficiency maps ease the visual contrast among the efficiency of open-walled cross-sections and that of close-walled cross-sections. As expected, the maps show the relative inefficiency of the former compared to the latter. They can also set the validity range of thin- and thick-walled theory in torsion stiffness design. The analytical results are validated with the numerical data obtained from ANSYS to guarantee the consistency of the models. The thesis concludes with three case studies that demonstrate the method.

Multi-asset credit derivatives trade in huge volumes, yet no models exist that are capable of properly accounting for the spread behaviour of dependent companies. In this thesis we consider new ways of incorporating a richer and more realistic dependence structure into multi-firm models. We focus on the structural framework in which firm value is modelled as a geometric Brownian motion, with default as the first hitting time of an exponential default threshold. Specification of a dependence structure consisting of a common driving influence and firm-specific inter-company ties allows for both default causality and default asymmetry and we incorporate default contagion in the first passage framework for the first time. Building on the work by Zhou (2001a), we propose an analytical model for corporate bond yields in the presence of default contagion and two-firm credit default swap baskets. We derive closed-form solutions for credit spreads, and results clearly highlight the importance of dependence assumptions. Extending this framework numerically, we calculate CDS spreads for baskets of three firms with a wide variety of credit dependence specifications. We examine the impact of firm value correlation and credit contagion for symmetric and asymmetric baskets, and incorporate contagion that has a declining impact over time.

Genetic regulatory network (GRN) is a fundamental research area in systems biology. This thesis studies the stability of a class of GRN models. First, a condition is proposed to ensure the robust stability of uncertain GRNs with SUM regulatory functions. It is assumed that the uncertainties are in the form of a parameter vector that determines the coefficients of the model via given functions. Then, the global asymptotic stability conditions of uncertain GRNs affected by disturbances and time delays are further explored. The conditions are obtained by solving a convex optimization problem by exploring the sum of squares (SOS) of matrix polynomials and by introducing polynomially parameter-dependent Lyapunov-Krasovskii functionals (LKFs). Moreover, based on the uncertain GRNs with guaranteed disturbance attenuation, it is shown that estimates of the sought stable uncertainty sets can be obtained through a recursive strategy based on parameter-dependent Lyapunov functions and the SOS. Second, the stability conditions of GRNs described by piecewise models are considered. Depending on whether the state partitions and mode transitions are known or unknown as priori, the proposed networks are divided into two categories, i.e., switched GRNs and hybrid GRNs. It is shown that, by using common polynomial Lyapunov functions and piecewise polynomial Lyapunov functions, two conditions are established to ensure the global asymptotic stability for switched and hybrid GRNs, respectively. In addition, it is shown that, by using the SOS techniques, stability conditions in the form of LMIs for both models can be obtained. Third, the multi-stability of uncertain GRNs with multivariable regulation functions is investigated. It is shown that, by using the Lyapunov functional method and LMI technology, a criterion is established to ensure the robust asymptotical stability of the uncertain GRNs, and such condition can be extended to deal with the multi-stability problem. Moreover, it is shown that by using the square matrix representation (SMR) and by adopting polynomially parameter-dependent Lyapunov functions, a condition in the form of LMIs for robust stability for all admissible uncertainties can be obtained. Examples with synthetic and real biological models are presented in each section to illustrate the applicability and effectiveness of the theoretical results.<br>published_or_final_version<br>Electrical and Electronic Engineering<br>Doctoral<br>Doctor of Philosophy

Mathematical models for rotary lip seals is developed to study the basic stability and dynamic response of the lip seals. In this thesis, a linear stability analysis is performed to find the stability characteristics of such a mechanical system. Then, a finite element algorithm for the numerical integration of the system of coupled differential equations governing the dynamic behavior of the lip seals is presented.

Proper mathematical models of structures are beneficial for designers and analysts. The accuracy of the results is essential. Therefore, verification and/or correction of the models is vital. This can be done by utilizing experimental results or other analytical solutions. There are different methods of generating the accurate mathematical models. These methods range from completely analytically derived models, completely experimentally derived models, to a combination of the two. These model generation procedures are called System Identification. Today a popular method is to create an analytical model as accurately as possible and then improve this model using experimental results. This thesis provides a review of System Identification methods as applied to vibrating structures. One simple method and three more complex methods, chosen from current engineering literature, are implemented on the computer. These methods offer the capability to correct a discrete (for example, finite element based) model through the use of experimental measurements. The validity of the methods is checked on a two degree of freedom problem, an eight degree of freedom example frequently used in the literature, and with experimentally derived vibration results of a free-free beam.<br>Master of Science

Determination of the stresses and displacements which occur in response to random excitations cannot be accomplished by traditional deterministic analysis methods. As the specification of the excitation and the response of the structure become more complex, solutions by direct, closed-form methods require extensive computations. Two methods are presented which can be used in the analysis of structures which are subjected to random excitations. The Power Spectrum Method is a procedure which determines the random vibration response of the structure based upon a frequency response analysis of a structural model. The Response Spectrum Method is a method which is based upon specified forces or displacements as a function of time. A derivation of each of the methods is presented and followed by comparisons of the results which were obtained for single and multiple-degree-of-freedom systems. Assumptions and limitations of the methods are discussed as well as their accuracy over ranges of frequency, damping and loading specification. As a direct application and comparison of the two methods, an analysis of the support system for the primary mirror of the Space Infrared Telescope Facility (SIRTF) has been performed. In addition, a method for the evaluation of the critical damping in a single-degree-of-freedom structure is demonstrated.

<p>The thesis presents a three dimensional shape optimization program which analyzes models made up of linear isoparametric elements. The goal of the program is to achieve a near uniform model stress state and thereby to minimize material volume.</p> <p> The algorithm is iterative, and performs two analyses per iteration. The first analysis is a static stress analysis of the model for one or more load cases. Based on results from the static analysis, an expansion analysis is performed. Model elements are expanded or contracted based on whether they are stressed higher or lower than a reference stress. The shape changing is done by creating an expansion load vector using the differences between the calculated element stresses and the reference stress. Expansion displacements are solved for, and instead of using them to calculate stresses, the displacements are added to the nodal coordinates to reshape the structure. This process continues until a user defined convergence tolerance is met.</p> <p> Four programs were used for the analysis process. Models were created using a finite element modeling program called I-IDEAS or CAIEDS. The I-IDEAS output files were converted to input files for the optimizer by a conversion program. The model was optimized using the shape optimization process described above. Post- processing was done using a program written with a graphical programming language called graPHIGS.</p> <p>Models used to test the program were: a cylindrical pressure vessel with nonuniform thickness, a spherical pressure vessel with non-uniform thickness, a torque arm, and a draft sill casting o a railroad hopper car. Results were compared to similar studies from selected references.</p> <p> Both pressure vessels converged to near uniform thicknesses, which compared ell with the reference work. In a two dimensional analysis, the torque arm volume decreased 24 percent, which compared well with published results. A three dimensional analysis showed a volume reduction of l3 percent, but there were convergence problems. Finally, the draft sill casting was reduced in volume by 9 percent from a manually optimized design.</p><br>Master of Science

A numerical model has been developed which simulates the three-dimensional stability and transition of a periodically forced free shear layer in an incompressible fluid. Unlike previous simulations of temporally evolving shear layers, the current simulations examine spatial stability. The spatial model accommodates features of free shear flow, observed in experiments, which in the temporal model are precluded by the assumption of streamwise periodicity; e.g., divergence of the mean flow and wave dispersion. The Navier-Stokes equations in vorticity-velocity form are integrated using a combination of numerical methods tailored to the physical problem. A spectral method is adopted in the spanwise dimension in which the flow variables, assumed to be periodic, are approximated by finite Fourier series. In complex Fourier space, the governing equations are spatially two-dimensional. Standard central finite differences are exploited in the remaining two spatial dimensions. For computational efficiency, time evolution is accomplished by a combination of implicit and explicit methods. Linear diffusion terms are advanced by an Alternating Direction Implicit/Crank-Nicolson scheme whereas the Adams-Bashforth method is applied to convection terms. Nonlinear terms are evaluated at each new time level by the pseudospectral (collocation) method. Solutions to the velocity equations, which are elliptic, are obtained iteratively by approximate factorization. The spatial model requires that inflow-outflow boundary conditions be prescribed. Inflow conditions are derived from a similarity solution for the mean inflow profile onto which periodic forcing is superimposed. Forcing functions are derived from inviscid linear stability theory. A numerical test case is selected which closely parallels a well-known physical experiment. Many of the aspects of forced shear layer behavior observed in the physical experiment are captured by the spatial simulation. These include initial linear growth of the fundamental, vorticity roll-up, fundamental saturation, eventual domination of the subharmonic, vortex pairing, emergence of streamwise vorticity, and temporary stabilization of the secondary instability. Moreover, the spatial simulation predicts the experimentally observed superlinear growth of harmonics at rates 1.5 times that of the fundamental. Superlinear growth rates suggest nonlinear resonances between fundamental and harmonic modes which are not captured by temporal simulations.

This Thesis is composed by three independent papers that investigate<p>central debates in empirical macroeconomic modeling.<p><p>Chapter 1, entitled “A Model for Real-Time Data Assessment with an Application to GDP Growth Rates”, provides a model for the data<p>revisions of macroeconomic variables that distinguishes between rational expectation updates and noise corrections. Thus, the model encompasses the two polar views regarding the publication process of statistical agencies: noise versus news. Most of the studies previous studies that analyze data revisions are based<p>on the classical noise and news regression approach introduced by Mankiew, Runkle and Shapiro (1984). The problem is that the statistical tests available do not formulate both extreme hypotheses as collectively exhaustive, as recognized by Aruoba (2008). That is, it would be possible to reject or accept both of them simultaneously. In turn, the model for the<p>DPP presented here allows for the simultaneous presence of both noise and news. While the “regression approach” followed by Faust et al. (2005), along the lines of Mankiew et al. (1984), identifies noise in the preliminary<p>figures, it is not possible for them to quantify it, as done by our model. <p><p>The second and third chapters acknowledge the possibility that macroeconomic data is measured with errors, but the approach followed to model the missmeasurement is extremely stylized and does not capture the complexity of the revision process that we describe in the first chapter.<p><p><p>Chapter 2, entitled “Revisiting the Success of the RBC model”, proposes the use of dynamic factor models as an alternative to the VAR based tools for the empirical validation of dynamic stochastic general equilibrium (DSGE) theories. Along the lines of Giannone et al. (2006), we use the state-space parameterisation of the factor models proposed by Forni et al. (2007) as a competitive benchmark that is able to capture weak statistical restrictions that DSGE models impose on the data. Our empirical illustration compares the out-of-sample forecasting performance of a simple RBC model augmented with a serially correlated noise component against several specifications belonging to classes of dynamic factor and VAR models. Although the performance of the RBC model is comparable<p>to that of the reduced form models, a formal test of predictive accuracy reveals that the weak restrictions are more useful at forecasting than the strong behavioral assumptions imposed by the microfoundations in the model economy.<p><p>The last chapter, “What are Shocks Capturing in DSGE modeling”, contributes to current debates on the use and interpretation of larger DSGE<p>models. Recent tendency in academic work and at central banks is to develop and estimate large DSGE models for policy analysis and forecasting. These models typically have many shocks (e.g. Smets and Wouters, 2003 and Adolfson, Laseen, Linde and Villani, 2005). On the other hand, empirical studies point out that few large shocks are sufficient to capture the covariance structure of macro data (Giannone, Reichlin and<p>Sala, 2005, Uhlig, 2004). In this Chapter, we propose to reconcile both views by considering an alternative DSGE estimation approach which<p>models explicitly the statistical agency along the lines of Sargent (1989). This enables us to distinguish whether the exogenous shocks in DSGE<p>modeling are structural or instead serve the purpose of fitting the data in presence of misspecification and measurement problems. When applied to the original Smets and Wouters (2007) model, we find that the explanatory power of the structural shocks decreases at high frequencies. This allows us to back out a smoother measure of the natural output gap than that<p>resulting from the original specification.<br>Doctorat en Sciences économiques et de gestion<br>info:eu-repo/semantics/nonPublished

Motivated by a practical interest in noise generated by turbofan engine, this thesis studies the stability of parallel coaxial jets with velocity and temperature profiles characteristic of the exhaust region of the engine. Because the bypass stream mixes with both the exhaust and the ambient air, these profiles contain thin layers in which the velocity and temperature may vary rapidly. As a consequence, multiple instability modes are possible. In accordance with Rayleigh's theorem for axisymmetric incompressible shear flows, it follows that there are three possible modes, only two of which are unstable. To complement the study of parallel flow stability, this thesis also includes the derivation of the amplitude evolution equation for slowly varying axisymmetric incompressible flows.

We introduce random fluctuations on contact and recovery rates in three basic deterministic models in mathematical epidemiology and obtain stochastic counterparts. This paper addresses qualitative and quantitative analysis of stochastic SIS model with disease deaths and demographic effects, and stochastic SIR models with/without disease deaths and demographic effects. We prove the global existence of a unique strong solution and discuss stochastic asymptotic stability of disease free and endemic equilibria. We also investigate numerical properties of these models and prove the convergence of the Balanced Implicit Method approximation to the analytic solution. We simulate the models with fairly realistic parameters to visualize our conclusions.

<p>This report presents an analysis of a partial differential equation, resulting from population model with age structure. The existence and uniqueness of a solution to the equation are proved. We look at stability of the solution. The asymptotic behaviour of the solution is treated. The report also contains a section about the connection between the solution to the age structure population model and a simple model without age structure.</p>

The aim of this study is to investigate means of efficiently assessing the effects of distributed structural modification on the dynamic properties of a complex structure. The helicopter structure is normally designed to avoid resonance at the main rotor rotational frequency. However, very often military helicopters have to be modified (such as to carry a different weapon system or an additional fuel tank) to fulfill operational requirements. Any modification to a helicopter structure has the potential of changing its resonance frequencies and mode shapes. The dynamic properties of the modified structure can be determined by experimental testing or numerical simulation, both of which are complex, expensive and time-consuming. Assuming that the original dynamic characteristics are already established and that the modification is a relatively simple attachment such as beam or plate modification, the modified dynamic properties may be determined numerically without solving the equations of motion of the full-modified structure. The frequency response functions (FRFs) of the modified structure can be computed by coupling the original FRFs and a delta dynamic stiffness matrix for the modification introduced. The validity of this approach is investigated by applying it to several cases, 1) 1D structure with structural modification but no change in the number of degree of freedom (DOFs). A simply supported beam with double thickness in the middle section is treated as an example for this case; 2) 1D structure with additional DOFs. A cantilever beam to which a smaller beam is attached is treated as an example for this case, 3) 2D structure with a reduction in DOFs. A four-edge-clamped plate with a cut-out in the centre is treated as an example for this case; and 4) 3D structure with additional DOFs. A box frame with a plate attached to it as structural modification with additional DOFs and combination of different structures. The original FRFs were obtained numerically and experimentally except for the first case. The delta dynamic stiffness matrix was determined numerically by modelling the part of the modified structure including the modifying structure and part of the original structure at the same location. The FRFs of the modified structure were then computed. Good agreement is obtained by comparing the results to the FRFs of the modified structure determined experimentally as well as by numerical modelling of the complete modified structure.

A new approach to structural equation modeling based on so-called extended redundancy analysis (ERA) is proposed. In ERA, latent variables are obtained as exact linear combinations of observed variables, and model parameters are estimated by consistently minimizing a single criterion. As a result, the method can avoid limitations of covariance structure analysis (e.g., stringent distributional assumptions, improper solutions, and factor score indeterminacy) in addition to those of partial least squares (e.g., the lack of a global optimization procedure). The method is simple yet versatile enough to fit more complex models; e.g., those with higher-order latent variables and direct effects of observed variables. It can also fit a model to more than one sample simultaneously. Other relevant topics are also discussed, including data transformations, missing data, metric matrices, robust estimation, and efficient estimation. Examples are given to illustrate the proposed method.

Structural reliability technology provides analytical tools for management of uncertainty in all relevant design factors in structural and mechanical systems. Generally, the goal of analysis is to compute probabilities of failure in structural components or system having single or multiple failure mode. Alternately, modern optimization methods provide efficient numerical algorithms for locating optima, particularly in large-scale systems having prescribed deterministic constraints. Optimization procedure can accommodate random variables either directly in its objective function or as one of the primary constraints. The combination of elementary optimization and probabilistic design techniques is the subject of this study. Presented herein is a general strategy for optimization when the design factors are random variables and some or all of the constraints are probability statements. A literature review has indicated that optimization technology in a reliability context has not been fully explored for the general case of nonlinear performance functions and nonnormal variates associated multiple failure modes. This research focuses upon development of the theory to address this general problem. Because analysis algorithms are complicated, a computer code, program RELOPT, is constructed to automate the analysis. The objective function to be minimized is arbitrary, but would generally be the total expected lifetime costs including all initial costs as well as all costs associated with failure. Uncertainty is assumed to be possible in all design factors (including the factors to be determined), and they are modeled as random variables. In general, all of the constraints can be probability statements. The generalized reduce gradient (GRG) method was used for optimization calculations. Options for point probability calculations are first order reliability analysis using the Rackwitz-Fiessler (R-F) or advanced reliability analysis using Wu/FPI. For system reliability analysis either the first order Cornell's bounds or the second order Ditlevsen's bounds can be specified. Several examples are presented to illustrate the full range of capabilities of RELOPT. The program is validated by checking with independent and exact solutions. An example is provided which demonstrates that the cost of running RELOPT can be substantial as the size of the problem increases.

In estimating econometric time series models, it is assumed that the parameters remain constant over the period examined. This assumption may not always be valid when using data which span an extended period, as the underlying relationships between the variables in these models are exposed to various exogenous shifts. It is therefore imperative to examine the stability of models as failure to identify any changes could result in wrong predictions or inappropriate policy recommendations. This research proposes a method of estimating the location of break points in linear econometric models with endogenous regressors, estimated using Generalised Method of Moments (GMM). The proposed estimation method is based on Wald, Lagrange Multiplier and Difference type test statistics of parameter variation. In this study, the equation which sets out the relationship between the endogenous regressor and the instruments is referred to as the Jacobian Equation (JE). The thesis is presented along two main categories: Stable JE and Unstable JE. Under the Stable JE, models with a single and multiple breaks in the Structural Equation (SE) are examined. The break fraction estimators obtained are shown to be consistent for the true break fraction in the model. Additionally, using the fixed break approach, their $T$-convergence rates are established. Monte Carlo simulations which support the asymptotic properties are presented. Two main types of Unstable JE models are considered: a model with a single break only in the JE and another with a break in both the JE and SE. The asymptotic properties of the estimators obtained from these models are intractable under the fixed break approach, hence the thesis provides essential steps towards establishing the properties using the shrinking breaks approach. Nonetheless, a series of Monte Carlo simulations conducted provide strong support for the consistency of the break fraction estimators under the Unstable JE. A combined procedure for testing and estimating significant break points is detailed in the thesis. This method yields a consistent estimator of the true number of breaks in the model, as well as their locations. Lastly, an empirical application of the proposed methodology is presented using the New Keynesian Phillips Curve (NKPC) model for U.S. data. A previous study has found this NKPC model is unstable, having two endogenous regressors with Unstable JE. Using the combined testing and estimation approach, similar break points were estimated at 1975:2 and 1981:1. Therefore, using the GMM estimation approach proposed in this study, the presence of a Stable or Unstable JE does not affect estimations of breaks in the SE. A researcher can focus directly on estimating potential break points in the SE without having to pre-estimate the breaks in the JE, as is currently performed using Two Stage Least Squares.

Thesis (MScEng)-- Stellenbosch University, 2013.<br>ENGLISH ABSTRACT: Most of the parameters involved in the design and analysis of structures are of stochastic nature. This is, therefore, of paramount importance to be able to perform a fully stochastic analysis of structures both in component and system level to take into account the uncertainties involved in structural analysis and design. To the contrary, in practice, the (computerised) analysis of structures is based on a deterministic analysis which fails to address the randomness of design and analysis parameters. This means that an investigation on the algorithmic methodologies for a component and system reliability analysis can help pave the way towards the implementation of fully stochastic analysis of structures in a computer environment. This study is focused on algorithm development for component and system reliability analysis based on the various proposed methodologies. Truss structures were selected for this purpose due to their simplicity as well as their wide use in the industry. Nevertheless, the algorithms developed in this study can be used for other types of structures such as moment-resisting frames with some simple modi cations. For a component level reliability analysis of structures different methods such as First Order Reliability Methods (FORM) and simulation methods are proposed. However, implementation of these methods for the statistically indeterminate structures is complex due to the implicit relation between the response of the structural system and the load effect. As a result, the algorithm developed for the purpose of component reliability analysis should be based on the concepts of Stochastic Finite Element Methods (SFEM) where a proper link between the finite element analysis of the structure and the reliability analysis methodology is ensured. In this study various algorithms are developed based on the FORM method, Monte Carlo simulation, and the Response Surface Method (RSM). Using the FORM method, two methodologies are considered: one is based on the development of a finite element code where required alterations are made to the FEM code and the other is based on the usage of a commercial FEM package. Different simulation methods are also implemented: Direct Monte Carlo Simulation (DMCS), Latin Hypercube Sampling Monte Carlo (LHCSMC), and Updated Latin Hypercube Sampling Monte Carlo (ULHCSMC). Moreover, RSM is used together with simulation methods. Throughout the thesis, the effciency of these methods was investigated. A Fully Stochastic Finite Element Method (FSFEM) with alterations to the finite element code seems the fastest approach since the linking between the FEM package and reliability analysis is avoided. Simulation methods can also be effectively used for the reliability evaluation where ULHCSMC seemed to be the most efficient method followed by LHCSMC and DMCS. The response surface method is the least straight forward method for an algorithmic component reliability analysis; however, it is useful for the system reliability evaluation. For a system level reliability analysis two methods were considered: the ß-unzipping method and the branch and bound method. The ß-unzipping method is based on a level-wise system reliability evaluation where the structure is modelled at different damaged levels according to its degree of redundancy. In each level, the so-called unzipping intervals are defined for the identification of the critical elements. The branch and bound method is based on the identification of different failure paths of the structure by the expansion of the structural failure tree. The evaluation of the damaged states for both of the methods is the same. Furthermore, both of the methods lead to the development of a parallel-series model for the structural system. The only difference between the two methods is in the search approach used for the failure sequence identification. It was shown that the ß-unzipping method provides a better algorithmic approach for evaluating the system reliability compared to the branch and bound method. Nevertheless, the branch and bound method is a more robust method in the identification of structural failure sequences. One possible way to increase the efficiency of the ß-unzipping method is to define bigger unzipping intervals in each level which can be possible through a computerised analysis. For such an analysis four major modules are required: a general intact structure module, a damaged structure module, a reliability analysis module, and a system reliability module. In this thesis different computer programs were developed for both system and component reliability analysis based on the developed algorithms. The computer programs are presented in the appendices of the thesis.<br>AFRIKAANSE OPSOMMING: Meeste van die veranderlikes betrokke by die ontwerp en analise van strukture is stogasties in hul aard. Om die onsekerhede betrokke in ontwerp en analise in ag te neem is dit dus van groot belang om 'n ten volle stogastiese analise te kan uitvoer op beide komponent asook stelsel vlak. In teenstelling hiermee is die gerekenariseerde analise van strukture in praktyk gebaseer op deterministiese analise wat nie suksesvol is om die stogastiese aard van ontwerp veranderlikes in ag te neem nie. Dit beteken dat die ondersoek na die algoritmiese metodiek vir komponent en stelsel betroubaarheid analise kan help om die weg te baan na die implementering van ten volle rekenaarmatige stogastiese analise van strukture. Di e studie se fokus is op die ontwikkeling van algoritmes vir komponent en stelsel betroubaarheid analise soos gegrond op verskeie voorgestelde metodes. Vakwerk strukture is gekies vir die doeleinde as gevolg van hulle eenvoud asook hulle wydverspreide gebruik in industrie. Die algoritmes wat in die studie ontwikkel is kan nietemin ook vir ander tipes strukture soos moment-vaste raamwerke gebruik word, gegewe eenvoudige aanpassings. Vir 'n komponent vlak betroubaarheid analise van strukture word verskeie metodes soos die "First Order Reliability Methods" (FORM) en simulasie metodes voorgestel. Die implementering van die metodes vir staties onbepaalbare strukture is ingewikkeld as gevolg van die implisiete verband tussen die gedrag van die struktuur stelsel en die las effek. As 'n gevolg, moet die algoritme wat ontwikkel word vir die doel van komponent betroubaarheid analise gebaseer word op die konsepte van stogastiese eindige element metodes ("SFEM") waar 'n duidelike verband tussen die eindige element analise van die struktuur en die betroubaarheid analise verseker is. In hierdie studie word verskeie algoritmes ontwikkel wat gebaseer is op die FORM metode, Monte Carlo simulasie, en die sogenaamde "Response Surface Method" (RSM). Vir die gebruik van die FORM metode word twee verdere metodologieë ondersoek: een gebaseer op die ontwikkeling van 'n eindige element kode waar nodige verandering aan die eindige element kode self gemaak word en die ander waar 'n kommersiële eindige element pakket gebruik word. Verskillende simulasie metodes word ook geïmplimenteer naamlik Direkte Monte Carlo Simulasie (DMCS), "Latin Hypercube Sampling Monte Carlo" (LHCSMC) en sogenaamde "Updated Latin Hypercube Sampling Monte Carlo" (ULHCSMC). Verder, word RSM tesame met die simulasie metodes gebruik. In die tesis word die doeltreffendheid van die bostaande metodes deurgaans ondersoek. 'n Ten volle stogastiese eindige element metode ("FSFEM") met verandering aan die eindige element kode blyk die vinnigste benadering te wees omdat die koppeling tussen die eindige element metode pakket en die betroubaarheid analise verhoed word. Simulasie metodes kan ook effektief aangewend word vir die betroubaarheid evaluasie waar ULHCSMC as die mees doeltre end voorgekom het, gevolg deur LHCSMC en DMCS. The RSM metode is die mees komplekse metode vir algoritmiese komponent betroubaarheid analise. Die metode is egter nuttig vir sisteem betroubaarheid analise. Vir sisteem-vlak betroubaarheid analise is twee metodes oorweeg naamlik die "ß-unzipping" metode and die "branch-and-bound" metode. Die "ß-unzipping" metode is gebaseer op 'n sisteem-vlak betroubaarheid ontleding waar die struktuur op verskillende skade vlakke gemodelleer word soos toepaslik vir die hoeveelheid addisionele las paaie. In elke vlak word die sogenaamde "unzipping" intervalle gedefinieer vir die identifikasie van die kritiese elemente. Die "branch-and-bound" metode is gebaseer op die identifikasie van verskillende faling roetes van die struktuur deur uitbreiding van die falingsboom. The ondersoek van die skade toestande vir beide metodes is dieselfde. Verder kan beide metodes lei tot die ontwikkeling van 'n parallelserie model van die strukturele stelsel. Die enigste verskil tussen die twee metodes is in die soek-benadering vir die uitkenning van falingsmodus volgorde. Dit word getoon dat die "ß-unzipping" metode 'n beter algoritmiese benadering is vir die ontleding van sisteem betroubaarheid vergeleke met die "branch-and-bound" metode. Die "branch-and- bound" metode word nietemin as 'n meer robuuste metode vir die uitkenning van die falings volgorde beskou. Een moontlike manier om die doeltre endheid van die "ß-unzipping" metode te verhoog is om groter "unzipping" intervalle te gebruik, wat moontlik is vir rekenaarmatige analise. Vir so 'n analise word vier hoof modules benodig naamlik 'n algemene heel-struktuur module, 'n beskadigde-struktuur module, 'n betroubaarheid analise module en 'n sisteem betroubaarheid analise module. In die tesis word verskillende rekenaar programme ontwikkel vir beide sisteem en komponent betroubaarheid analise. Die rekenaar programme word in die aanhangsels van die tesis aangebied.

The stability criteria for single-mode standing-wave laser oscillators in the strongly homogeneously broadened limit are reported for the first time. Two types of stability criteria are presented. The first type, called type 1, corresponds to the minimum value of threshold parameter for which an infinitesimal perturbation away from steady state grows into an oscillatory solution. Another type of stability criteria, called type 2, corresponds to the minimum value of threshold parameter for which large amplitude oscillatory solutions do not decay to the steady state solution. Undamped pulsations in single mode strongly homogeneously broadened standing-wave laser oscillators are found to occur at a much higher excitation level than that of ring-laser oscillators with the same type of line broadening. The effect of detuning on stability criteria is also investigated. We discovered that detuning tends to raise the type 1 instability threshold and to decrease the type 2 instability threshold.

Mount Etna, Europe's largest active volcano, shows a long history of changing structure and environment, culminating in the modern volcanic edifice with its observed slope instability and region of past collapse (the Valle del Bove). The structure and evolution of the volcano and, more importantly, the Valle del Bove are poorly understood but have major effects on its present day behaviour. Several geophysical techniques have been used in order to determine new models for the sub-surface structure of the volcano, concentrating on the Eastern Flank and the Valle del Bove. The Valle del Bove is an important feature on the Eastern Flank. It measures 5 by 7 km and is 1200m deep at its maximum. Its formation and evolution are poorly understood and represent the main thrust of this work. The primary work has been gravity and aeromagnetic surveys combined with 2.5-D and 3-D modelling to develop a better understanding of the sub-surface structures of the area. This work has identified several large gravity and magnetic anomalies indicating areas of contrasting geophysical properties. A 16mGal positive gravity anomaly over the Southern Wall of the Valle del Bove is interpreted as a large (volume = 38km3) high density (2950 kg m-3) body, related to the old Trifoglietto centre, possibly representing the ancient feeder system. A second high density body is seen under the present day summit region and is interpreted as an area of shallow level magma storage within the upper flanks of the volcano. A negative gravity anomaly of 10mGal towards the coast, over the Chiancone sedimentary fan deposit, is interpreted as reworked debris flow material, derived from the Valle del Bove. The shape of the anomaly is strongly asymmetrical relative to the geographical extent of the deposit, with the centre of the anomaly sitting over its Northern extent. The resultant model of this material gives a thickness of 700m, with the material being deposited within a fault controlled basin, open to the sea. Such a shape suggests that a sizeable volume of material may be deposited off-shore. Below the Etnean volcanics lie sedimentary layers which slope in an easterly direction, providing a surface over which the Eastern Flank. is free to slide. Finite element modelling of the stress fields within the volcanic edifice and basement shows that the effects of sea-level variations and glaciations may be of a sufficient magnitude to affect the volcanic system, however, the time over which these changes occur may be more significant than the changes themselves. Similarly the Valle del Bove is shown to have had a significant effect on the stress patterns, and has resulted in a self-reinforcing process whereby the tension caused by the removal of mass encourages further collapse. Palaeomagnetic measurements show that rotational failure has not been important in the formation of the Valle del Bove, and combined with the results of the other methods, show the Valle's formation to have been via a series of small piecemeal collapses, possibly relating to oversteepening of the walls following dyke emplacement. These results are combined together to show that the Valle del Bove has been developing over much of the history of Etna, and is not a recent addition to the volcano.

Online social and information networks, like Facebook and Twitter, exploit the influence of neighbors to achieve effective information sharing and spreading. The process that information is spread via the connected nodes in social and information networks is referred to as diffusion. In the literature, a number of diffusion models have been proposed for different applications like influential user identification and personalized recommendation. However, comprehensive studies to discover the hidden diffusion mechanisms governing the information diffusion using the data-driven paradigm are still lacking. This thesis research aims to design novel diffusion models with the structural and behaviorable dependency of neighboring nodes for representing social networks, and to develop computational algorithms to infer the diffusion models as well as the underlying diffusion mechanisms based on information cascades observed in real social networks. By incorporating structural dependency and diversity of node neighborhood into a widely used diffusion model called Independent Cascade (IC) Model, we first propose a component-based diffusion model where the influence of parent nodes is exerted via connected components. Instead of estimating the node-based diffusion probabilities as in the IC Model, component-based diffusion probabilities are estimated using an expectation maximization (EM) algorithm derived under a Bayesian framework. Also, a newly derived structural diversity measure namely dynamic effective size is proposed for quantifying the dynamic information redundancy within each parent component. The component-based diffusion model suggests that node connectivity is a good proxy to quantify how a node's activation behavior is affected by its node neighborhood. To model directly the behavioral dependency of node neighborhood, we then propose a co-activation pattern based diffusion model by integrating the latent class model into the IC Model where the co-activation patterns of parent nodes form the latent classes for each node. Both the co-activation patterns and the corresponding pattern-based diffusion probabilities are inferred using a two-level EM algorithm. As compared to the component-based diffusion model, the inferred co-activation patterns can be interpreted as the soft parent components, providing insights on how each node is influenced by its neighbors as reflected by the observed cascade data. With the motivation to discover a common set of the over-represented temporal activation patterns (motifs) characterizing the overall diffusion in a social network, we further propose a motif-based diffusion model. By considering the temporal ordering of the parent activations and the social roles estimated for each node, each temporal activation motif is represented using a Markov chain with the social roles being its states. Again, a two-level EM algorithm is proposed to infer both the temporal activation motifs and the corresponding diffusion network simultaneously. The inferred activation motifs can be interpreted as the underlying diffusion mechanisms characterizing the diffusion happening in the social network. Extensive experiments have been carried out to evaluate the performance of all the proposed diffusion models using both synthetic and real data. The results obtained and presented in the thesis demonstrate the effectiveness of the proposed models. In addition, we discuss in detail how to interpret the inferred co-activation patterns and interaction motifs as the diffusion mechanisms under the context of different real social network data sets.

ix, 111 p.<br>This dissertation contains the results obtained from a study of two subjects in mathematical general relativity. The first part of this dissertation is about the existence of Killing symmetries in spacetimes containing a compact Cauchy horizon. We prove the existence of a nontrivial Killing symmetry in a large class of analytic cosmological spacetimes with a compact Cauchy horizon for any spacetime dimension. In doing so, we also remove the restrictive analyticity condition and obtain a generalization to the smooth case. The second part of the dissertation presents our results on the global stability problem for a class of cosmological models. We investigate the power law inflating cosmological models in the presence of electromagnetic fields. A stability result for such cosmological spacetimes is proved. This dissertation includes unpublished co-authored material.<br>Committee in charge: James Brau, Chair; James Isenberg, Advisor; Paul Csonka, Member; John Toner, Member; Peng Lu, Outside Member