Multi-directional polymer matrix composite materials are increasingly used in load-bearing structural applications ranging from primary aircraft structures and automotive parts to rehabilitation of bridges. Long-term durability, characterized by time-dependent degradation in strength (known as creep-rupture) and modulus (known as creep), is an important concern in these applications. Despite the experimental evidence on the influence of time-dependent damage on creep and creep rupture of multi-directional composites, current level of understanding of this is very limited. Hence, the focus of this thesis is to develop a clear understanding of the time dependent evolution of various damage modes and their influence on creep rupture of polymer matrix composite laminates.Three laminates [0/90/0], [±45/902]s, and [0/902]s were subjected to a wide range of constant stresses at various test temperatures and creep rupture time was recorded.The various damage modes that developed, with stress during tensile testing, and with time during constant stress creep rupture testing were transverse cracking, vertical cracking, delamination, vertical splitting and fiber fracture.The appearance of these damages were time dependent confirming that the FPF stress is time-dependent, while the conventional wisdom is to consider it to be time-independent in design. Beyond FPF, the damage continued to evolve for a certain period of time beyond which additional damage modes started to evolve influencing the evolution rate of one-another.The percentage of creep rupture time during which a single mode of damage was evolving decreased with increase in applied stress and test temperature.Based on these results it is concluded that creep rupture of multidirectional laminates is influenced by contributions from a complex interaction of various damage modes that evolve with time, suggesting that creep rupture predictions could be good approximations only.

Multi-directional polymer matrix composite materials are increasingly used in load-bearing structural applications ranging from primary aircraft structures and automotive parts to rehabilitation of bridges. Long-term durability, characterized by time-dependent degradation in strength (known as creep-rupture) and modulus (known as creep), is an important concern in these applications. Despite the experimental evidence on the influence of time-dependent damage on creep and creep rupture of multi-directional composites, current level of understanding of this is very limited. Hence, the focus of this thesis is to develop a clear understanding of the time dependent evolution of various damage modes and their influence on creep rupture of polymer matrix composite laminates.Three laminates [0/90/0], [±45/902]s, and [0/902]s were subjected to a wide range of constant stresses at various test temperatures and creep rupture time was recorded.The various damage modes that developed, with stress during tensile testing, and with time during constant stress creep rupture testing were transverse cracking, vertical cracking, delamination, vertical splitting and fiber fracture.The appearance of these damages were time dependent confirming that the FPF stress is time-dependent, while the conventional wisdom is to consider it to be time-independent in design. Beyond FPF, the damage continued to evolve for a certain period of time beyond which additional damage modes started to evolve influencing the evolution rate of one-another.The percentage of creep rupture time during which a single mode of damage was evolving decreased with increase in applied stress and test temperature.Based on these results it is concluded that creep rupture of multidirectional laminates is influenced by contributions from a complex interaction of various damage modes that evolve with time, suggesting that creep rupture predictions could be good approximations only.

Multi-directional polymer matrix composite materials are increasingly used in load-bearing structural applications ranging from primary aircraft structures and automotive parts to rehabilitation of bridges. Long-term durability, characterized by time-dependent degradation in strength (known as creep-rupture) and modulus (known as creep), is an important concern in these applications. Despite the experimental evidence on the influence of time-dependent damage on creep and creep rupture of multi-directional composites, current level of understanding of this is very limited. Hence, the focus of this thesis is to develop a clear understanding of the time dependent evolution of various damage modes and their influence on creep rupture of polymer matrix composite laminates.Three laminates [0/90/0], [±45/902]s, and [0/902]s were subjected to a wide range of constant stresses at various test temperatures and creep rupture time was recorded.The various damage modes that developed, with stress during tensile testing, and with time during constant stress creep rupture testing were transverse cracking, vertical cracking, delamination, vertical splitting and fiber fracture.The appearance of these damages were time dependent confirming that the FPF stress is time-dependent, while the conventional wisdom is to consider it to be time-independent in design. Beyond FPF, the damage continued to evolve for a certain period of time beyond which additional damage modes started to evolve influencing the evolution rate of one-another.The percentage of creep rupture time during which a single mode of damage was evolving decreased with increase in applied stress and test temperature.Based on these results it is concluded that creep rupture of multidirectional laminates is influenced by contributions from a complex interaction of various damage modes that evolve with time, suggesting that creep rupture predictions could be good approximations only. / May 2008

In this thesis, we study time-dependent empirical processes, which extend the classical empirical processes to have a time parameter; for example the empirical process for a sequence of independent stochastic processes {Yi : i ∈ N}: (1) ν_n(t, y) = n^(−1/2 )Sigma[1_(Y i(t)¬<=y) – P(Yi(t) <= y)] from i=1 to n, t ∈ E, y ∈ R. In the case of independent identically distributed samples (that is {Yi(t) : i ∈ N} are iid), Kuelbs et al. (2013) proved a Central Limit Theorem for ν_n(t, y) for a large class of stochastic processes. In Chapter 3, we give a sufficient condition for the weak convergence of the weighted empirical process for iid samples from a uniform process: (2) α_n(t, y) := n^(−1/2 )Sigma[w(y)(1_(X (t)<=y) – y)] from i=1 to n, t ∈ E, y ∈ [0, 1] where {X (t), X1(t), X2(t), • • • } are independent and identically distributed uniform processes (for each t ∈ E, X (t) is uniform on (0, 1)) and w(x) is a “weight” function satisfying some regularity properties. Then we give an example when X (t) := Ft(Bt) : t ∈ E = [1, 2], where Bt is a Brownian motion and Ft is the distribution function of Bt. In Chapter 4, we investigate the weak convergence of the empirical processes for non-iid samples. We consider the weak convergence of the empirical process: (3) β_n(t, y) := n^(−1/2 )Sigma[(1_(Y (t)<=y) – Fi(t,y))] from i=1 to n, t ∈ E ⊂ R, y ∈ R where {Yi(t) : i ∈ N} are independent processes and Fi(t, y) is the distribution function of Yi(t). We also prove that the covariance function of the empirical process for non-iid samples indexed by a uniformly bounded class of functions necessarily uniformly converges to the covariance function of the limiting Gaussian process for a CLT.

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This thesis presents analytic and computational advances in the prediction of perturbative nonlinear optical spectroscopies. The contributions of this thesis are packaged together in an open source, freely available piece of software called ultrafast spectroscopy suite (UFSS). It is designed to automatically simulate nonlinear optical spectroscopies for any phase-matching or phase-cycling condition, including finite pulse effects. UFSS includes an algorithm called the diagram generator (DG) that automates the process of writing out all of the Feynman diagrams that contribute to a desired phase-matching or phase-cycling condition, and includes all pulse overlap diagrams when relevant, paving the way toward automation of perturbative calculations. Further, many diagrams can be automatically combined into composite diagrams, giving an exponential decrease in computation time of high-order calculations. Composite diagrams even allow for the efficient study of Rabi oscillations as a function of pulse amplitude, by summing many orders of perturbation theory. The perturbative calculations are done using a novel algorithm presented in this thesis called Ultrafast Ultrafast spectroscopy (UF2). UF2 is an efficient method for determining diagrammatic contributions to spectra including arbitrary (whether analytical or experimentally measured) pulse shapes. It uses the speed of the fast Fourier transform to be as much as 500 times faster than direct propagation techniques for small model Hamiltonians (for Hamiltonian dimension of 100 or less). UF2 outperforms direct propagation techniques for a wide range of model systems, with the speed boost diminishing as the dimension of the model Hamiltonian increases. UF2 can predict spectra for any model system whose relevant Hilbert space that can be described using a finite basis and that can be diagonalized numerically, and users are free to specify their own model. UFSS includes a model generator that generates Hamiltonians and Liouvillians of vibronic systems, allowing users to easily simulate NLOSs for a wide range of model system parameters. UFSS is a fully functional piece of software for simulating any NLOS, to any desired order in perturbation theory.

Application of polymer matrix composites in engineering structures has been steadily increasing over the past five decades. Multidirectional polymer composites are one class of continuous fiber reinforced polymer matrix composites used in aerospace structures, where the desired mechanical performance outweighs the cost. Their modulus and strength degrade with time (known as creep and creep rupture) during the service, owing to the viscos-elasticity of the polymer matrix. Additional contribution to this degradation comes from various damage modes developed in the plies of the composite with time and identified in this thesis as TDD (Time Dependent Damage). These damage modes may also develop due to process-induced residual stresses, and during loading to the service load, identified as TID (Time Independent Damage). TID influences the TDD, the creep and the creep rupture. The objective of this thesis is to develop a model to predict the evolution of TID and TDD in multiple plies of a laminate and their influence on creep. The predominant damage mode, transverse cracking, is modeled in this study. The model consists of four modules, PIS, QSL, SL, and VA. The PIS, QSL, and SL moduli predict changes in ply stresses for incremental change in temperature, stress, and time respectively, using lamination theory and assuming linear elastic behavior of the plies during an incremental step. In parallel, each module predicts the stored elastic energy in each ply after each incremental step and compares it with a critical stored elastic energy criterion to determine if a ply would crack. If fracture is predicted, the VA module based on variational analysis, is invoked to determine the crack density and the perturbation in ply stresses due to cracking. The perturbation stresses are used by the module that invoked the VA module to determine the ply stresses after cracking during the current incremental step. The model predictions for a [±45/90]s laminate, at two test temperatures (80C and 180C) and four stresses in the range of 20–54 MPa, compare very well with experimental results validating the model.

Application of polymer matrix composites in engineering structures has been steadily increasing over the past five decades. Multidirectional polymer composites are one class of continuous fiber reinforced polymer matrix composites used in aerospace structures, where the desired mechanical performance outweighs the cost. Their modulus and strength degrade with time (known as creep and creep rupture) during the service, owing to the viscos-elasticity of the polymer matrix. Additional contribution to this degradation comes from various damage modes developed in the plies of the composite with time and identified in this thesis as TDD (Time Dependent Damage). These damage modes may also develop due to process-induced residual stresses, and during loading to the service load, identified as TID (Time Independent Damage). TID influences the TDD, the creep and the creep rupture. The objective of this thesis is to develop a model to predict the evolution of TID and TDD in multiple plies of a laminate and their influence on creep. The predominant damage mode, transverse cracking, is modeled in this study. The model consists of four modules, PIS, QSL, SL, and VA. The PIS, QSL, and SL moduli predict changes in ply stresses for incremental change in temperature, stress, and time respectively, using lamination theory and assuming linear elastic behavior of the plies during an incremental step. In parallel, each module predicts the stored elastic energy in each ply after each incremental step and compares it with a critical stored elastic energy criterion to determine if a ply would crack. If fracture is predicted, the VA module based on variational analysis, is invoked to determine the crack density and the perturbation in ply stresses due to cracking. The perturbation stresses are used by the module that invoked the VA module to determine the ply stresses after cracking during the current incremental step. The model predictions for a [±45/90]s laminate, at two test temperatures (80C and 180C) and four stresses in the range of 20–54 MPa, compare very well with experimental results validating the model.

South African metropolitan areas are experiencing rapid growth and require an increase in network infrastructure. Increased congestion negatively impacts both public and freight transport costs. The concept of City Logistics is concerned with the mobility of cities, and entails the process of optimizing urban logistics activities by concerning the social, environmental, economic, financial, and energy impacts of urban freight movement. In a costcompetitive environment, freight transporters often use sophisticated vehicle routing and scheduling applications to improve fleet utilization and reduce the cost of meeting customer demands. In this thesis, the candidate builds on the observation that vehicle routing and scheduling algorithms are inherent problem specific, with no single algorithm providing a dominant solution to all problem environments. Commercial applications mostly deploy a single algorithm in a multitude of environments which would often be better serviced by various different algorithms. This thesis algorithmically implements the ability of human decision makers to choose an appropriate solution algorithm when solving scheduling problems. The intent of the routing agent is to classify the problem as representative of a traditional problem set, based on its characteristics, and then to solve the problem with the most appropriate solution algorithm known for the traditional problem set. A not-so-artificially-intelligent-vehicle-routing-agent™ is proposed and developed in this thesis. To be considered intelligent, an agent is firstly required to be able to recognize its environment. Fuzzy c-means clustering is employed to analyze the geographic dispersion of the customers (nodes) from an unknown routing problem to determine to which traditional problem set it relates best. Cluster validation is used to classify the routing problem into a traditional problem set. Once the routing environment is classified, the agent selects an appropriate metaheuristic to solve the complex variant of the Vehicle Routing Problem. Multiple soft time windows, a heterogeneous fleet, and multiple scheduling are addressed in the presence of time-dependent travel times. A new initial solution heuristic is proposed that exploits the inherent configuration of customer service times through a concept referred to as time window compatibility. A high-quality initial solution is subsequently improved by the Tabu Search metaheuristic through both an adaptive memory, and a self-selection structure. As an alternative to Tabu Search, a Genetic Algorithm is developed in this thesis. Two new crossover mechanisms are proposed that outperform a number of existing crossover mechanisms. The first proposed mechanism successfully uses the concept of time window compatibility, while the second builds on an idea used from a different sweeping-arc heuristic. A neural network is employed to assist the intelligent routing agent to choose, based on its knowledge base, between the two metaheuristic algorithms available to solve the unknown problem at hand. The routing agent then not only solves the complex variant of the problem, but adapts to the problem environment by evaluating its decisions, and updating, or reaffirming its knowledge base to ensure improved decisions are made in future. / Thesis (PhD (Industrial Engineering))--University of Pretoria, 2007. / Industrial and Systems Engineering / PhD / unrestricted

Survival models are used in analysing time-to-event data. This type of data is very common in medical research. The Cox proportional hazard model is commonly used in analysing time-to-event data. However, this model is based on the proportional hazard (PH) assumption. Violation of this assumption often leads to biased results and inferences. Once non-proportionality is established, there is a need to consider time-varying effects of the covariates. Several models have been developed that relax the proportionality assumption making it possible to analyse data with time-varying effects of both baseline and time-updated covariates. I present various approaches for handling time-varying covariates and time-varying effects in time-to-event models. They include the extended Cox model which handles exogenous time-dependent covariates using the counting process formulation introduced by cite{andersen1982cox}. Andersen and Gill accounts for time varying covariates by each individual having multiple observations with the total-at-risk follow up for each individual being further divided into smaller time intervals. The joint models for the longitudinal and time-to-event processes and its extensions (parametrization and multivariate joint models) were used as it handles endogenous time-varying covariates appropriately. Another is the Aalen model, an additive model which accounts for time-varying effects. However, there are situations where all the covariates of interest do not have time-varying effects. Hence, the semi-parametric additive model can be used. In conclusion, comparisons are made on the results of all the fitted models and it shows that choice of a particular model to fit is influenced by the aim and objectives of fitting the model. In 2002, an AntiRetroviral Treatment (ART) service was established in the Cape Town township of Gugulethu, South Africa. These models will be applied to an HIV/AIDS observational dataset obtained from all patients who initiated ART within the programme between September 2002 and June 2007.