The stochastic process algebra PEPA is a powerful modelling formalism for concurrent systems, which has enjoyed considerable success over the last decade. Such modelling can help designers by allowing aspects of a system which are not readily tested, such as protocol validity and performance, to be analysed before a system is deployed. However, model construction and analysis can be challenged by the size and complexity of large scale systems, which consist of large numbers of components and thus result in state-space explosion problems. Both structural and quantitative analysis of large scale PEPA models suffers from this problem, which has limited wider applications of the PEPA language. This thesis focuses on developing PEPA, to overcome the state-space explosion problem, and make it suitable to validate and evaluate large scale computer and communications systems, in particular a content adaption framework proposed by the Mobile VCE. In this thesis, a new representation scheme for PEPA is proposed to numerically capture the structural and timing information in a model. Through this numerical representation, we have found that there is a Place/Transition structure underlying each PEPA model. Based on this structure and the theories developed for Petri nets, some important techniques for the structural analysis of PEPA have been given. These techniques do not suffer from the state-space explosion problem. They include a new method for deriving and storing the state space and an approach to finding invariants which can be used to reason qualitatively about systems. In particular, a novel deadlock-checking algorithm has been proposed to avoid the state-space explosion problem, which can not only efficiently carry out deadlock-checking for a particular system but can tell when and how a system structure lead to deadlocks. In order to avoid the state-space explosion problem encountered in the quantitative analysis of a large scale PEPA model, a fluid approximation approach has recently been proposed, which results in a set of ordinary differential equations (ODEs) to approximate the underlying CTMC. This thesis presents an improved mapping from PEPA to ODEs based on the numerical representation scheme, which extends the class of PEPA models that can be subjected to fluid approximation. Furthermore, we have established the fundamental characteristics of the derived ODEs, such as the existence, uniqueness, boundedness and nonnegativeness of the solution. The convergence of the solution as time tends to infinity for several classes of PEPA models, has been proved under some mild conditions. For general PEPA models, the convergence is proved under a particular condition, which has been revealed to relate to some famous constants of Markov chains such as the spectral gap and the Log-Sobolev constant. This thesis has established the consistency between the fluid approximation and the underlying CTMCs for PEPA, i.e. the limit of the solution is consistent with the equilibrium probability distribution corresponding to a family of underlying density dependent CTMCs. These developments and investigations for PEPA have been applied to both qualitatively and quantitatively evaluate the large scale content adaptation system proposed by the Mobile VCE. These analyses provide an assessment of the current design and should guide the development of the system and contribute towards efficient working patterns and system optimisation.

This thesis is concerned with the numerical solutions of initial value problems with ordinary differential equations and covers single step integration methods. focus is to study the numerical the various aspects of Specifically, its main methods of non-linear integration formula with a variety of means based on the Contraharmonic mean (C.M) (Evans and Yaakub [1995]), the Centroidal mean (C.M) (Yaakub and Evans [1995]) and the Root-Mean-Square (RMS) (Yaakub and Evans [1993]) for solving initial value problems. the applications of the second It includes a study of order C.M method for parallel implementation of extrapolation methods for ordinary differential equations with the ExDaTa schedule by Bahoshy [1992]. Another important topic presented in this thesis is that a fifth order five-stage explicit Runge Kutta method or weighted Runge Kutta formula [Evans and Yaakub [1996]) exists which is contrary to Butcher [1987] and the theorem in Lambert ([1991] ,pp 181). The thesis is organized as follows. An introduction to initial value problems in ordinary differential equations and parallel computers and software in Chapter 1, the basic preliminaries and fundamental concepts in mathematics, an algebraic manipulation package, e.g., Mathematica and basic parallel processing techniques are discussed in Chapter 2. Following in Chapter 3 is a survey of single step methods to solve ordinary differential equations. In this chapter, several single step methods including the Taylor series method, Runge Kutta method and a linear multistep method for non-stiff and stiff problems are also considered. Chapter 4 gives a new Runge Kutta formula for solving initial value problems using the Contraharmonic mean (C.M), the Centroidal mean (C.M) and the Root-MeanSquare (RMS). An error and stability analysis for these variety of means and numerical examples are also presented. Chapter 5 discusses the parallel implementation on the Sequent 8000 parallel computer of the Runge-Kutta contraharmonic mean (C.M) method with extrapolation procedures using explicit assignment scheduling Kutta RK(4, 4) method (EXDATA) strategies. A is introduced and the data task new Rungetheory and analysis of its properties are investigated and compared with the more popular RKF(4,5) method, are given in Chapter 6. Chapter 7 presents a new integration method with error control for the solution of a special class of second order ODEs. In Chapter 8, a new weighted Runge-Kutta fifth order method with 5 stages is introduced. By comparison with the currently recommended RK4 ( 5) Merson and RK5(6) Nystrom methods, the new method gives improved results. Chapter 9 proposes a new fifth order Runge-Kutta type method for solving oscillatory problems by the use of trigonometric polynomial interpolation which extends the earlier work of Gautschi [1961]. An analysis of the convergence and stability of the new method is given with comparison with the standard Runge-Kutta methods. Finally, Chapter 10 summarises and presents conclusions on the topics discussed throughout the thesis.

This research effort develops a comprehensive computational framework to support the parametric optimal design of uncertain dynamical systems. Uncertainty comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; not accounting for uncertainty may result in poor robustness, sub-optimal performance and higher manufacturing costs. Contemporary methods for the quantification of uncertainty in dynamical systems are computationally intensive which, so far, have made a robust design optimization methodology prohibitive. Some existing algorithms address uncertainty in sensors and actuators during an optimal design; however, a comprehensive design framework that can treat all kinds of uncertainty with diverse distribution characteristics in a unified way is currently unavailable. The computational framework uses Generalized Polynomial Chaos methodology to quantify the effects of various sources of uncertainty found in dynamical systems; a Least-Squares Collocation Method is used to solve the corresponding uncertain differential equations. This technique is significantly faster computationally than traditional sampling methods and makes the construction of a parametric optimal design framework for uncertain systems feasible. The novel framework allows to directly treat uncertainty in the parametric optimal design process. Specifically, the following design problems are addressed: motion planning of fully-actuated and under-actuated systems; multi-objective robust design optimization; and optimal uncertainty apportionment concurrently with robust design optimization. The framework advances the state-of-the-art and enables engineers to produce more robust and optimally performing designs at an optimal manufacturing cost. / Ph. D.

<p>Thorium dioxide (ThO₂) and metallic uranium (alpha-U) represent important alternative nuclear fuels. Investigating the behavior of defects introduced into these materials in an irradiation environment is critical for understanding microstructure evolution and property changes. The objective of this dissertation is to investigate the clustering of point defects in ThO₂ and alpha-U under irradiation, into voids and prismatic dislocation loops as a function of irradiation dose rate and temperature. To achieve this, we have developed a mean-field cluster dynamics (CD) model based on reaction rate theory to predict the evolution of self-interstitial atom (SIA) and vacancy loops in neutron-irradiated alpha-U. Detailed atomistic simulations have been carried out using molecular dynamics (MD) to study the configuration of such loops and compute their energetics, which are essential parameters of the CD model. Bond-boost hyper-MD simulations have been performed to compute the diffusivity of uranium SIA and vacancies, which govern the kinetics of the clustering phenomenon. Another CD model has been demonstrated for proton-irradiated ThO₂, considering the clustering of Th and O SIA and vacancies into SIA loops and voids, respectively, with varying sizes and stoichiometry. The compositions of all SIA loops and voids dictated by crystallography of ThO₂ in its fluorite structure have been presented in their respective cluster composition space (CCS). The CD model solves the density evolution of off-stoichiometric loops and voids, with irradiation, in their respective CCS. MD simulations have been performed to compute the energetics of different clusters in their CCS, as parameters of the CD model. Temperature-accelerated MD simulations have been performed to compute the diffusivity of Th and O point defects, that dictates the kinetics of defect clustering on irradiation. In alpha-U, the CD predictions show an accumulation of small sized vacancy loops and the growth of SIA loops with irradiation dose, which closely fits the reported size distribution of loops in neutron-irradiated alpha-U by Hudson and coworkers. The CD predicted density of defect clusters in proton-irradiated ThO₂, shows the evolution of near-stoichiometric SIA loops in their CCS. The size distribution of SIA loops at high irradiation doses closely corresponds to the transmission electron microscopy (TEM) observations reported in the literature. Also, the CD model did not predict the growth of voids and vacancy clusters, which is consistent with findings in literature. The model was further used to predict the density of sub-nanometric defect clusters and point defects, on low-dose irradiation, that significantly impairs the thermal conductivity of ThO₂. An extensive TEM and CD investigation has also been carried out to study the growth and coarsening of SIA loop and voids during post-irradiation isochronal annealing of ThO₂ at high temperatures.</p>