Discrete event systems (DESs) are systems which involve quantities that take a discrete set of values, called states, and which evolve according to the occurrence of certain discrete qualitative changes, called events. Examples of DESs include many man-made systems such as computer and communication networks, robotics and manufacturing systems, computer programs, and automated trac systems. Supervisory control and failure diagnosis are two important problems in the study of DESs. This dissertation presents a temporal logic approach to the control and failure diagnosis of DESs. For the control of DESs, full branching time temporal logic-CTL* is used to express control specifications. Control problem of DES in the temporal logic setting is formulated; and the controllability of DES is defined. By encoding the system with a CTL formula, the control problem of CTL* is reduced to the decision problem of CTL*. It is further shown that the control problem of CTL* (resp., CTL{computation tree logic) is complete for deterministic double (resp., single) exponential time. A sound and complete supervisor synthesis algorithm for the control of CTL* is provided. Special cases of the control of computation tree logic (CTL) and linear-time temporal logic (LTL) are also studied; and for which algorithms of better complexity are provided. For the failure diagnosis of DESs, LTL is used to express fault specifications. Failure diagnosis problem of DES in the temporal logic setting is formulated; and the diagnosability of DES is defined. The problem of testing the diagnosability is reduced to that of model checking. An algorithm for the test of diagnosability and the synthesis of a diagnoser is obtained. The algorithm has a polynomial complexity in the number of system states and the number of fault specifications. For the diagnosis of repeated failures in DESs, different notions of repeated failure diagnosability, K-diagnosability, [1,K]-diagnosability, and [1,1]-diagnosability, are introduced. Polynomial algorithms for checking these various notions of repeated failure diagnosability are given, and a procedure of polynomial complexity for the on-line diagnosis of repeated failures is also presented.

The research project reported in this thesis considers Multiple Distributed Replications in Parallel (MDRIP), a hybrid approach to parallelisation of quantitative stochastic discrete-event simulation. Parallel Discrete-Event Simulation (PDES) generally covers distributed simulation or simulation with replicated trials. Distributed simulation requires model partitioning and synchronisation among submodels. Simulation with replicated trials can be executed on-line by applying Multiple Replications in Parallel (MRIP). MDRIP has been proposed for overcoming problems related to the large size of simulated models and their complexity, as well as with the problem of controlling the accuracy of the final simulation results. A survey of PDES investigates several primary issues which are directly related to the parallelisation of DES. A secondary issue related to implementation efficiency is also covered. Statistical analysis as a supporting issue is described. The AKAROA2 package is an implementation of making such supporting issue effortless. Existing solutions proposed for PDES have exclusively focused on collecting of output data during simulation and conducting analysis of these data when simulation is finished. Such off-line statistical analysis of output data offers no control of statistical errors of the final estimates. On-line control of statistical errors during simulation has been successfully implemented in AKAROA2, an automated controller of output data analysis during simulation executed in MRIP. However, AKAROA2 cannot be applied directly to distributed simulation. This thesis reports results of a research project aimed at employing AKAROA2 for launching multiple replications of distributed simulation models and for on-line sequential control of statistical errors associated with a distributed performance measure; i.e. with a performance measure which depends on output data being generated by a number of submodels of distributed simulation. We report changes required in the architecture of AKAROA2 to make MDRIP possible. A new MDRIP-related component of AKAROA2, a distributed simulation engine mdrip engine, is introduced. Stochastic simulation in its MDRIP version, as implemented in AKAROA2, has been tested in a number of simulation scenarios. We discuss two specific simulation models employed in our tests: (i) a model consisting of independent queues, and (ii) a queueing network consisting of tandem connection of queueing systems. In the first case, we look at the correctness of message orderings from the distributed messages. In the second case, we look at the correctness of output data analysis when the analysed performance measures require data from all submodels of a given (distributed) simulation model. Our tests confirm correctness of our mdrip engine design in the cases considered; i.e. in models in which causality errors do not occur. However, we argue that the same design principles should be applicable in the case of distributed simulation models with (potential) causality errors.

Discrete event simulation is well known to be a powerful approach to investigate behaviour of complex dynamic stochastic systems, especially when the system is analytically not tractable. The estimation of mean values has traditionally been the main goal of simulation output analysis, even though it provides limited information about the analysed system's performance. Because of its complexity, quantile analysis is not as frequently applied, despite its ability to provide much deeper insights into the system of interest. A set of quantiles can be used to approximate a cumulative distribution function, providing fuller information about a given performance characteristic of the simulated system. This thesis employs the distributed computing power of multiple computers by proposing new methods for sequential and automated analysis of quantile-based performance measures of such dynamic systems. These new methods estimate steady state quantiles based on replicating simulations on clusters of workstations as simulation engines. A general contribution to the problem of the length of the initial transient is made by considering steady state in terms of the underlying probability distribution. Our research focuses on sequential and automated methods to guarantee a satisfactory level of confidence of the final results. The correctness of the proposed methods has been exhaustively studied by means of sequential coverage analysis. Quantile estimates are used to investigate underlying probability distributions. We demonstrate that synchronous replications greatly assist this kind of analysis.

Large-eddy simulation is rapidly becoming the preferred method for calculations involving turbulent phenomena. However, filtering equations as performed in traditional LES procedures leads to significant problems. In this work we present some key components in the construction of a novel LES solver for compressible turbulent flow, designed to overcome most of the problems faced by traditional LES procedures. We describe the construction of the large-scale algorithm, which employs fairly standard numerical techniques to solve the Navier{Stokes equations. We validate the algorithm for both transonic and supersonic ow scenarios. We further explicitly show that the solver is capable of capturing boundary layer effects. We present a detailed derivation of the chaotic map termed the \compressible poor man's Navier{Stokes (CPMNS) equation" starting from the Navier{Stokes equations themselves via a Galerkin procedure, which we propose to use as the fluctuating component in the SGS model. We provide computational results to show that the chaotic map can produce a wide range of temporal behaviors when the bifurcation parameters are varied over their ranges of stable behaviors. Investigations of the overall dynamics of the CPMNS equation demonstrates that its use increases the potential realism of the corresponding SGS model.

This thesis investigates using an approach based on the Actors paradigm for implementing a discrete event simulation system and comparing the results with more traditional approaches. The goal of this work is to determine if using Actors for sequential programming is viable. If Actors are viable for this type of programming, then it follows that they would be usable for general programming. One potential advantage of using Actors instead of traditional paradigms for general programming would be the elimination of a distinction between designing for a sequential environment and a concurrent/distributed one. Using Actors for general programming may also allow for a single implementation that can be deployed on both single core and multiple core systems. Most of the existing discussions about the Actors model focus on its strengths in distributed environments and its ability to scale with the amount of available computing resources. The chosen system for implementation is intentionally sequential to allow for examination of the behaviour of existing Actors implementations where managing concurrency complexity is not the primary task. Multiple implementations of the simulation system were built using different languages (C++, Erlang, and Java) and different paradigms, including traditional ones and Actors. These different implementations were compared quantitatively, based on their execution time, memory usage, and code complexity. The analysis of these comparisons indicates that for certain existing development environments, Erlang/OTP, following the Actors paradigm, produces a comparable or better implementation than traditional paradigms. Further research is suggested to solidify the validity of the results presented in this research and to extend their applicability.

Discrete choice models (DCMs) are used to forecast demand in a variety of engineering, marketing, and policy contexts, and understanding the uncertainty associated with model forecasts is crucial to inform decision-making. This thesis evaluates the suitability of DCMs for forecasting automotive demand. The entire scope of this investigation is too broad to be covered here, but I explore several elements with a focus on three themes: defining how to measure forecast accuracy, comparing model specifications and forecasting methods in terms of prediction accuracy, and comparing the implications of model specifications and forecasting methods on vehicle design. Specifically I address several questions regarding the accuracy and uncertainty of market share predictions resulting from choice of utility function and structural specification, estimation method, and data structure assumptions. I1 compare more than 9,000 models based on those used in peer-reviewed literature and academic and government studies. Firstly, I find that including more model covariates generally improves predictive accuracy, but that the form those covariates take in the utility function is less important. Secondly, better model fit correlates well with better predictive accuracy; however, the models I construct— representative of those in extant literature— exhibit substantial prediction error stemming largely from limited model fit due to unobserved attributes. Lastly, accuracy of predictions in existing markets is neither a necessary nor sufficient condition for use in design. Much of the econometrics literature on vehicle market modeling has presumed that biased coefficients make for bad models. For purely predictive purposes, the drawbacks of potentially mitigating bias using generalized method of moments estimation coupled with instrumental variables outweigh the expected benefits in the experiments conducted in this dissertation. The risk of specifying invalid instruments is high, and my results suggest that the instruments frequently used in the automotive demand literature are likely invalid. Furthermore, biased coefficients are not necessarily bad for maximizing the predictive power of the model. Bias can even aid predictions by implicitly capturing persistent unobserved effects in some circumstances. Including alternative specific constants (ASCs) in DCM utility functions improves model fit but not necessarily forecast accuracy. For frequentist estimated models all tested methods of forecasting ASCs improved share predictions of the whole midsize sedan market over excluding ASC in predictions, but only one method results in improved long term new vehicle, or entrant, forecasts. As seen in a synthetic data study, assuming an incorrect relationship between observed attributes and the ASC for forecasting risks making worse forecasts than would be made by a model that excludes ASCs entirely. Treating the ASCs as model parameters with full distributions of uncertainty via Bayesian estimation is more robust to selection of ASC forecasting method and less reliant on persistent market structures, however it comes at increased computational cost. Additionally, the best long term forecasts are made by the frequentist model that treats ASCs as calibration constants fit to the model post estimation of other parameters.

Noble metal nanoparticles are of great interest due to their tunable optical and radiative properties. The specific wavelength of light at which the localized surface plasmon resonance occurs is dependent upon the shape, size and composition of the particle as well as the dielectric constant of the host medium. Thus, the optical properties of noble metal nanoparticles can be systematically tuned by altering these specific parameters. The purpose of this thesis is to investigate some of these properties related to metallic nanoparticles. The first several chapters focus on theoretical modeling to predict and explain various plasmonic properties of gold and silver nanoparticles while the later chapters focus on more accurately combining experimental and theoretical methods to explain the plasmonic properties of hollow gold nanoparticles of various shapes. The appendix contains a detailed description of the theoretical methods used throughout the thesis. It is intended to serve as a guide such that a user could carry out the various types of calculations discussed in this thesis simply by reading this appendix.

In this diploma work, two versions of the discrete nonlinear Schrödinger (DNLS) equation are used to model a nonlinear layered photonic crystal system; the cubic DNLS (cDNLS) equation and the saturable DNLS (sDNLS) equation. They both have site-dependent coefficients to break mirror symmetry with respect to propagation direction, as well as to describe the linear and nonlinear properties of the system. Analytical solutions taking on plane wave form are, via the backward transfer map, used to derive a transmission coefficient as well as a rectifying factor to quantify the diode effect. The effect of varying site-dependent coefficients is studied in detail. Numerical simulations of Gaussian wave packets impinging on the system, using open boundary conditions, show the breaking of parity symmetry. Evidence of a change in the wave packet dynamics occurring in the transition between the cubic and the saturable DNLS model is presented. A saturated system prevents the wave packet from getting stuck in the nonlinear lattice layers. The transmission properties were found to be very sensitive to slight changes of the system parameters.

The objectives of the study were to evaluate the soil disturbances and manure dispersion created by the AerWay aerator in a silt loam soil; and to generate a calibrated and validated soil-tool model using Discrete Element Methods (DEM) that simulate the draft and vertical forces of the aerator. The experimental results showed that a trend indicated that the faster tractor speeds would disturb more soil. After one hour with the manure application rate of 42 000 L/ha, manure was spread to a depth of 250 mm, 200 mm in the forward direction and 100 mm in the lateral direction. The model draft forces had a relative error of 13.4-31.2% when compared to the literature data between 100-150 mm depth while the predicted vertical force was found to linearly increase until 150 mm depth at around 700 N per rolling tine and plateaus until the full insertion of 200 mm.

Consider a probability distribution on the permutations of n elements. If the probability of each permutation is proportional to θK, where K is the number of cycles in the permutation, then we say that the distribution generates a θ-biased random permutation. A random permutation is a special θ-biased random permutation with θ = 1. The mth moment of the rth longest cycle of a random permutation is Θ(nm), regardless of r and θ. The joint moments are derived, and it is shown that the longest cycles of a permutation can either be positively or negatively correlated, depending on θ. The mth moments of the rth shortest cycle of a random permutation is Θ(nm−θ/(ln n)r−1) when θ < m, Θ((ln n)r) when θ = m, and Θ(1) when θ > m. The exponent of cycle lengths at the 100qth percentile goes to q with zero variance. The exponent of the expected cycle lengths at the 100qth percentile is at least q due to the Jensen’s inequality, and the exact value is derived.