Continuum percolation with discs having a distribution of radii

It is shown that for continuum percolation with overlapping discs having a distribution of radii, the net areal density of discs at percolation threshold depends non-trivially on the distribution, and is not bounded by any finite constant. Results of a Monte Carlo simulation supporting the argument are presented.

Hierarchical Bayesian modelling of plant pest invasions with human-mediated dispersal

Hierarchical Bayesian models can assimilate surveillance and ecological information to estimate both invasion extent and model parameters for invading plant pests spread by people. A reliability analysis framework that can accommodate multiple dispersal modes is developed to estimate human-mediated dispersal parameters for an invasive species. Uncertainty in the observation process is modelled by accounting for local natural spread and population growth within spatial units. Broad scale incursion dynamics are based on a mechanistic gravity model with a Weibull distribution modification to incorporate a local pest build-up phase. The model uses Markov chain Monte Carlo simulations to infer the probability of colonisation times for discrete spatial units and to estimate connectivity parameters between these units. The hierarchical Bayesian model with observational and ecological components is applied to a surveillance dataset for a spiralling whitefly (Aleurodicus dispersus) invasion in Queensland, Australia. The model structure provides a useful application that draws on surveillance data and ecological knowledge that can be used to manage the risk of pest movement.

Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic

Uncertainties associated with the structural model and measured vibration data may lead to unreliable damage detection. In this paper, we show that geometric and measurement uncertainty cause considerable problem in damage assessment which can be alleviated by using a fuzzy logic-based approach for damage detection. Curvature damage factor (CDF) of a tapered cantilever beam are used as damage indicators. Monte Carlo simulation (MCS) is used to study the changes in the damage indicator due to uncertainty in the geometric properties of the beam. Variation in these CDF measures due to randomness in structural parameter, further contaminated with measurement noise, are used for developing and testing a fuzzy logic system (FLS). Results show that the method correctly identifies both single and multiple damages in the structure. For example, the FLS detects damage with an average accuracy of about 95 percent in a beam having geometric uncertainty of 1 percent COV and measurement noise of 10 percent in single damage scenario. For multiple damage case, the FLS identifies damages in the beam with an average accuracy of about 94 percent in the presence of above mentioned uncertainties. The paper brings together the disparate areas of probabilistic analysis and fuzzy logic to address uncertainty in structural damage detection.

Bayesian fisheries stock assessment: integrating and updating knowledge

In this thesis the use of the Bayesian approach to statistical inference in fisheries stock assessment is studied. The work was conducted in collaboration of the Finnish Game and Fisheries Research Institute by using the problem of monitoring and prediction of the juvenile salmon population in the River Tornionjoki as an example application. The River Tornionjoki is the largest salmon river flowing into the Baltic Sea. This thesis tackles the issues of model formulation and model checking as well as computational problems related to Bayesian modelling in the context of fisheries stock assessment. Each article of the thesis provides a novel method either for extracting information from data obtained via a particular type of sampling system or for integrating the information about the fish stock from multiple sources in terms of a population dynamics model. Mark-recapture and removal sampling schemes and a random catch sampling method are covered for the estimation of the population size. In addition, a method for estimating the stock composition of a salmon catch based on DNA samples is also presented. For most of the articles, Markov chain Monte Carlo (MCMC) simulation has been used as a tool to approximate the posterior distribution. Problems arising from the sampling method are also briefly discussed and potential solutions for these problems are proposed. Special emphasis in the discussion is given to the philosophical foundation of the Bayesian approach in the context of fisheries stock assessment. It is argued that the role of subjective prior knowledge needed in practically all parts of a Bayesian model should be recognized and consequently fully utilised in the process of model formulation.

An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA)problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max-min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga-Bhadra river system in India.

Conceptual and statistical modelling of environmental effects in population dynamics

Population dynamics are generally viewed as the result of intrinsic (purely density dependent) and extrinsic (environmental) processes. Both components, and potential interactions between those two, have to be modelled in order to understand and predict dynamics of natural populations; a topic that is of great importance in population management and conservation. This thesis focuses on modelling environmental effects in population dynamics and how effects of potentially relevant environmental variables can be statistically identified and quantified from time series data. Chapter I presents some useful models of multiplicative environmental effects for unstructured density dependent populations. The presented models can be written as standard multiple regression models that are easy to fit to data. Chapters II IV constitute empirical studies that statistically model environmental effects on population dynamics of several migratory bird species with different life history characteristics and migration strategies. In Chapter II, spruce cone crops are found to have a strong positive effect on the population growth of the great spotted woodpecker (Dendrocopos major), while cone crops of pine another important food resource for the species do not effectively explain population growth. The study compares rate- and ratio-dependent effects of cone availability, using state-space models that distinguish between process and observation error in the time series data. Chapter III shows how drought, in combination with settling behaviour during migration, produces asymmetric spatially synchronous patterns of population dynamics in North American ducks (genus Anas). Chapter IV investigates the dynamics of a Finnish population of skylark (Alauda arvensis), and point out effects of rainfall and habitat quality on population growth. Because the skylark time series and some of the environmental variables included show strong positive autocorrelation, the statistical significances are calculated using a Monte Carlo method, where random autocorrelated time series are generated. Chapter V is a simulation-based study, showing that ignoring observation error in analyses of population time series data can bias the estimated effects and measures of uncertainty, if the environmental variables are autocorrelated. It is concluded that the use of state-space models is an effective way to reach more accurate results. In summary, there are several biological assumptions and methodological issues that can affect the inferential outcome when estimating environmental effects from time series data, and that therefore need special attention. The functional form of the environmental effects and potential interactions between environment and population density are important to deal with. Other issues that should be considered are assumptions about density dependent regulation, modelling potential observation error, and when needed, accounting for spatial and/or temporal autocorrelation.

Comparison of the Radar and Seeker Modes of Pursuer Guidance

This paper compares closed-loop performance of seeker-based and radar-based estimators for surface-to-air interception through 6-degree-of-freedom simulation using proportional navigation guidance.Ground radar measurements are evader range, azimuth and elevation angles contaminated by Gaussian noise. Onboard seeker measurements are pursuer-evader relative range, range rate also contaminated by Gaussian noise. The gimbal angles and line-of-sight rates in the gimbal frame,contaminated by time-correlated non-Gaussian noise with realistic numerical values are also available as measurements. In both the applications, extended Kalman filter with Gaussian noise assumption are used for state estimation. For a typical engagement, it is found that,based on Monte Carlo studies, seeker estimator outperforms radar estimator in terms of autopilot demand and reduces the miss distance.Thus, a seeker estimator with white Gaussian assumption is found to be adequate to handle the measurements even in the presence of non-Gaussian correlated noise. This paper uses realistic numerical values of all noise parameters.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

Geant4 Hadronic Cascade Models and CMS Data Analysis : Computational Challenges in the LHC era

This work belongs to the field of computational high-energy physics (HEP). The key methods used in this thesis work to meet the challenges raised by the Large Hadron Collider (LHC) era experiments are object-orientation with software engineering, Monte Carlo simulation, the computer technology of clusters, and artificial neural networks. The first aspect discussed is the development of hadronic cascade models, used for the accurate simulation of medium-energy hadron-nucleus reactions, up to 10 GeV. These models are typically needed in hadronic calorimeter studies and in the estimation of radiation backgrounds. Various applications outside HEP include the medical field (such as hadron treatment simulations), space science (satellite shielding), and nuclear physics (spallation studies). Validation results are presented for several significant improvements released in Geant4 simulation tool, and the significance of the new models for computing in the Large Hadron Collider era is estimated. In particular, we estimate the ability of the Bertini cascade to simulate Compact Muon Solenoid (CMS) hadron calorimeter HCAL. LHC test beam activity has a tightly coupled cycle of simulation-to-data analysis. Typically, a Geant4 computer experiment is used to understand test beam measurements. Thus an another aspect of this thesis is a description of studies related to developing new CMS H2 test beam data analysis tools and performing data analysis on the basis of CMS Monte Carlo events. These events have been simulated in detail using Geant4 physics models, full CMS detector description, and event reconstruction. Using the ROOT data analysis framework we have developed an offline ANN-based approach to tag b-jets associated with heavy neutral Higgs particles, and we show that this kind of NN methodology can be successfully used to separate the Higgs signal from the background in the CMS experiment.

Irradiation-mediated tailoring of carbon nanotubes

The ever-increasing demand for faster computers in various areas, ranging from entertaining electronics to computational science, is pushing the semiconductor industry towards its limits on decreasing the sizes of electronic devices based on conventional materials. According to the famous law by Gordon E. Moore, a co-founder of the world s largest semiconductor company Intel, the transistor sizes should decrease to the atomic level during the next few decades to maintain the present rate of increase in the computational power. As leakage currents become a problem for traditional silicon-based devices already at sizes in the nanometer scale, an approach other than further miniaturization is needed to accomplish the needs of the future electronics. A relatively recently proposed possibility for further progress in electronics is to replace silicon with carbon, another element from the same group in the periodic table. Carbon is an especially interesting material for nanometer-sized devices because it forms naturally different nanostructures. Furthermore, some of these structures have unique properties. The most widely suggested allotrope of carbon to be used for electronics is a tubular molecule having an atomic structure resembling that of graphite. These carbon nanotubes are popular both among scientists and in industry because of a wide list of exciting properties. For example, carbon nanotubes are electronically unique and have uncommonly high strength versus mass ratio, which have resulted in a multitude of proposed applications in several fields. In fact, due to some remaining difficulties regarding large-scale production of nanotube-based electronic devices, fields other than electronics have been faster to develop profitable nanotube applications. In this thesis, the possibility of using low-energy ion irradiation to ease the route towards nanotube applications is studied through atomistic simulations on different levels of theory. Specifically, molecular dynamic simulations with analytical interaction models are used to follow the irradiation process of nanotubes to introduce different impurity atoms into these structures, in order to gain control on their electronic character. Ion irradiation is shown to be a very efficient method to replace carbon atoms with boron or nitrogen impurities in single-walled nanotubes. Furthermore, potassium irradiation of multi-walled and fullerene-filled nanotubes is demonstrated to result in small potassium clusters in the hollow parts of these structures. Molecular dynamic simulations are further used to give an example on using irradiation to improve contacts between a nanotube and a silicon substrate. Methods based on the density-functional theory are used to gain insight on the defect structures inevitably created during the irradiation. Finally, a new simulation code utilizing the kinetic Monte Carlo method is introduced to follow the time evolution of irradiation-induced defects on carbon nanotubes on macroscopic time scales. Overall, the molecular dynamic simulations presented in this thesis show that ion irradiation is a promisingmethod for tailoring the nanotube properties in a controlled manner. The calculations made with density-functional-theory based methods indicate that it is energetically favorable for even relatively large defects to transform to keep the atomic configuration as close to the pristine nanotube as possible. The kinetic Monte Carlo studies reveal that elevated temperatures during the processing enhance the self-healing of nanotubes significantly, ensuring low defect concentrations after the treatment with energetic ions. Thereby, nanotubes can retain their desired properties also after the irradiation. Throughout the thesis, atomistic simulations combining different levels of theory are demonstrated to be an important tool for determining the optimal conditions for irradiation experiments, because the atomic-scale processes at short time scales are extremely difficult to study by any other means.

Theoretical and computational approaches on heterogeneous nucleation

Nucleation is the first step of a first order phase transition. A new phase is always sprung up in nucleation phenomena. The two main categories of nucleation are homogeneous nucleation, where the new phase is formed in a uniform substance, and heterogeneous nucleation, when nucleation occurs on a pre-existing surface. In this thesis the main attention is paid on heterogeneous nucleation. This thesis wields the nucleation phenomena from two theoretical perspectives: the classical nucleation theory and the statistical mechanical approach. The formulation of the classical nucleation theory relies on equilibrium thermodynamics and use of macroscopically determined quantities to describe the properties of small nuclei, sometimes consisting of just a few molecules. The statistical mechanical approach is based on interactions between single molecules, and does not bear the same assumptions as the classical theory. This work gathers up the present theoretical knowledge of heterogeneous nucleation and utilizes it in computational model studies. A new exact molecular approach on heterogeneous nucleation was introduced and tested by Monte Carlo simulations. The results obtained from the molecular simulations were interpreted by means of the concepts of the classical nucleation theory. Numerical calculations were carried out for a variety of substances nucleating on different substances. The classical theory of heterogeneous nucleation was employed in calculations of one-component nucleation of water on newsprint paper, Teflon and cellulose film, and binary nucleation of water-n-propanol and water-sulphuric acid mixtures on silver nanoparticles. The results were compared with experimental results. The molecular simulation studies involved homogeneous nucleation of argon and heterogeneous nucleation of argon on a planar platinum surface. It was found out that the use of a microscopical contact angle as a fitting parameter in calculations based on the classical theory of heterogeneous nucleation leads to a fair agreement between the theoretical predictions and experimental results. In the presented cases the microscopical angle was found to be always smaller than the contact angle obtained from macroscopical measurements. Furthermore, molecular Monte Carlo simulations revealed that the concept of the geometrical contact parameter in heterogeneous nucleation calculations can work surprisingly well even for very small clusters.

Molecular Dynamics Simulations of Homogeneous Nucleation

Nucleation is the first step in a phase transition where small nuclei of the new phase start appearing in the metastable old phase, such as the appearance of small liquid clusters in a supersaturated vapor. Nucleation is important in various industrial and natural processes, including atmospheric new particle formation: between 20 % to 80 % of atmospheric particle concentration is due to nucleation. These atmospheric aerosol particles have a significant effect both on climate and human health. Different simulation methods are often applied when studying things that are difficult or even impossible to measure, or when trying to distinguish between the merits of various theoretical approaches. Such simulation methods include, among others, molecular dynamics and Monte Carlo simulations. In this work molecular dynamics simulations of the homogeneous nucleation of Lennard-Jones argon have been performed. Homogeneous means that the nucleation does not occur on a pre-existing surface. The simulations include runs where the starting configuration is a supersaturated vapor and the nucleation event is observed during the simulation (direct simulations), as well as simulations of a cluster in equilibrium with a surrounding vapor (indirect simulations). The latter type are a necessity when the conditions prevent the occurrence of a nucleation event in a reasonable timeframe in the direct simulations. The effect of various temperature control schemes on the nucleation rate (the rate of appearance of clusters that are equally able to grow to macroscopic sizes and to evaporate) was studied and found to be relatively small. The method to extract the nucleation rate was also found to be of minor importance. The cluster sizes from direct and indirect simulations were used in conjunction with the nucleation theorem to calculate formation free energies for the clusters in the indirect simulations. The results agreed with density functional theory, but were higher than values from Monte Carlo simulations. The formation energies were also used to calculate surface tension for the clusters. The sizes of the clusters in the direct and indirect simulations were compared, showing that the direct simulation clusters have more atoms between the liquid-like core of the cluster and the surrounding vapor. Finally, the performance of various nucleation theories in predicting simulated nucleation rates was investigated, and the results among other things highlighted once again the inadequacy of the classical nucleation theory that is commonly employed in nucleation studies.

Optimum Design for External Seismic Stability of Geosynthetic Reinforced Soil Walls: Reliability Based Approach

In this paper, an analytical study considering the effect of uncertainties in the seismic analysis of geosynthetic-reinforced soil (GRS) walls is presented. Using limit equilibrium method and assuming sliding wedge failure mechanism, analysis is conducted to evaluate the external stability of GRS walls when subjected to earthquake loads. Target reliability based approach is used to estimate the probability of failure in three modes of failure, viz., sliding, bearing, and eccentricity failure. The properties of reinforced backfill, retained backfill, foundation soil, and geosynthetic reinforcement are treated as random variables. In addition, the uncertainties associated with horizontal seismic acceleration and surcharge load acting on the wall are considered. The optimum length of reinforcement needed to maintain the stability against three modes of failure by targeting various component and system reliability indices is obtained. Studies have also been made to study the influence of various parameters on the seismic stability in three failure modes. The results are compared with those given by first-order second moment method and Monte Carlo simulation methods. In the illustrative example, external stability of the two walls, Gould and Valencia walls, subjected to Northridge earthquake is reexamined.

Nonlinear vibration analysis of composite laminated and sandwich plates with random material properties

Nonlinear vibration analysis is performed using a C-0 assumed strain interpolated finite element plate model based on Reddy's third order theory. An earlier model is modified to include the effect of transverse shear variation along the plate thickness and Von-Karman nonlinear strain terms. Monte Carlo Simulation with Latin Hypercube Sampling technique is used to obtain the variance of linear and nonlinear natural frequencies of the plate due to randomness in its material properties. Numerical results are obtained for composite plates with different aspect ratio, stacking sequence and oscillation amplitude ratio. The numerical results are validated with the available literature. It is found that the nonlinear frequencies show increasing non-Gaussian probability density function with increasing amplitude of vibration and show dual peaks at high amplitude ratios. This chaotic nature of the dispersion of nonlinear eigenvalues is also r

Optimum Design for External Seismic Stability of Geosynthetic Reinforced Soil Walls: Reliability Based Approach

In this paper, an analytical study considering the effect of uncertainties in the seismic analysis of geosynthetic-reinforced soil (GRS) walls is presented. Using limit equilibrium method and assuming sliding wedge failure mechanism, analysis is conducted to evaluate the external stability of GRS walls when subjected to earthquake loads. Target reliability based approach is used to estimate the probability of failure in three modes of failure, viz., sliding, bearing, and eccentricity failure. The properties of reinforced backfill, retained backfill, foundation soil, and geosynthetic reinforcement are treated as random variables. In addition, the uncertainties associated with horizontal seismic acceleration and surcharge load acting on the wall are considered. The optimum length of reinforcement needed to maintain the stability against three modes of failure by targeting various component and system reliability indices is obtained. Studies have also been made to study the influence of various parameters on the seismic stability in three failure modes. The results are compared with those given by first-order second moment method and Monte Carlo simulation methods. In the illustrative example, external stability of the two walls, Gould and Valencia walls, subjected to Northridge earthquake is reexamined.