On Topological Solitons in The Faddeev-Skyrme Model and its Extensions

The topological solitons of two classical field theories, the Faddeev-Skyrme model and the Ginzburg-Landau model are studied numerically and analytically in this work. The aim is to gain information on the existence and properties of these topological solitons, their structure and behaviour under relaxation. First, the conditions and mechanisms leading to the possibility of topological solitons are explored from the field theoretical point of view. This leads one to consider continuous deformations of the solutions of the equations of motion. The results of algebraic topology necessary for the systematic treatment of such deformations are reviewed and methods of determining the homotopy classes of topological solitons are presented. The Faddeev-Skyrme and Ginzburg-Landau models are presented, some earlier results reviewed and the numerical methods used in this work are described. The topological solitons of the Faddeev-Skyrme model, Hopfions, are found to follow the same mechanisms of relaxation in three different domains with three different topological classifications. For two of the domains, the necessary but unusual topological classification is presented. Finite size topological solitons are not found in the Ginzburg-Landau model and a scaling argument is used to suggest that there are indeed none unless a certain modification to the model, due to R. S. Ward, is made. In that case, the Hopfions of the Faddeev-Skyrme model are seen to be present for some parameter values. A boundary in the parameter space separating the region where the Hopfions exist and the area where they do not exist is found and the behaviour of the Hopfion energy on this boundary is studied.

Model for interevent times with long tails and multifractality in human communications: An application to financial trading

Social, technological, and economic time series are divided by events which are usually assumed to be random, albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics has therefore become a central issue. The approach we present is taken from the continuous-time random-walk formalism and represents an analytical alternative to models of nontrivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the intertransaction time intervals of several financial markets. We observe that empirical data describe a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. A stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region.

A Practical Micro Mechanical Model Based Local Approach Methodology for the Analysis of Ductile Fracture of Welded T-Joints

This thesis concentrates on developing a practical local approach methodology based on micro mechanical models for the analysis of ductile fracture of welded joints. Two major problems involved in the local approach, namely the dilational constitutive relation reflecting the softening behaviour of material, and the failure criterion associated with the constitutive equation, have been studied in detail. Firstly, considerable efforts were made on the numerical integration and computer implementation for the non trivial dilational Gurson Tvergaard model. Considering the weaknesses of the widely used Euler forward integration algorithms, a family of generalized mid point algorithms is proposed for the Gurson Tvergaard model. Correspondingly, based on the decomposition of stresses into hydrostatic and deviatoric parts, an explicit seven parameter expression for the consistent tangent moduli of the algorithms is presented. This explicit formula avoids any matrix inversion during numerical iteration and thus greatly facilitates the computer implementation of the algorithms and increase the efficiency of the code. The accuracy of the proposed algorithms and other conventional algorithms has been assessed in a systematic manner in order to highlight the best algorithm for this study. The accurate and efficient performance of present finite element implementation of the proposed algorithms has been demonstrated by various numerical examples. It has been found that the true mid point algorithm (a = 0.5) is the most accurate one when the deviatoric strain increment is radial to the yield surface and it is very important to use the consistent tangent moduli in the Newton iteration procedure. Secondly, an assessment of the consistency of current local failure criteria for ductile fracture, the critical void growth criterion, the constant critical void volume fraction criterion and Thomason's plastic limit load failure criterion, has been made. Significant differences in the predictions of ductility by the three criteria were found. By assuming the void grows spherically and using the void volume fraction from the Gurson Tvergaard model to calculate the current void matrix geometry, Thomason's failure criterion has been modified and a new failure criterion for the Gurson Tvergaard model is presented. Comparison with Koplik and Needleman's finite element results shows that the new failure criterion is fairly accurate indeed. A novel feature of the new failure criterion is that a mechanism for void coalescence is incorporated into the constitutive model. Hence the material failure is a natural result of the development of macroscopic plastic flow and the microscopic internal necking mechanism. By the new failure criterion, the critical void volume fraction is not a material constant and the initial void volume fraction and/or void nucleation parameters essentially control the material failure. This feature is very desirable and makes the numerical calibration of void nucleation parameters(s) possible and physically sound. Thirdly, a local approach methodology based on the above two major contributions has been built up in ABAQUS via the user material subroutine UMAT and applied to welded T joints. By using the void nucleation parameters calibrated from simple smooth and notched specimens, it was found that the fracture behaviour of the welded T joints can be well predicted using present methodology. This application has shown how the damage parameters of both base material and heat affected zone (HAZ) material can be obtained in a step by step manner and how useful and capable the local approach methodology is in the analysis of fracture behaviour and crack development as well as structural integrity assessment of practical problems where non homogeneous materials are involved. Finally, a procedure for the possible engineering application of the present methodology is suggested and discussed.

Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.

Bartlett-Lewis of rectangular pulse modified model: estimate of parameters for simulation of precipitation in sub-hourly duration

The Bartlett-Lewis Rectangular Pulse Modified (BLPRM) model simulates the precipitous slide in the hourly and sub-hourly and has six parameters for each of the twelve months of the year. This study aimed to evaluate the behavior of precipitation series in the duration of 15 min, obtained by simulation using the model BLPRM in situations: (a) where the parameters are estimated from a combination of statistics, creating five different sets; (b) suitability of the model to generate rain. To adjust the parameters were used rain gauge records of Pelotas/RS/Brazil, which statistics were estimated - mean, variance, covariance, autocorrelation coefficient of lag 1, the proportion of dry days in the period considered. The results showed that the parameters related to the time of onset of precipitation (λ) and intensities (μx) were the most stable and the most unstable were ν parameter, related to rain duration. The BLPRM model adequately represented the mean, variance, and proportion of the dry period of the series of precipitation lasting 15 min and, the time dependence of the heights of rain, represented autocorrelation coefficient of the first retardation was statistically less simulated series suitability for the duration of 15 min.

Novel Methods for Error Modeling and Parameter Identification of a Redundant Serial-Parallel Hybrid Robot

To obtain the desirable accuracy of a robot, there are two techniques available. The first option would be to make the robot match the nominal mathematic model. In other words, the manufacturing and assembling tolerances of every part would be extremely tight so that all of the various parameters would match the “design” or “nominal” values as closely as possible. This method can satisfy most of the accuracy requirements， but the cost would increase dramatically as the accuracy requirement increases. Alternatively, a more cost-effective solution is to build a manipulator with relaxed manufacturing and assembling tolerances. By modifying the mathematical model in the controller, the actual errors of the robot can be compensated. This is the essence of robot calibration. Simply put, robot calibration is the process of defining an appropriate error model and then identifying the various parameter errors that make the error model match the robot as closely as possible. This work focuses on kinematic calibration of a 10 degree-of-freedom (DOF) redundant serial-parallel hybrid robot. The robot consists of a 4-DOF serial mechanism and a 6-DOF hexapod parallel manipulator. The redundant 4-DOF serial structure is used to enlarge workspace and the 6-DOF hexapod manipulator is used to provide high load capabilities and stiffness for the whole structure. The main objective of the study is to develop a suitable calibration method to improve the accuracy of the redundant serial-parallel hybrid robot. To this end, a Denavit–Hartenberg (DH) hybrid error model and a Product-of-Exponential (POE) error model are developed for error modeling of the proposed robot. Furthermore, two kinds of global optimization methods, i.e. the differential-evolution (DE) algorithm and the Markov Chain Monte Carlo (MCMC) algorithm, are employed to identify the parameter errors of the derived error model. A measurement method based on a 3-2-1 wire-based pose estimation system is proposed and implemented in a Solidworks environment to simulate the real experimental validations. Numerical simulations and Solidworks prototype-model validations are carried out on the hybrid robot to verify the effectiveness, accuracy and robustness of the calibration algorithms.

Parameter estimation and use of gamma interferon assay for the diagnosis of bovine tuberculosis in Brazil

This study aimed to evaluate the interference of tuberculin test on the gamma-interferon (INFg) assay, to estimate the sensitivity and specificity of the INFg assay in Brazilian conditions, and to simulate multiple testing using the comparative tuberculin test and the INFg assay. Three hundred-fifty cattle from two TB-free and two TB-infected herds were submitted to the comparative tuberculin test and the INFg assay. The comparative tuberculin test was performed using avian and bovine PPD. The INFg assay was performed by the BovigamTM kit (CSL Veterinary, Australia), according to the manufacturer's specifications. Sensitivity and specificity of the INFg assay were assessed by a Bayesian latent class model. These diagnostic parameters were also estimate for multiple testing. The results of INFg assay on D0 and D3 after the comparative tuberculin test were compared by the McNemar's test and kappa statistics. Results of mean optical density from INFg assay on both days were similar. Sensitivity and specificity of the INFg assay showed results varying (95% confidence intervals) from 72 to 100% and 74 to 100% respectively. Sensitivity of parallel testing was over 97.5%, while specificity of serial testing was over 99.7%. The INFg assay proved to be a very useful diagnostic method.

Reflexive Space. A Constructionist Model of the Russian Reflexive Marker

This study examines the structure of the Russian Reflexive Marker ( ся/-сь) and offers a usage-based model building on Construction Grammar and a probabilistic view of linguistic structure. Traditionally, reflexive verbs are accounted for relative to non-reflexive verbs. These accounts assume that linguistic structures emerge as pairs. Furthermore, these accounts assume directionality where the semantics and structure of a reflexive verb can be derived from the non-reflexive verb. However, this directionality does not necessarily hold diachronically. Additionally, the semantics and the patterns associated with a particular reflexive verb are not always shared with the non-reflexive verb. Thus, a model is proposed that can accommodate the traditional pairs as well as for the possible deviations without postulating different systems. A random sample of 2000 instances marked with the Reflexive Marker was extracted from the Russian National Corpus and the sample used in this study contains 819 unique reflexive verbs. This study moves away from the traditional pair account and introduces the concept of Neighbor Verb. A neighbor verb exists for a reflexive verb if they share the same phonological form excluding the Reflexive Marker. It is claimed here that the Reflexive Marker constitutes a system in Russian and the relation between the reflexive and neighbor verbs constitutes a cross-paradigmatic relation. Furthermore, the relation between the reflexive and the neighbor verb is argued to be of symbolic connectivity rather than directionality. Effectively, the relation holding between particular instantiations can vary. The theoretical basis of the present study builds on this assumption. Several new variables are examined in order to systematically model variability of this symbolic connectivity, specifically the degree and strength of connectivity between items. In usage-based models, the lexicon does not constitute an unstructured list of items. Instead, items are assumed to be interconnected in a network. This interconnectedness is defined as Neighborhood in this study. Additionally, each verb carves its own niche within the Neighborhood and this interconnectedness is modeled through rhyme verbs constituting the degree of connectivity of a particular verb in the lexicon. The second component of the degree of connectivity concerns the status of a particular verb relative to its rhyme verbs. The connectivity within the neighborhood of a particular verb varies and this variability is quantified by using the Levenshtein distance. The second property of the lexical network is the strength of connectivity between items. Frequency of use has been one of the primary variables in functional linguistics used to probe this. In addition, a new variable called Constructional Entropy is introduced in this study building on information theory. It is a quantification of the amount of information carried by a particular reflexive verb in one or more argument constructions. The results of the lexical connectivity indicate that the reflexive verbs have statistically greater neighborhood distances than the neighbor verbs. This distributional property can be used to motivate the traditional observation that the reflexive verbs tend to have idiosyncratic properties. A set of argument constructions, generalizations over usage patterns, are proposed for the reflexive verbs in this study. In addition to the variables associated with the lexical connectivity, a number of variables proposed in the literature are explored and used as predictors in the model. The second part of this study introduces the use of a machine learning algorithm called Random Forests. The performance of the model indicates that it is capable, up to a degree, of disambiguating the proposed argument construction types of the Russian Reflexive Marker. Additionally, a global ranking of the predictors used in the model is offered. Finally, most construction grammars assume that argument construction form a network structure. A new method is proposed that establishes generalization over the argument constructions referred to as Linking Construction. In sum, this study explores the structural properties of the Russian Reflexive Marker and a new model is set forth that can accommodate both the traditional pairs and potential deviations from it in a principled manner.

A simulation model of the optimal maintenance strategy: conceptual agent-based approach

In this Master’s thesis agent-based modeling has been used to analyze maintenance strategy related phenomena. The main research question that has been answered was: what does the agent-based model made for this study tell us about how different maintenance strategy decisions affect profitability of equipment owners and maintenance service providers? Thus, the main outcome of this study is an analysis of how profitability can be increased in industrial maintenance context. To answer that question, first, a literature review of maintenance strategy, agent-based modeling and maintenance modeling and optimization was conducted. This review provided the basis for making the agent-based model. Making the model followed a standard simulation modeling procedure. With the simulation results from the agent-based model the research question was answered. Specifically, the results of the modeling and this study are: (1) optimizing the point in which a machine is maintained increases profitability for the owner of the machine and also the maintainer with certain conditions; (2) time-based pricing of maintenance services leads to a zero-sum game between the parties; (3) value-based pricing of maintenance services leads to a win-win game between the parties, if the owners of the machines share a substantial amount of their value to the maintainers; and (4) error in machine condition measurement is a critical parameter to optimizing maintenance strategy, and there is real systemic value in having more accurate machine condition measurement systems.

Turbulent shallow-water model for orographic subgrid-scale perturbations

A parallel pseudo-spectral method for the simulation in distributed memory computers of the shallow-water equations in primitive form was developed and used on the study of turbulent shallow-waters LES models for orographic subgrid-scale perturbations. The main characteristics of the code are: momentum equations integrated in time using an accurate pseudo-spectral technique; Eulerian treatment of advective terms; and parallelization of the code based on a domain decomposition technique. The parallel pseudo-spectral code is efficient on various architectures. It gives high performance onvector computers and good speedup on distributed memory systems. The code is being used for the study of the interaction mechanisms in shallow-water ows with regular as well as random orography with a prescribed spectrum of elevations. Simulations show the evolution of small scale vortical motions from the interaction of the large scale flow and the small-scale orographic perturbations. These interactions transfer energy from the large-scale motions to the small (usually unresolved) scales. The possibility of including the parametrization of this effects in turbulent LES subgrid-stress models for the shallow-water equations is addressed.

A New Model to Determine the Dispersion of Fatigue Damage Evaluations

Reliable predictions of remaining lives of civil or mechanical structures subjected to fatigue damage are very difficult to be made. In general, fatigue damage is extremely sensitive to the random variations of material mechanical properties, environment and loading. These variations may induce large dispersions when the structural fatigue life has to be predicted. Wirsching (1970) mentions dispersions of the order of 30 to 70 % of the mean calculated life. The presented paper introduces a model to estimate the fatigue damage dispersion based on known statistical distributions of the fatigue parameters (material properties and loading). The model is developed by expanding into Taylor series the set of equations that describe fatigue damage for crack initiation.

On state and parameter estimation in chaotic systems

State-of-the-art predictions of atmospheric states rely on large-scale numerical models of chaotic systems. This dissertation studies numerical methods for state and parameter estimation in such systems. The motivation comes from weather and climate models and a methodological perspective is adopted. The dissertation comprises three sections: state estimation, parameter estimation and chemical data assimilation with real atmospheric satellite data. In the state estimation part of this dissertation, a new filtering technique based on a combination of ensemble and variational Kalman filtering approaches, is presented, experimented and discussed. This new filter is developed for large-scale Kalman filtering applications. In the parameter estimation part, three different techniques for parameter estimation in chaotic systems are considered. The methods are studied using the parameterized Lorenz 95 system, which is a benchmark model for data assimilation. In addition, a dilemma related to the uniqueness of weather and climate model closure parameters is discussed. In the data-oriented part of this dissertation, data from the Global Ozone Monitoring by Occultation of Stars (GOMOS) satellite instrument are considered and an alternative algorithm to retrieve atmospheric parameters from the measurements is presented. The validation study presents first global comparisons between two unique satellite-borne datasets of vertical profiles of nitrogen trioxide (NO3), retrieved using GOMOS and Stratospheric Aerosol and Gas Experiment III (SAGE III) satellite instruments. The GOMOS NO3 observations are also considered in a chemical state estimation study in order to retrieve stratospheric temperature profiles. The main result of this dissertation is the consideration of likelihood calculations via Kalman filtering outputs. The concept has previously been used together with stochastic differential equations and in time series analysis. In this work, the concept is applied to chaotic dynamical systems and used together with Markov chain Monte Carlo (MCMC) methods for statistical analysis. In particular, this methodology is advocated for use in numerical weather prediction (NWP) and climate model applications. In addition, the concept is shown to be useful in estimating the filter-specific parameters related, e.g., to model error covariance matrix parameters.

Modeling and Parameter Estimation of Double-Star Permanent Magnet Synchronous Machines

The power rating of wind turbines is constantly increasing; however, keeping the voltage rating at the low-voltage level results in high kilo-ampere currents. An alternative for increasing the power levels without raising the voltage level is provided by multiphase machines. Multiphase machines are used for instance in ship propulsion systems, aerospace applications, electric vehicles, and in other high-power applications including wind energy conversion systems. A machine model in an appropriate reference frame is required in order to design an efficient control for the electric drive. Modeling of multiphase machines poses a challenge because of the mutual couplings between the phases. Mutual couplings degrade the drive performance unless they are properly considered. In certain multiphase machines there is also a problem of high current harmonics, which are easily generated because of the small current path impedance of the harmonic components. However, multiphase machines provide special characteristics compared with the three-phase counterparts: Multiphase machines have a better fault tolerance, and are thus more robust. In addition, the controlled power can be divided among more inverter legs by increasing the number of phases. Moreover, the torque pulsation can be decreased and the harmonic frequency of the torque ripple increased by an appropriate multiphase configuration. By increasing the number of phases it is also possible to obtain more torque per RMS ampere for the same volume, and thus, increase the power density. In this doctoral thesis, a decoupled d–q model of double-star permanent-magnet (PM) synchronous machines is derived based on the inductance matrix diagonalization. The double-star machine is a special type of multiphase machines. Its armature consists of two three-phase winding sets, which are commonly displaced by 30 electrical degrees. In this study, the displacement angle between the sets is considered a parameter. The diagonalization of the inductance matrix results in a simplified model structure, in which the mutual couplings between the reference frames are eliminated. Moreover, the current harmonics are mapped into a reference frame, in which they can be easily controlled. The work also presents methods to determine the machine inductances by a finite-element analysis and by voltage-source inverters on-site. The derived model is validated by experimental results obtained with an example double-star interior PM (IPM) synchronous machine having the sets displaced by 30 electrical degrees. The derived transformation, and consequently, the decoupled d–q machine model, are shown to model the behavior of an actual machine with an acceptable accuracy. Thus, the proposed model is suitable to be used for the model-based control design of electric drives consisting of double-star IPM synchronous machines.

Parameter identification in time series models

Time series analysis can be categorized into three different approaches: classical, Box-Jenkins, and State space. Classical approach makes a basement for the analysis and Box-Jenkins approach is an improvement of the classical approach and deals with stationary time series. State space approach allows time variant factors and covers up a broader area of time series analysis. This thesis focuses on parameter identifiablity of different parameter estimation methods such as LSQ, Yule-Walker, MLE which are used in the above time series analysis approaches. Also the Kalman filter method and smoothing techniques are integrated with the state space approach and MLE method to estimate parameters allowing them to change over time. Parameter estimation is carried out by repeating estimation and integrating with MCMC and inspect how well different estimation methods can identify the optimal model parameters. Identification is performed in probabilistic and general senses and compare the results in order to study and represent identifiability more informative way.

A simple model for circadian timing by mammals

Circadian timing is structured in such a way as to receive information from the external and internal environments, and its function is the timing organization of the physiological and behavioral processes in a circadian pattern. In mammals, the circadian timing system consists of a group of structures, which includes the suprachiasmatic nucleus (SCN), the intergeniculate leaflet and the pineal gland. Neuron groups working as a biological pacemaker are found in the SCN, forming a biological master clock. We present here a simple model for the circadian timing system of mammals, which is able to reproduce two fundamental characteristics of biological rhythms: the endogenous generation of pulses and synchronization with the light-dark cycle. In this model, the biological pacemaker of the SCN was modeled as a set of 1000 homogeneously distributed coupled oscillators with long-range coupling forming a spherical lattice. The characteristics of the oscillator set were defined taking into account the Kuramoto's oscillator dynamics, but we used a new method for estimating the equilibrium order parameter. Simultaneous activities of the excitatory and inhibitory synapses on the elements of the circadian timing circuit at each instant were modeled by specific equations for synaptic events. All simulation programs were written in Fortran 77, compiled and run on PC DOS computers. Our model exhibited responses in agreement with physiological patterns. The values of output frequency of the oscillator system (maximal value of 3.9 Hz) were of the order of magnitude of the firing frequencies recorded in suprachiasmatic neurons of rodents in vivo and in vitro (from 1.8 to 5.4 Hz).