Numerical Studies of Dark Energy Models and Observations

The cosmological standard view is based on the assumptions of homogeneity, isotropy and general relativistic gravitational interaction. These alone are not sufficient for describing the current cosmological observations of accelerated expansion of space. Although general relativity is extremely accurately tested to describe the local gravitational phenomena, there is a strong demand for modifying either the energy content of the universe or the gravitational interaction itself to account for the accelerated expansion. By adding a non-luminous matter component and a constant energy component with negative pressure, the observations can be explained with general relativity. Gravitation, cosmological models and their observational phenomenology are discussed in this thesis. Several classes of dark energy models that are motivated by theories outside the standard formulation of physics were studied with emphasis on the observational interpretation. All the cosmological models that seek to explain the cosmological observations, must also conform to the local phenomena. This poses stringent conditions for the physically viable cosmological models. Predictions from a supergravity quintessence model was compared to Supernova 1a data and several metric gravity models were studied with local experimental results. Polytropic stellar configurations of solar, white dwarf and neutron stars were numerically studied with modified gravity models. The main interest was to study the spacetime around the stars. The results shed light on the viability of the studied cosmological models.

Initialization of Continuous Nonlinear Models Using Extended Kalman Filter

The two main objectives of Bayesian inference are to estimate parameters and states. In this thesis, we are interested in how this can be done in the framework of state-space models when there is a complete or partial lack of knowledge of the initial state of a continuous nonlinear dynamical system. In literature, similar problems have been referred to as diffuse initialization problems. This is achieved first by extending the previously developed diffuse initialization Kalman filtering techniques for discrete systems to continuous systems. The second objective is to estimate parameters using MCMC methods with a likelihood function obtained from the diffuse filtering. These methods are tried on the data collected from the 1995 Ebola outbreak in Kikwit, DRC in order to estimate the parameters of the system.

Simulation and material calibration of ultra high strength steel (UHSS) S960 welded joint under static tensile test utilizing finite element method (FEM)

The aim of this work was to calibrate the material properties including strength and strain values for different material zones of ultra-high strength steel (UHSS) welded joints under monotonic static loading. The UHSS is heat sensitive and softens by heat due to welding, the affected zone is heat affected zone (HAZ). In this regard, cylindrical specimens were cut out from welded joints of Strenx® 960 MC and Strenx® Tube 960 MH, were examined by tensile test. The hardness values of specimens’ cross section were measured. Using correlations between hardness and strength, initial material properties were obtained. The same size specimen with different zones of material same as real specimen were created and defined in finite element method (FEM) software with commercial brand Abaqus 6.14-1. The loading and boundary conditions were defined considering tensile test values. Using initial material properties made of hardness-strength correlations (true stress-strain values) as Abaqus main input, FEM is utilized to simulate the tensile test process. By comparing FEM Abaqus results with measured results of tensile test, initial material properties will be revised and reused as software input to be fully calibrated in such a way that FEM results and tensile test results deviate minimum. Two type of different S960 were used including 960 MC plates, and structural hollow section 960 MH X-joint. The joint is welded by BöhlerTM X96 filler material. In welded joints, typically the following zones appear: Weld (WEL), Heat affected zone (HAZ) coarse grained (HCG) and fine grained (HFG), annealed zone, and base material (BaM). Results showed that: The HAZ zone is softened due to heat input while welding. For all the specimens, the softened zone’s strength is decreased and makes it a weakest zone where fracture happens while loading. Stress concentration of a notched specimen can represent the properties of notched zone. The load-displacement diagram from FEM modeling matches with the experiments by the calibrated material properties by compromising two correlations of hardness and strength.

Variance reduction properties of dynamic hedging models - empirical evidence from BRICS countries

This Master’s Thesis analyses the effectiveness of different hedging models on BRICS (Brazil, Russia, India, China, and South Africa) countries. Hedging performance is examined by comparing two different dynamic hedging models to conventional OLS regression based model. The dynamic hedging models being employed are Constant Conditional Correlation (CCC) GARCH(1,1) and Dynamic Conditional Correlation (DCC) GARCH(1,1) with Student’s t-distribution. In order to capture the period of both Great Moderation and the latest financial crisis, the sample period extends from 2003 to 2014. To determine whether dynamic models outperform the conventional one, the reduction of portfolio variance for in-sample data with contemporaneous hedge ratios is first determined and then the holding period of the portfolios is extended to one and two days. In addition, the accuracy of hedge ratio forecasts is examined on the basis of out-of-sample variance reduction. The results are mixed and suggest that dynamic hedging models may not provide enough benefits to justify harder estimation and daily portfolio adjustment. In this sense, the results are consistent with the existing literature.

Bayesian analysis of SEIR epidemic models

This thesis concerns the analysis of epidemic models. We adopt the Bayesian paradigm and develop suitable Markov Chain Monte Carlo (MCMC) algorithms. This is done by considering an Ebola outbreak in the Democratic Republic of Congo, former Zaïre, 1995 as a case of SEIR epidemic models. We model the Ebola epidemic deterministically using ODEs and stochastically through SDEs to take into account a possible bias in each compartment. Since the model has unknown parameters, we use different methods to estimate them such as least squares, maximum likelihood and MCMC. The motivation behind choosing MCMC over other existing methods in this thesis is that it has the ability to tackle complicated nonlinear problems with large number of parameters. First, in a deterministic Ebola model, we compute the likelihood function by sum of square of residuals method and estimate parameters using the LSQ and MCMC methods. We sample parameters and then use them to calculate the basic reproduction number and to study the disease-free equilibrium. From the sampled chain from the posterior, we test the convergence diagnostic and confirm the viability of the model. The results show that the Ebola model fits the observed onset data with high precision, and all the unknown model parameters are well identified. Second, we convert the ODE model into a SDE Ebola model. We compute the likelihood function using extended Kalman filter (EKF) and estimate parameters again. The motivation of using the SDE formulation here is to consider the impact of modelling errors. Moreover, the EKF approach allows us to formulate a filtered likelihood for the parameters of such a stochastic model. We use the MCMC procedure to attain the posterior distributions of the parameters of the SDE Ebola model drift and diffusion parts. In this thesis, we analyse two cases: (1) the model error covariance matrix of the dynamic noise is close to zero , i.e. only small stochasticity added into the model. The results are then similar to the ones got from deterministic Ebola model, even if methods of computing the likelihood function are different (2) the model error covariance matrix is different from zero, i.e. a considerable stochasticity is introduced into the Ebola model. This accounts for the situation where we would know that the model is not exact. As a results, we obtain parameter posteriors with larger variances. Consequently, the model predictions then show larger uncertainties, in accordance with the assumption of an incomplete model.

Factors Affecting the Forecasting Accuracy of Diffusion Models

Tutkielman tavoitteena oli tarkastella innovaatioiden leviämismallien ennustetarkkuuteen vaikuttavia tekijöitä. Tutkielmassa ennustettiin logistisella mallilla matkapuhelinliittymien leviämistä kolmessa Euroopan maassa: Suomessa, Ranskassa ja Kreikassa. Teoriaosa keskittyi innovaatioiden leviämisen ennustamiseen leviämismallien avulla. Erityisesti painotettiin mallien ennustuskykyä ja niiden käytettävyyttä eri tilanteissa. Empiirisessä osassa keskityttiin ennustamiseen logistisella leviämismallilla, joka kalibroitiin eri tavoin koostetuilla aikasarjoilla. Näin tehtyjä ennusteita tarkasteltiin tiedon kokoamistasojen vaikutusten selvittämiseksi. Tutkimusasetelma oli empiirinen, mikä sisälsi logistisen leviämismallin ennustetarkkuuden tutkimista otosdatan kokoamistasoa muunnellen. Leviämismalliin syötettävä data voidaan kerätä kuukausittain ja operaattorikohtaisesti vaikuttamatta ennustetarkkuuteen. Dataan on sisällytettävä leviämiskäyrän käännöskohta, eli pitkän aikavälin huippukysyntäpiste.

Analysis of Industrial Granular Flow Applications by Using Advanced Collision Models

Granular flow phenomena are frequently encountered in the design of process and industrial plants in the traditional fields of the chemical, nuclear and oil industries as well as in other activities such as food and materials handling. Multi-phase flow is one important branch of the granular flow. Granular materials have unusual kinds of behavior compared to normal materials, either solids or fluids. Although some of the characteristics are still not well-known yet, one thing is confirmed: the particle-particle interaction plays a key role in the dynamics of granular materials, especially for dense granular materials. At the beginning of this thesis, detailed illustration of developing two models for describing the interaction based on the results of finite-element simulation, dimension analysis and numerical simulation is presented. The first model is used to describing the normal collision of viscoelastic particles. Based on some existent models, more parameters are added to this model, which make the model predict the experimental results more accurately. The second model is used for oblique collision, which include the effects from tangential velocity, angular velocity and surface friction based on Coulomb's law. The theoretical predictions of this model are in agreement with those by finite-element simulation. I n the latter chapters of this thesis, the models are used to predict industrial granular flow and the agreement between the simulations and experiments also shows the validation of the new model. The first case presents the simulation of granular flow passing over a circular obstacle. The simulations successfully predict the existence of a parabolic steady layer and show how the characteristics of the particles, such as coefficients of restitution and surface friction affect the separation results. The second case is a spinning container filled with granular material. Employing the previous models, the simulation could also reproduce experimentally observed phenomena, such as a depression in the center of a high frequency rotation. The third application is about gas-solid mixed flow in a vertically vibrated device. Gas phase motion is added to coherence with the particle motion. The governing equations of the gas phase are solved by using the Large eddy simulation (LES) and particle motion is predicted by using the Lagrangian method. The simulation predicted some pattern formation reported by experiment.

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.