The modeling of nuclear reactors involves the solution of a multi-physics problem with widely varying time and length scales. This translates mathematically to solving a system of coupled, non-linear, and stiff partial differential equations (PDEs). Multi-physics applications possess the added complexity that most of the solution fields participate in various physics components, potentially yielding spatial and/or temporal coupling errors. This dissertation deals with the verification aspects associated with such a multi-physics code, i.e., the substantiation that the mathematical description of the multi-physics equations are solved correctly (both in time and space). Conventional paradigms used in reactor analysis problems employed to couple various physics components are often non-iterative and can be inconsistent in their treatment of the non-linear terms. This leads to the usage of smaller time steps to maintain stability and accuracy requirements, thereby increasing the overall computational time for simulation. The inconsistencies of these weakly coupled solution methods can be overcome using tighter coupling strategies and yield a better approximation to the coupled non-linear operator, by resolving the dominant spatial and temporal scales involved in the multi-physics simulation. A multi-physics framework, KARMA (K(c)ode for Analysis of Reactor and other Multi-physics Applications), is presented. KARMA uses tight coupling strategies for various physical models based on a Matrix-free Nonlinear-Krylov (MFNK) framework in order to attain high-order spatio-temporal accuracy for all solution fields in amenable wall clock times, for various test problems. The framework also utilizes traditional loosely coupled methods as lower-order solvers, which serve as efficient preconditioners for the tightly coupled solution. Since the software platform employs both lower and higher-order coupling strategies, it can easily be used to test and evaluate different coupling strategies and numerical methods and to compare their efficiency for problems of interest. Multi-physics code verification efforts pertaining to reactor applications are described and associated numerical results obtained using the developed multi-physics framework are provided. The versatility of numerical methods used here for coupled problems and feasibility of general non-linear solvers with appropriate physics-based preconditioners in the KARMA framework offer significantly efficient techniques to solve multi-physics problems in reactor analysis.

In order to make use of Newton&rsquo / s method for complex flow domains, an Euler multi-block Newton solver is developed. The generated Newton solver uses Analytical Jacobian derivation technique to construct the Jacobian matrices with different flux discretization schemes up to the second order face interpolations. Constructed sparse matrices are solved by parallel and series matrix solvers. In order to use structured grids for complex domains, multi-block grid construction is needed. Each block has its own Jacobian matrices and during the iterations the communication between the blocks should be performed. Required communication is performed with &ldquo / halo&rdquo / nodes. Increase in the number of grids requires parallelization to minimize the solution time. Parallelization of the analyses is performed by using matrix solvers having parallelization capability. In this thesis, some applications of the multi-block Newton method to different problems are given. Results are compared by using different flux discretization schemes. Convergence, analysis time and matrix solver performances are examined for different number of blocks.

<p>This thesis investigates the X-ray properties of the entire Stanghellini et al. (1998) complete sample of GHz Peaked Spectrum galaxies with redshift lower than 1. In total 19 sources are included mainly from observations made by the European space telescope, XMM-Newton. Out of these the analysis of seven "new" observations made between 2006 and 2008 are throughout described. Data from the new observations shows consistency with already analysed data. As a new result a tentative discovery of a bi-modal structure in the X-ray to radio luminosity ratio within the sample is presented.</p>

<p>XMM-Newton is a X-ray telescope launched december 1999, by the European Space Agency, ESA. On board XMM-Newton are two EPIC-MOS X-ray detectors. The detectors are build by Charged Coupled Devices (CCDs), of Metal Oxide Semi-conductor type. The EPIC-MOS cameras have four science operating modes. This project aims to evaluate the calibration for one of these four modes, the timing mode.</p><p>The evaluation is divided into two parts. The first part is the evaluation of the flux calibration, performed by analysing various observation made in timing mode. The second part is the evaluation of timing properties by performing timing analysis of XMM-Newton observations of the Crab nebula compared to observations made in the radio wavelengths.</p>

<p>The steadily increasing demand of wood forces sawmills to increase the efficiency and effectiveness of their equipments. The weak parts and the twist in wooden logs have been documented as the most common and crucial defect in sawn lumber.</p><p>In this thesis we are going to implement a program which is able to determine the weak parts in wooden logs. The implementation will be in two languages C++ and Matlab. Parts of the program are going to be implemented sometimes by C++ and sometimes by Matlab therefore different designs are going to be tested. The aim of this thesis is to check whether these designs will meet the real time bound of 10 m/s.</p><p>The result shows that there is a huge difference in time performance for the different designs. Therefore, different discretization levels were used in order to meet the deadline of 10m/s. We found that in order to get better speed one should calculate the matrix for the function <em>F </em>and the Jacobian function <em>J </em>by using C++ not by Matlab. Also we found that when we called functions from one language to another an extra time is added.</p>

Methods for estimating vehicle-terrain interaction parameters for small scale robotic vehicles have been formulated and evaluated using both simulation and experimental studies. A model basis was developed, guided by experimental studies with an iRobot PackBot. The intention was to demonstrate whether a nominally instrumented robotic vehicle could be used as a test platform for generating data for vehicle-terrain parameter estimation. A comprehensive skid-steered model was found to be sensitive enough to distinguish between various forms of unknown terrains. This simulation study also verified that the Bekker model for large scale vehicles adopted for this research was applicable to the small scale robotic vehicle used in this work. This fact was also confirmed by estimating coefficients of friction and establishing their dependence on forward velocity and turning radius as the vehicle traverses different terrains. On establishing that mobility measurements for this robotic were sufficiently sensitive, it was found that estimates could be made of key dynamic variables and vehicle-terrain interaction parameters. Four main contributions are described for reliably and robustly using PackBot data for vehicle-terrain property estimation. These estimation methods should contribute to efforts in improving mobility of small scale tracked vehicles on uncertain terrains. The approach is embodied in a multi-tiered algorithm based on the dynamic and kinematic models for skid-steering as well as tractive force models parameterized by key vehicle-terrain parameters. In order to estimate and characterize the key parameters, nonlinear estimation techniques such as the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and a General Newton Raphson (GNR) method are integrated into this multi-tiered algorithm. A unique idea in using an EKF with an added State Noise Compensation algorithm is presented which shows its robustness and consistency in estimating slip variables and other parameters for deformable terrains. In the multi-tiered algorithm, a kinematic model of the robotic vehicle is used to estimate slip variables and turning radius. These estimated variables are stored in a truth table and used in a skid-steered dynamic model to estimate the coefficients of friction. The total estimated slip on the left and right track, along with the total tractive force computed using a motor model, are then used in the GNR algorithm to estimate the key vehicle-terrain parameters. These estimated parameters are cross-checked and confirmed with EKF estimation results. Further, these simulation results verify that the tracked vehicle tractive force is not dependent on cohesion for frictional soils. This sequential algorithm is shown to be effective in estimating vehicle-terrain interaction properties with relatively good accuracy. The estimated results obtained from UKF and EKF are verified and compared with available experimental data, and tested on a PackBot traversing specified terrains at the Southwest Research Institute (SwRI), Small Robotics Testbed in San Antonio, Texas. In the end, based on the development and evaluation of small scale vehicle testing, the effectiveness of on-board sensing methods and estimation techniques are also discussed for potential use in real time estimation of vehicle-terrain parameters. / text

The numerical treatment of linear-quadratic regulator problems for parabolic partial differential equations (PDEs) on infinite time horizons requires the solution of large scale algebraic Riccati equations (ARE). The Newton-ADI iteration is an efficient numerical method for this task. It includes the solution of a Lyapunov equation by the alternating directions implicit (ADI) algorithm in each iteration step. On finite time intervals the solution of a large scale differential Riccati equation is required. This can be solved by a backward differentiation formula (BDF) method, which needs to solve an ARE in each time step. Here, we study the selection of shift parameters for the ADI method. This leads to a rational min-max-problem which has been considered by many authors. Since knowledge about the complete complex spectrum is crucial for computing the optimal solution, this is infeasible for the large scale systems arising from finite element discretization of PDEs. Therefore several alternatives for computing suboptimal parameters are discussed and compared for numerical examples.

In this paper we discuss the inverse problem of the identification of mechanical stresses by measuring the deformation of an electric potential field in a so called differential strain gauge (D-DMS). We derive a mathematical model, where the forward operator is given in terms of an elliptic boundary value problem. Derivatives of the forward operator are considered and the solution of the inverse problem via a least-squares minimization is introduced. Here, the discretized problem is solved with the Gauss-Newton method. Numerical studies of practical interest are presented.

This thesis investigates the X-ray properties of the entire Stanghellini et al. (1998) complete sample of GHz Peaked Spectrum galaxies with redshift lower than 1. In total 19 sources are included mainly from observations made by the European space telescope, XMM-Newton. Out of these the analysis of seven "new" observations made between 2006 and 2008 are throughout described. Data from the new observations shows consistency with already analysed data. As a new result a tentative discovery of a bi-modal structure in the X-ray to radio luminosity ratio within the sample is presented.

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