The goal of this Master's Thesis is finding a SAT solving heuristic by the application of an evolutionary algorithm. This thesis surveys various approaches used in SAT solving and some variants of evolutionary algorithms that are relevant to this topic. Afterwards the implementation of a linear genetic programming system that searches for a suitable heuristic for SAT problem instances is described, together with the implementation of a custom SAT solver which expoloits the output of the genetic program. Finally, the achieved results are summarized.

The goal of this diploma thesis is to design a new shape of the draft tube, which will be easier to manufacture while maintaining good strength and hydraulic properties. First part of this thesis is devoted to the formulation of the problem, description of the swirl turbine, principle of operation, the basic variants of arrangement, also the function of the draft tube, its efficiency and other formulas. In the second part of this thesis is a CFD and strength analysis of the original design, also a new design is proposed and the possibility of optimization using ANSYS Fluent Adjoint solver.

This thesis deals with the simulation of fluid dynamics in environmental scanning electron microscope and evaluate solvers setup, the degree of discretization, choice of turbulent model and proposal optimal design of environmental scanning electron microscope. The theoretical part describes the issue of environmental scanning electron microscopy, software SolidWorks and ANSYS Fluent, basic equations describing fluid status, fluid turbulence, the mean free path of molecules and electron scattering. The practical part of the thesis is to create the model of environmental scanning electron microscope AQUASEM II in CAD system SolidWorks and simulation of fluid flow in the sample chamber before aperture PLA1 by ANSYS Fluent. A series of simulations provided the perfect setting solver. These knowledge are used in the second stage of the practical part, where is proposed optimal shape of the table sample and the input aperture PLA1.

Nous avons étudié des méthodes de volumes finis pour la simulation numérique d'un flux impliquant deux phases incompressibles ou deux phases générales compressibles en déséquilibre mécanique. Les principales difficultés du régime où il y a une apparition de phase ou une disparition de phase est la singularité de la vitesse. Nous montrons que l'utilisation du l'entropie correction améliorer beaucoup ces problèmes. Enfin, nous simulons certains tests numériques importants pour vérifier les méthodes numériques, telles que la séparation de phase par gravité ou un canal bouillant. / We investigated some finite volume methods for the numerical simulation of a flow involving two incompressible phases or general two compressible phases in mechanical disequilibrium. The main difficulties of the regime where there is either a phase appearance or a phase disappearance is the singularity of the velocity. We show that using the entropy fix will much improve these problems. Finally, we perfom some important numerical tests to verify the numerical methods, such as a phase separation by gravity or a boiling channel.

Magister Educationis - MEd / This study argues that not all children in the Junior Primary phase benefit from the Problem Centred Approach in mathematics that was adapted by the Research, Unit for Mathematics at the University of Stellenbosch (RUMEUS). \One of the reasons could be that not all pupils can construct their own knowledge and methods. There are the highly capable pupils who cope well with this approach. These pupils are able to solve mathematical problems with little or no teacher interaction. Then there are the average and weaker pupils who cannot solve a mathematical problem on their own. These pupils need strategies and skills to solve problems and they need the teacher to mediate these strategies and skills to them, which will help these pupils to become autonomous problem solvers. ,Working in groups can, to some extent, supplement mediation or teacher interaction. Peer group teaching can be effective, whereby pupils are placed in groups so that the more capable pupils can teach concepts or make concepts clearer to the average or weaker pupils). There is, however, the possibility that when pupils of mixed abilities are placed in groups of four there might be one pupil who might refuse to work with the group. This pupil will work on her own and will not share ideas with the other members of the group. If this happens, mediation is necessary for those pupils who cannot solve a mathematical problem on their own. The purpose of this study is to investigate how exposure to mediation can improve pupils' problem solving abilities. As directions for my research I've chosen the first six criteria of Feuerstein's Mediated Learning Experiences (MLE). The first three parameters: intentionality and reciprocity, mediation of transcendence and mediation of meaning _are conditions for an interaction to qualify as MLE. Mediation of competence and regulation of behaviour are functions of specific experiences that combine with the first three to make an adult-child interaction one of mediated learning. Mediation of sharing behaviour . can be added. Here the child and the mediator are engaged in a shared quest for structural change in the child. In addition to this, the five mechanisms of mediational teaching, i.e. process questioning; challenging or asking reasons; bridging; teaching about rules; and emphasising order, predictability, system, sequence and strategy are also used in the implementation of mediation as described by Haywood. Two methods of investigation were chosen. The pupils' problem solving abilities were studied by means of eight word sums, of which the first four word sums were done in the pre-test and the other four word sums in the post-test. After the pre-test and before the post-test there was a period of mediational teaching for the experimental group. During this period and during the post-test the control group was denied mediation. After this research, mediation was also available for the control group. Two pupils from the experimental group were then chosen for further in-depth, think-aloud, person-to-person interviews. The aim of the interviews was to determine why these pupils could not solve the problem in the pre-test, but could successfully solve the post-test question. The results of the word sums in the pre-test and the post-test were compared. The role of strategies and thinking skills is concentrated on in the results. Mediation was not equally successful in all of the four different types of problem sums. Questions one and five contained two or more numbers and here pupils tended to either plus or minus these numbers. Questions two and six also contained numbers, but this is a problem situated in a real life situation. Questions three and seven contained no numbers and questions four and eight compelled pupils to first work out a plan. Mediation was most successful in problem sums situated in a real life situation, followed by problem sums which compelled pupils to first work out a plan, and then by problem sums where there were no numbers. Mediation was least; successful in problem sums that contained two or more numbers. Analysis of these results shows that with mediation there is an improvement in the pupils' problem solving abilities; Mediation can be viewed as S-H-O-H-R, in which the human mediator (H) is interposed between the stimulus (S) and the organism (0), and between the organism and the response (R). We can argue that the Problem Centred Approach without mediation can produce individuals who are little, if at all, affected by their encounter and interaction with new situations. Due to the lack of support in the Problem Centred Approach to Mathematics, it is the aim of this mini-thesis to propose mediation as an essential component in the Problem Centred Approach to Mathematics in the Junior Primary phase.

The ground state of a quantum system is the minimizer of the total energy of that system. The aim of this thesis is to present and numerically solve the Gross-Pitaevskii eigenvalue problem (GPE) as a physical model for the formation of ground states of dilute Bose gases at ultra-low temperatures in a disordered potential. The first part of the report introduces the quantum mechanical phenomenon that arises at ground states of the Bose gases; the Anderson localization, and presents the nonlinear eigenvalue problem and the finite element method (FEM) used to discretize the GPE. The numerical method used to solve the eigenvalue problem for the smallest eigenvalue is called the inverse power iteration method, which is presented and explained. In the second part of the report, the smallest eigenvalue of a linear Schrödinger equation is compared with the numerically computed smallest eigenvalue (ground state) in order to evaluate the accuracy of a linear numerical scheme constructed as first step for numerically solving the non-linear problem. In the next part of the report, the numerical methods are implemented to solve for the eigenvalue and eigenfunction of the (non-linear) GPE at ground state (smallest eigenvalue). The mathematical expression for the quantum energy and smallest eigenvalue of the non-linear system are presented in the report. The methods used to solve the GPE are the FEM and inverse power iteration method and different instances of the Anderson localization are produced. The study shows that the error of the smallest eigenvalue approximation for the linear case without disorder is satisfying when using FEM and Power iteration method. The accuracy of the approximation obtained for the linear case without disorder is satisfying, even for a low numbers of iterations. The methods require many more iterations for solving the GPE with a strong disorder. On the other hand, pronounced instances of Anderson localizations are produced in a certain scaling regime. The study shows that the GPE indeed works well as a physical model for the Anderson localization. / Syftet med denna avhandling är att undersöka hur väl Gross-Pitaevskii egenvärdesekvation (GPE) passar som en fysisk modell för bildandet av stationära elektronstater i utspädda Bose-gaser vid extremt låga temperaturer. Fenomenet som skall undersökas heter Anderson lokalisering och uppstår när potentialfältets styrka och störning i systemet är tillräckligt hög. Undersökningen görs i denna avhandling genom att numeriskt lösa GPE samt illustrera olika utfall av Anderson lokaliseringen vid olika numeriska värden. Den första delen av rapporten introducerar det icke-linjära matematiska uttrycket för GPE samt de numeriska metoderna som används för att lösa problemet numerisk: finita elementmetoden (FEM) samt egenvärdesalgoritmen som heter inversiiteration. Finita elementmetoden används för att diskretisera variationsproblemet av GPE och ta fram en enkel algebraisk ekvation. Egenvärdesalgoritmen tillämpas på den algebraiska ekvation för att iterativt beräkna egenfunktionen som motsvarar det minsta egenvärdet. Det minsta egenvärdet av en fullt definierad (linjär) Schrödinger ekvation löses i rapportens andra del. Den linjära ekvationen löses för att ta fram en förenklad numerisk algoritm att utgå ifrån innan den icke-linjära algoritmen tas fram. För att försäkra sig att den linjära algoritmen stämmer bra jämförs det exakta egenvärdet för problemet med ett numeriskt framtaget värde. Undersökningen av den linjära algoritmen visar att vi får en bra uppskattning av egenvärdet - även vid få iterationer. Vidare konstrueras den ickelinjära algoritmen baserat på den linjära. Ekvationen löses och undersökes. Egenfunktionen som motsvarar minsta egenvärdet framtas och beskriver kvantsystemet i lägsta energitillståndet, så kallade grundtillståndet. Undersökningen av GPE visar att de numeriska metoderna kräver många fler iterationer innan en tillräckligt bra uppskattning av egenvärdet fås. Å andra sidan fås markanta Anderson lokaliseringar för ett skalningsområde som beskrivs av styrkan av potentialfältet i relation till dess störning. Slutsatsen är att Gross-Pitaevskii egenvärdesekvation passar bra som en fysisk modell för detta kvantsystem.

In this thesis we consider three challenging vehicle routing problems representing specific aspects of complex real-world problems: (i) the vehicle routing problem with unit demands, (ii) the preemptive stacker crane problem and (iii) a multi-period vehicle and technician routing problem. For the vehicle routing problem with units demands we continue research on the exponential multi-insertion neighborhood, investigate its properties and propose heuristic solution methods utilizing the neighborhood. For the preemptive stacker crane problem we study structural properties and provide bounds on the benefits of preemption and the benefits of so-called explicit drop nodes that are used exclusively to facilitate preemption. We propose construction heuristics that improve on the state-of-the-art in computational time and solution quality. The multi-period vehicle and technician routing problem is the subject of the VeRoLog Solver Challenge 2019. We develop a solution method that adapts to the limited computational budget and the given instance parameters. In summary, this thesis contributes to the structural analysis of the considered problems and proposes efficient heuristic solution methods that are effective even on large-scale instances and under tight restrictions of the computational budget. The methods combine global and local search approaches and take the available computational budget into account to realize an adaptive best-effort allocation of the resources.

<p> This study focuses on developing a new online recursive numerical algorithm for a coupled nonlinear inverse heat conduction-microstructure problem. This algorithm is essential in identifying, designing and controlling many industrial applications such as the quenching process for heat treating of materials, chemical vapor deposition and industrial baking. In order to develop the above algorithm, a systematic four stage research plan has been conducted. </P> <p> The first and second stages were devoted to thoroughly reviewing the existing inverse heat conduction techniques. Unlike most inverse heat conduction solution methods that are batch form techniques, the online input estimation algorithm can be used for controlling the process in real time. Therefore, in the first stage, the effect of different parameters of the online input estimation algorithm on the estimate bias has been investigated. These parameters are the stabilizing parameter, the measurement errors standard deviation, the temporal step size, the spatial step size, the location of the thermocouple as well as the initial assumption of the state error covariance and error covariance of the input estimate. Furthermore, three different discretization schemes; namely: explicit, implicit and Crank-Nicholson have been employed in the input estimation algorithm to evaluate their effect on the algorithm performance. </p> <p> The effect of changing the stabilizing parameter has been investigated using three different forms of boundary conditions covering most practical boundary heat flux conditions. These cases are: square, triangular and mixed function heat fluxes. The most important finding of this investigation is that a robust range of the stabilizing parameter has been found which achieves the desired trade-off between the filter tracking ability and its sensitivity to measurement errors. For the three considered cases, it has been found that there is a common optimal value of the stabilizing parameter at which the estimate bias is minimal. This finding is important for practical applications since this parameter is usually unknown. Therefore, this study provides a needed guidance for assuming this parameter. </p> <p> In stage three of this study, a new, more efficient direct numerical algorithm has been developed to predict the thermal and microstructure fields during quenching of steel rods. The present algorithm solves the full nonlinear heat conduction equation using a central finite-difference scheme coupled with a fourth-order Runge-Kutta nonlinear solver. Numerical results obtained using the present algorithm have been validated using experimental data and numerical results available in the literature. In addition to its accurate predictions, the present algorithm does not require iterations; hence, it is computationally more efficient than previous numerical algorithms. </p> <p> The work performed in stage four of this research focused on developing and applying an inverse algorithm to estimate the surface temperatures and surface heat flux of a steel cylinder during the quenching process. The conventional online input estimation algorithm has been modified and used for the first time to handle this coupled nonlinear problem. The nonlinearity of the problem has been treated explicitly which resulted in a non-iterative algorithm suitable for real-time control of the quenching process. The obtained results have been validated using experimental data and numerical results obtained by solving the direct problem using the direct solver developed in stage three of this work. These results showed that the algorithm is efficiently reconstructing the shape of the convective surface heat flux. </p> / Thesis / Doctor of Philosophy (PhD)

No / Owing to unpredictable bed topography conditions in natural shallow flows, various numerical methods have been developed to improve the treatment of source terms in the shallow water equations. The surface gradient method is an attractive approach as it includes a numerically simple approach to model flows over topographically-varied channels. To further improve the performance of this method, this study deals with the numerical improvement of the shallow-flow source terms. The so-called surface gradient upwind method (SGUM) integrates the source term treatment in the inviscid discretization scheme. A finite volume model (FVM) with the monotonic upwind scheme for conservative laws is used. The Harten–Lax–van Leer-contact approximate Riemann solver is used to reconstruct the Riemann problem in the FVM. The proposed method is validated against published analytical, numerical, and experimental data, indicating that the SGUM is robust and treats the source terms in different flow conditions well.

Yes / Based on the common approach, the adaptation length in sediment transport is normally estimated in the temporal independence. However, this approach might not be theoretically justified as the process of reaching of the sediment transport equilibrium stage is affected by the flow conditions in time, especially for those fast sediment moving flows, such as scour-hole developing flow. In this study, the 2D shallow water formulation together with a sediment continuity-concentration (SCC) model were applied to flow with mobile sediment boundary. A time-varying approach was proposed to determine the sediment transport adaptation length to treat the flow sediment erosion-deposition rate. The proposed computational model was based on the Finite Volume (FV) method. The Monotone Upwind Scheme of Conservative Laws (MUSCL)-Hancock scheme was used with the Harten Lax van Leer-contact (HLLC) approximate Riemann solver to discretize the FV model. In the flow applications of this paper, a highly discontinuous dam-break fast sediment transport flow was used to calibrate the proposed time-varying sediment adaptation length model. Then the calibrated model was further applied to two separate experimental sediment transport flow applications documented in literature, i.e. a highly concentrated sediment transport flow in a wide alluvial channel and a sediment aggradation flow. Good agreements with the experimental data were presented by the proposed model simulations. The tests prove that the proposed model, which was calibrated by the discontinuous dam-break bed scouring flow, also performed well to represent the rapid bed change and the steady sediment mobility conditions. / The National Natural Science Foundation of China NSFC (Grant Number 20101311246), Major State Basic Research Development Program (973 program) of China (Grant Number 2013CB036402) and Open Fund of the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University of China (Grant Number SKLH-OF-1103).