Hierarchy and Expansiveness in Two-Dimensional Subshifts of Finite Type

Subshifts are sets of configurations over an infinite grid defined by a set of forbidden patterns. In this thesis, we study two-dimensional subshifts offinite type (2D SFTs), where the underlying grid is Z2 and the set of for-bidden patterns is finite. We are mainly interested in the interplay between the computational power of 2D SFTs and their geometry, examined through the concept of expansive subdynamics. 2D SFTs with expansive directions form an interesting and natural class of subshifts that lie between dimensions 1 and 2. An SFT that has only one non-expansive direction is called extremely expansive. We prove that in many aspects, extremely expansive 2D SFTs display the totality of behaviours of general 2D SFTs. For example, we construct an aperiodic extremely expansive 2D SFT and we prove that the emptiness problem is undecidable even when restricted to the class of extremely expansive 2D SFTs. We also prove that every Medvedev class contains an extremely expansive 2D SFT and we provide a characterization of the sets of directions that can be the set of non-expansive directions of a 2D SFT. Finally, we prove that for every computable sequence of 2D SFTs with an expansive direction, there exists a universal object that simulates all of the elements of the sequence. We use the so called hierarchical, self-simulating or fixed-point method for constructing 2D SFTs which has been previously used by Ga´cs, Durand, Romashchenko and Shen.

Dynamic Workload Parallelization and System Calibration on Single-Chip Cloud Computer

Many-core systems are emerging from the need of more computational power and power efficiency. However there are many issues which still revolve around the many-core systems. These systems need specialized software before they can be fully utilized and the hardware itself may differ from the conventional computational systems. To gain efficiency from many-core system, programs need to be parallelized. In many-core systems the cores are small and less powerful than cores used in traditional computing, so running a conventional program is not an efficient option. Also in Network-on-Chip based processors the network might get congested and the cores might work at different speeds. In this thesis is, a dynamic load balancing method is proposed and tested on Intel 48-core Single-Chip Cloud Computer by parallelizing a fault simulator. The maximum speedup is difficult to obtain due to severe bottlenecks in the system. In order to exploit all the available parallelism of the Single-Chip Cloud Computer, a runtime approach capable of dynamically balancing the load during the fault simulation process is used. The proposed dynamic fault simulation approach on the Single-Chip Cloud Computer shows up to 45X speedup compared to a serial fault simulation approach. Many-core systems can draw enormous amounts of power, and if this power is not controlled properly, the system might get damaged. One way to manage power is to set power budget for the system. But if this power is drawn by just few cores of the many, these few cores get extremely hot and might get damaged. Due to increase in power density multiple thermal sensors are deployed on the chip area to provide realtime temperature feedback for thermal management techniques. Thermal sensor accuracy is extremely prone to intra-die process variation and aging phenomena. These factors lead to a situation where thermal sensor values drift from the nominal values. This necessitates efficient calibration techniques to be applied before the sensor values are used. In addition, in modern many-core systems cores have support for dynamic voltage and frequency scaling. Thermal sensors located on cores are sensitive to the core's current voltage level, meaning that dedicated calibration is needed for each voltage level. In this thesis a general-purpose software-based auto-calibration approach is also proposed for thermal sensors to calibrate thermal sensors on different range of voltages.

Computational modelling of non-equilibrium condensing steam flows in low-pressure steam turbines

The steam turbines play a significant role in global power generation. Especially, research on low pressure (LP) steam turbine stages is of special importance for steam turbine man- ufactures, vendors, power plant owners and the scientific community due to their lower efficiency than the high pressure steam turbine stages. Because of condensation, the last stages of LP turbine experience irreversible thermodynamic losses, aerodynamic losses and erosion in turbine blades. Additionally, an LP steam turbine requires maintenance due to moisture generation, and therefore, it is also affecting on the turbine reliability. Therefore, the design of energy efficient LP steam turbines requires a comprehensive analysis of condensation phenomena and corresponding losses occurring in the steam tur- bine either by experiments or with numerical simulations. The aim of the present work is to apply computational fluid dynamics (CFD) to enhance the existing knowledge and understanding of condensing steam flows and loss mechanisms that occur due to the irre- versible heat and mass transfer during the condensation process in an LP steam turbine. Throughout this work, two commercial CFD codes were used to model non-equilibrium condensing steam flows. The Eulerian-Eulerian approach was utilised in which the mix- ture of vapour and liquid phases was solved by Reynolds-averaged Navier-Stokes equa- tions. The nucleation process was modelled with the classical nucleation theory, and two different droplet growth models were used to predict the droplet growth rate. The flow turbulence was solved by employing the standard k-ε and the shear stress transport k-ω turbulence models. Further, both models were modified and implemented in the CFD codes. The thermodynamic properties of vapour and liquid phases were evaluated with real gas models. In this thesis, various topics, namely the influence of real gas properties, turbulence mod- elling, unsteadiness and the blade trailing edge shape on wet-steam flows, are studied with different convergent-divergent nozzles, turbine stator cascade and 3D turbine stator-rotor stage. The simulated results of this study were evaluated and discussed together with the available experimental data in the literature. The grid independence study revealed that an adequate grid size is required to capture correct trends of condensation phenomena in LP turbine flows. The study shows that accurate real gas properties are important for the precise modelling of non-equilibrium condensing steam flows. The turbulence modelling revealed that the flow expansion and subsequently the rate of formation of liquid droplet nuclei and its growth process were affected by the turbulence modelling. The losses were rather sensitive to turbulence modelling as well. Based on the presented results, it could be observed that the correct computational prediction of wet-steam flows in the LP turbine requires the turbulence to be modelled accurately. The trailing edge shape of the LP turbine blades influenced the liquid droplet formulation, distribution and sizes, and loss generation. The study shows that the semicircular trailing edge shape predicted the smallest droplet sizes. The square trailing edge shape estimated greater losses. The analysis of steady and unsteady calculations of wet-steam flow exhibited that in unsteady simulations, the interaction of wakes in the rotor blade row affected the flow field. The flow unsteadiness influenced the nucleation and droplet growth processes due to the fluctuation in the Wilson point.