In this dissertation we study positive solutions to a singular p-Laplacian elliptic boundary value problem on a bounded domain with smooth boundary when a positive parameter varies. Our main focus is the analysis of a challenging class of singular p-Laplacian problems. We establish the existence of a positive solution for all positive values of the parameter and the existence of at least two positive solutions for a certain explicit range of the parameter. In the Laplacian case, we also prove the uniqueness of the positive solution for large values of the parameter. We extend our existence and multiplicity results to classes of singular systems and to the case when a domain is an exterior domain. We prove our existence and multiplicity results by the method of sub and supersolutions and our uniqueness result by establishing apriori and boundary estimates. Such results are well known in the literature for the nonsingular case. In this study, we extend these results to the more difficult singular case.

As microcosms of German and Chinese societies, Munich Oktoberfest and Qingdao International Beer Festival are important manifestations of local culture. This study intends to answer the following question: to which extent are beer festivals in Germany and China related to local history and the local sense of place? A historical overview of the beer festivals in Munich and Qingdao is provided, as well as an analysis of how people seeking a sense of belonging creatively combine cognitive schemata of modernity with local cultural systems on a symbolic level. Through textual analysis and interviews, this study attempts to explore the historical development of beer festivals in Germany and China and provide an analysis case of place identity through beer symbols and tourist experience based on a historical and geographical framework regarding uniqueness, authenticity, liminality and local identity. Originating in local history, Oktoberfest has evolved from a folk festivity to a globally known tourist spectacle. Faced with modernisation, "Heimat" helps Germany in smoothing the tension between the traditional sense of place and the modern nation-state identity. As a former German colony, Qingdao celebrates its beer festival emphasising recreation and enjoyment above traditions. The local beer-related customs such as plastic bags and drinking with seafood reflect the cultural hybridity of Qingdao in which consumerism and nostalgia are combined in reaction to the vast tourism generated by globalisation and modernisation. It remains a challenge for beer festivals both in Germany and China facing homogenisation and commercialisation to maintain a genuine connection with people, especially the locals. Future work on beer festivals could explore a variety of beer events in other historical, national and contextual settings, different perspectives as well as genderisation, which will enrich the study on festival tourism and place identity.

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Physical Unclonable Functions (PUFs) provide a secure, power efficient and non-volatile means of chip identification. These are analogous to one-way functions that are easy to create but impossible to duplicate. They offer solutions to many of the FPGA (Field Programmable Gate Array) issues like intellectual property, chip authentication, cryptographic key generation and trusted computing. Moreover, FPGA evolving as an important platform for flexible logic circuit, present an attractive medium for PUF implementation to ensure its security. In this thesis, we explore the behavior of RO-PUF (Ring Oscillator Physical Unclonable Functions) on FPGA when subjected to low voltages. We investigate its stability by applying environmental variations, such as temperature changes to characterize its effectiveness. It is shown with the help of experiment results that the spread of frequencies of ROs widens with lowering of voltage and stability is expected. However, due to inherent circuit challenges of FPGA at low voltage, RO-PUF fails to generate a stable response. It is observed that more number of RO frequency crossover and counter value fluctuation at low voltage, lead to instability in PUF. We also explore different architectural components of FPGA to explain the unstable nature of RO-PUF. It is reasoned out that FPGA does not sustain data at low voltage giving out unreliable data. Thus a low voltage FPGA is required to verify the stability of RO-PUF. To emphasize our case, we look into the low power applications research being done on FPGA. We conclude that FPGA, though flexible, being power inefficient, requires optimization on architectural and circuit level to generate stable responses at low voltages. / Master of Science

Intermittent Convex Integration is a technique for constructing weak solutions to non-linear partial differential equations. It originates from Buckmaster and Vicol's celebrated result about non-uniqueness of distributional solutions to the three-dimensional Navier-Stokes equation. Their construction uses highly concentrated functions as building blocks in a recursively defined infinite series. The recursive definition stems from the method De Lellis and Székelyhidi developed for the Euler equation which later led to the proof of Onsager's conjecture by Isett. Using methods from but other building blocks, Modena and Székelyhidi proved the non-uniqueness of solutions to the transport equation with incompressible velocity fields with Sobolev regularity, relying on a much simpler construction than in the first instance of Intermittent Convex Integration mentioned above. In a similar manner Luo proved the existence of stationary solutions to the Navier-Stokes equation in dimension 4. Another step in the development was the introduction of temporal intermittency by Cheskidov and Luo - earlier constructions were highly concentrated in the spatial variable but homogeneous in time. This innovation admitted results on the two-dimensional Navier-Stokes equation as well as the transport equation with almost Lipschitz velocity field and almost smooth density. In a series of works which combine the iterative ansatz from the proof of Onsager's conjecture with methods and building blocks from Intermittent Convex Integration Novack et al. were able to prove an intermittent analog of the conjecture. The contrary approach, in some sense, was taken by the author of this thesis and Székelyhidi by showing that in most results which use Intermittent Convex Integration, iterations are unnecessary and can be replaced by a simple perturbation argument and applying the Baire category theorem. This allows for stronger results since not only existence but also genericity (in the Baire category sense) of solutions can be concluded. In this work all these developments are presented in an accessible and transparent manner; to this end we will not follow the historically correct order (which is outlined above) but the didactically optimal one: starting from the proof of Onsager's conjecture (which can be considered classical by now) we introduce 'concentrated Mikado flows' and show how they can be applied to the transport equation and the Navier-Stokes equation. In the next step we present building blocks which are entirely localised in space and therefore feature optimal concentration properties, and showcase their use in the transport equation. Then we introduce temporal intermittency as described in and show that it can be used in convex integration independently from spatial intermittency in order to give an elementary proof for non-uniqueness of solutions to the hypodissipative Navier-Stokes equation. The final step is the introduction of the 'Baire category method' and its application to transport and Navier-Stokes equations.:Contents Chapter I. Introduction Chapter II. Turbulent Energy Cascade and Onsager’s Conjecture 1. Observations and Heuristics: Richardson and Kolmogorov 2. Onsager’s conjecture on dissipation of energy 3. Proof of Conservation of energy and why it fails for low regularity 4. A proof of Onsager’s Conjecture by Convex Integration Chapter III. Intermittency in Turbulence and Intermittent Onsager Conjecture 5. Deviation from Homogeneity in Experiments and Modelling 6. Excursion into dyadic energy cascade models 7. Intermittent Energy Cascade and Onsager’s Conjecture Chapter IV. Concentrated Mikado Flows and Applications 8. Technical Prerequisites 9. Transport equation with Sobolev fields 10. Navier Stokes equation in dimension four and higher 11. Convex Integration for the Intermittent Onsager Conjecture Chapter V. Full Dimensional Concentration 12. Building blocks and methods 13. Transport equation with Sobolev fields 14. Three-dimensional Navier-Stokes equation Chapter VI. Temporal Intermittency 15. Hypodissipative Navier-Stokes equations 16. Two-dimensional Navier-Stokes equation and sharp non-uniqueness 17. Transport with almost Lipschitz fields and almost smooth density Chapter VII. Baire Category Method for Intermittent Convex Integration 18. Outline of the Baire category method 19. Genericity of three-dimensional Navier-Stokes solutions 20. Genericity of solutions to the transport equation with Sobolev fields Bibliography

Previous empirical research and anecdotal accounts suggest that “subclinical narcissism” or “average Joe’s narcissism” is one of the most prevalent social phenomena in many parts of the world. Research also suggests that there will be an unprecedented escalation “in average Joe narcissists” among future generations of consumers. The objective of this study is two-fold. The first objective of this study is to explore the moderating effect of the individual’s level of narcissistic personality on their word-of-mouth (WOM) communications. The second objective of this study is to explore the boundary conditions of the first objective. The data were collected from a large number of consumers through Amazon Mechanical Turk. The results support many of the hypotheses accordant with the characteristics of the subclinical narcissistic individual. Specifically, the moderating effect of an individual’s level of narcissistic personality trait on the decision to engage in different types of WOM communications varies across the tested contexts. This study is intended to respond to social scientists' recent call for studies that investigate the fundamental motives behind the individual’s propensity to engage in WOM communication as a function of individual characteristics. The results of this study provide some prescriptive guidance to help companies target appropriate consumers to increase the effectiveness of WOM communication. In addition, this study explores the effect of individual and contextual differences on consumers’ willingness to engage in different types of WOM communication.

Hydrogen fuel cells are devices used to generate electricity from the electrochemical reaction between air and hydrogen gas. An attractive advantage of these devices is that their byproduct is water, which is very safe to the environment. However, hydrogen fuel cells still lack some improvements in terms of increasing their life time and electricity production, decreasing power losses, and optimizing their operating conditions. In this thesis, the cathode part of the hydrogen fuel cell will be considered. This part mainly consists of an air gas channel and a gas diffusion layer. To simulate the fluid dynamics taking place in the cathode, we present two models, a general model and a simple model both based on a set of conservation laws governing the fluid dynamics and chemical reactions. A numerical method to solve these models is presented and verified in terms of accuracy. We also show that both models give similar results and validate the simple model by recovering a polarization curve obtained experimentally. Next, a shape optimization problem is introduced to find an optimal design of the air gas channel. This problem is defined from the simple model and a cost functional, $E$, that measures efficiency factors. The objective of this functional is to maximize the electricity production, uniformize the reaction rate in the catalytic layer and minimize the pressure drop in the gas channel. The impact of the gas channel shape optimization is investigated with a series of test cases in long and short fuel cell geometries. In most instances, the optimal design improves efficiency in on- and off-design operating conditions by shifting the polarization curve vertically and to the right. The second primary goal of the thesis is to analyze mathematical issues related to the introduced shape optimization problem. This involves existence and uniqueness of the solution for the presented model and differentiability of the state variables with respect to the domain of the air channel. The optimization problem is solved using the gradient method, and hence the gradient of $E$ must be found. The gradient of $E$ is obtained by introducing an adjoint system of equations, which is coupled with the state problem, namely the simple model of the fuel cell. The existence and uniqueness of the solution for the adjoint system is shown, and the shape differentiability of the cost functional $E$ is proved.

Hydrogen fuel cells are devices used to generate electricity from the electrochemical reaction between air and hydrogen gas. An attractive advantage of these devices is that their byproduct is water, which is very safe to the environment. However, hydrogen fuel cells still lack some improvements in terms of increasing their life time and electricity production, decreasing power losses, and optimizing their operating conditions. In this thesis, the cathode part of the hydrogen fuel cell will be considered. This part mainly consists of an air gas channel and a gas diffusion layer. To simulate the fluid dynamics taking place in the cathode, we present two models, a general model and a simple model both based on a set of conservation laws governing the fluid dynamics and chemical reactions. A numerical method to solve these models is presented and verified in terms of accuracy. We also show that both models give similar results and validate the simple model by recovering a polarization curve obtained experimentally. Next, a shape optimization problem is introduced to find an optimal design of the air gas channel. This problem is defined from the simple model and a cost functional, $E$, that measures efficiency factors. The objective of this functional is to maximize the electricity production, uniformize the reaction rate in the catalytic layer and minimize the pressure drop in the gas channel. The impact of the gas channel shape optimization is investigated with a series of test cases in long and short fuel cell geometries. In most instances, the optimal design improves efficiency in on- and off-design operating conditions by shifting the polarization curve vertically and to the right. The second primary goal of the thesis is to analyze mathematical issues related to the introduced shape optimization problem. This involves existence and uniqueness of the solution for the presented model and differentiability of the state variables with respect to the domain of the air channel. The optimization problem is solved using the gradient method, and hence the gradient of $E$ must be found. The gradient of $E$ is obtained by introducing an adjoint system of equations, which is coupled with the state problem, namely the simple model of the fuel cell. The existence and uniqueness of the solution for the adjoint system is shown, and the shape differentiability of the cost functional $E$ is proved.