Evolutionary game theory originated from the application of mathematical game theory to biological studies. Well-known examples in evolutionary game theory are the prisoner's dilemma, predator-prey models, the rock-paper-scissors game, etc. Recently, such well-known models have attracted increased interest in population dynamics to understand the emergence of biodiversity and species coexistence. Meanwhile, it has been realized that techniques from statistical physics can aid us to gain novel insights into this interdisciplinary field. In our research, we mainly employ individual-based Monte Carlo simulations to study emerging spatio-temporal patterns, spatial correlations, and the influence of quenched spatial disorder in rock-paper-scissors systems either with or without conserved total population number. In balanced rock-paper-scissors systems far away from the ``corner'' of configuration space, it is shown that quenched spatial disorder in the reaction rates has only minor effects on the co-evolutionary dynamics. However, in model variants with strongly asymmetric rates (i.e., ``corner'' rock-paper-scissors systems), we find that spatial rate variability can greatly enhance the fitness of both minor species in``corner'' systems, a phenomenon already observed in two-species Lotka-Volterra predator-prey models. Moreover, we numerically study the influence of either pure hopping processes or exchange processes on the emergence of spiral patterns in spatial rock-paper-scissors systems without conservation law (i.e., May-Leonard model). We also observe distinct extinction features for small spatial May-Leonard systems when the mobility rate crosses the critical threshold which separates the active coexistence state from an inactive absorbing state. In addition, through Monte Carlo simulation on a heterogeneous interacting agents model, we investigate the universal scaling properties in financial markets such as the fat-tail distributions in return and trading volume, the volatility clustering, and the long-range correlation in volatility. It is demonstrated that the long-tail feature in trading volume distribution results in the fat-tail distribution of asset return, and furthermore it is shown that the long tail in trading volume distribution is caused by the heterogeneity in traders' sensitivities to market risk. / Ph. D.

<p>We are in the midst of a technological revolution (popularly known as Industrie 4.0 or 4th Industrial Revolution) where our cars are being equipped with hundreds of sensors that make them safer, homes are becoming smarter, industry yields are at an all-time high, and internet-of-things is a reality. This was largely possible due to the developments in communication, electronics, motor controls, robotics, cyber security, software, efficient power distribution, etc. One of the major propellants of the 4th Industrial revolution is the ever-expanding applications of power electronics devices. All electrical energy will be provided, handled, and consumed through power electronics devices in the near future. Therefore, the reliability of power electronics devices will be instrumental in driving future technological advances. </p> <p> </p> <p><br></p><p>A myriad of devices is categorized as power electronics devices, and in the heart of those devices are the transistors. Although Silicon-based transistors still dominate the power electronics market, a paradigm shift towards wide bandgap semiconductors, such as silicon carbide (SiC), gallium nitride (GaN), beta-gallium oxide etc., is underway. However, realizing the full potential of these devices demands unconventional design, layout, and reliability. </p> <p> </p> <p>In this thesis, we try to establish a generalized model of reliability for power and logic transistors. We start by defining a comprehensive, substrate-, self-heating-, and reliability-aware safe operating area (SOA) that analytically establishes the optimum and self-consistent trade-off among breakdown voltage, power consumption, operating frequency, heat dissipation, and reliability before actual device fabrication. Then we take a deeper look into the reliability of individual transistors (a beta-gallium oxide transistor and a Silicon-based LDMOS), to test the predictions by the safe operating area, using both experiments and simulations. In the beta-gallium oxide transistor, we studied its implementation in a DC-DC voltage converter and concluded that the self-heating is a performance bottleneck and suggested approaches to alleviate it. For the LDMOS transistor, we investigated the hot carrier degradation (HCD) using experiments and simulations. We established that the HCD degradation kinetics is universal, and physics is the same as a classical transistor, despite a complicated geometry. Finally, we studied the correlation between HCD and radiation in LDMOS used in space shuttles, airplanes, etc., to determine its lifetime. </p><p><br></p> <p> </p> <p>We have holistically analyzed the reliability of power transistors by extending the theories of logic transistors in this thesis. Therefore, this thesis takes us a step closer to a generalized reliability model for power transistors by developing a comprehensive and predictive model for the safe operating area, encompassing all sources of stresses (e.g., electrical, thermal, and radiation) it experiences during operation.</p>