In 1831, Michael Faraday observed the formation of standing waves on the surface of a vibrating fluid body. Subsequent experiments have revealed the existence of a rich tapestry of patterned states that can be accessed by varying the frequency and amplitude of the vibration and have spurred vast research in hydrodynamics and pattern formation. These include linear analyses to determine the conditions for the onset of the patterns, weakly nonlinear studies to understand pattern selection, and dynamical systems approaches to study mode competition and chaos. Recently, there has been some work towards numerical simulations in various three-dimensional geometries. These methods however possess low orders of accuracy, making them unsuitable for nonlinear regimes.

We present a new technique for fast and accurate simulations of nonlinear Faraday waves in a cylinder. Beginning from a viscous potential flow model, we generalize the Transformed Field Expansion to this geometry for finding the highly non-local Dirichlet-to-Neumann operator (DNO) for the Laplace equation. A spectral method relying on Zernike polynomials is developed to rapidly compute the bulk potential. We prove the effectiveness of representing functions on the unit disc in terms of these polynomials and also show that the DNO algorithm possesses spectral accuracy, unlike a method based on Bessel functions.

The free surface evolution equations are solved in time using Picard iterations carried out by left-Radau quadrature. The results are in perfect agreement with the instability thresholds and surface patterns predicted for the linearized problem. The nonlinear simulations reproduce several qualitative features observed experimentally. In addition, by enabling one to switch between various nonlinear regimes, the technique allows a precise determination of the mechanisms triggering various experimental observations.

The development of pulp capping agents has been instrumental in promoting reparative dentin formation and facilitating pulpal repair in response to pulp exposure during extensive caries excavation. Although calcium hydroxide was long the gold standard for pulp capping, the development of mineral trioxide aggregate (MTA) has ushered in a new wave of therapeutic pulp capping agents and MTA derivatives, also known as hydraulic calcium-silicate cements (HCSCs). Unfortunately, little is known as to the pulpal toxicity and dentin regenerative capacity of these materials. In the current study, the physiologic effects of four HCSCs on reparative dentin and dentinal bridge formation and periapical bone loss were evaluated radiographically and histologically in mice. Pulp exposure was induced in maxillary first molars of C57/BL6 mice, and reparative potential of pulp capping materials was evaluated by CT analysis and Hematoxylin and Eosin (H&E) staining. Among the five HCSCs used for pulp capping, only Dycal failed to induce reparative dentin and dentinal bridge formation, instead inducing periapical bone loss. Although TheraCal LC also induced periapical bone loss, significantly more teeth treated with Dycal developed periapical radiolucency's. Histologically, dentinal bridge formation was observed in all HCSCs except Dycal. These findings indicate that with the exception of Dycal, all HCSC derivative materials evaluated are as effective, if not more so, than the original PROROOT� MTA in promoting reparative dentin formation and pulpal repair.

With technology advancement to the nanoscale level, 3D stacking of Integrated Circuits (ICs) provides significant advantages in saving device footprints, improving power management, and continuing performance enhancement which aim to increase energy efficiency and scalability particularly for many-core and NoCs systems. However, the benefits of these systems can be jeopardized because they became more subjected to elevated temperature induced by thermal management challenges as well as delay degradation (i.e. aging) caused by load imbalance.

On one hand, the elevated temperature in 3D systems can be solved by Thermal Through Silicon Vias (TTSVs). However, past research has either overestimated or underestimated the effects of TTSVs as a consequence of the lack of detailed 3D IC models or system-level simulations. In this dissertation, we propose a simulation flow to accurately simulate TTSV effects on 3D ICs. Furthermore, we present a hierarchical approach to optimize the floorplan of a 3D Nehalem-based multicore processor via Simulated Annealing (SA) with respect to the area, temperature, and wirelength. By using detailed 3D thermal model along with full system and validated thermal simulators, our results show accurate thermal analysis of 3D ICs. In addition, we found that the peak temperature of 3D IC such as 3D Nehalem is reduced with a minimal area overhead.

On the other hand, previous mitigation techniques to reduce aging phenomena effects on NoC system either ignore the runtime operating conditions or impose significant overheads to the system. Hence, this dissertation also presents an online monitoring method through a Centralized Aging Table (CAT) for routers in NoCs. Our methodology populates CAT by values that represent aging degradation for each different pairs of stress and temperature ranges during a given period of time. Moreover, utilizing CAT, we propose an online adaptive aging-aware routing algorithm in order to avoid highly aged routers in 2D NoC which eventually leads to age and load balancing between routers. We also extend this idea to 3D NoC by proposing AROMa, which is an aging-aware deadlock-free adaptive routing algorithm integrated with a novel online aging monitoring system for 3D NoCs. The monitoring system in AROMa exploits Distributed-Centralized-Aging-Table (D-CAT) to obtain routers' aging rates for each layer of 3D NoCs. Consequently, AROMa swaps between different k-best source-destination shortest paths periodically to avoid highly aged routers, force them in the recovery phase, and accordingly balance aging in the network. Our results demonstrate that our online routing algorithm and monitoring methodology improves delay degradation of maximum aged router and aging imbalance while ensuring that the impact of our proposed methodology on network latency, Energy-Delay-Product (EDP) and link utilization is negligible.