Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation

In this article we apply the technique proposed in Deng-Hou-Yu (Comm. PDE, 2005) to study the level set dynamics of the 2D quasi-geostrophic equation. Under certain assumptions on the local geometric regularity of the level sets of $\theta$, we obtain global regularity results with improved growth estimate on $| \nabla^{\bot} \theta |$. We further perform numerical simulations to study the local geometric properties of the level sets near the region of maximum $| \nabla^{\bot} \theta |$. The numerical results indicate that the assumptions on the local geometric regularity of the level sets of $\theta$ in our theorems are satisfied. Therefore these theorems provide a good explanation of the double exponential growth of $| \nabla^{\bot} \theta |$ observed in this and past numerical simulations.Comment: 25 pages, 10 figures. Corrected a few typo

Complex System Reliability Analysis Method: Goal‐Oriented Methodology

Goal‐oriented (GO) methodology is a success‐oriented method for complex system reliability analysis based on modeling the normal operating sequence of a system and all possible system states. Recently, GO method has been applied in reliability and safety analysis of a number of systems, spanning defense, transportation, and power systems. This chapter provides a new approach for reliability analysis of complex systems, first, by providing its development history, its engineering applications, and the future directions. Then, the basic theory of GO method is expounded. Finally, the comparison of GO method, fault tree analysis and Monte‐Carlo simulation is discussed

Coalescence of Carbon Atoms on Cu (111) Surface: Emergence of a Stable Bridging-Metal Structure Motif

By combining first principles transition state location and molecular dynamics simulation, we unambiguously identify a carbon atom approaching induced bridging metal structure formation on Cu (111) surface, which strongly modify the carbon atom coalescence dynamics. The emergence of this new structural motif turns out to be a result of the subtle balance between Cu-C and Cu-Cu interactions. Based on this picture, a simple theoretical model is proposed, which describes a variety of surface chemistries very well