Plenty of new two-dimensional materials including graphyne, graphdiyne, graphone, and graphane have been proposed and unveiled after the discovery of the “wonder material” graphene. Graphyne and graphdiyne are two-dimensional carbon allotropes of graphene with honeycomb structures. Graphone and graphane are hydrogenated derivatives of graphene. The advanced and unique properties of these new materials make them highly promising for applications in next generation nanoelectronics. Here, we briefly review their properties, including structural, mechanical, physical, and chemical properties, as well as their synthesis and applications in nanotechnology. Graphyne is better than graphene in directional electronic properties and charge carriers. With a band gap and magnetism, graphone and graphane show important applications in nanoelectronics and spintronics. Because these materials are close to graphene and will play important roles in carbon-based electronic devices, they deserve further, careful, and thorough studies for nanotechnology applications.

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Atomic-thick monolayer two-dimensional materials present advantageous properties compared to their bulk counterparts. The properties and behavior of these monolayers can be modified by introducing defects, namely defect engineering. In this paper, we review a group of common two-dimensional crystals, including graphene, graphyne, graphdiyne, graphn-yne, silicene, germanene, hexagonal boron nitride monolayers and MoS 2 monolayers, focusing on the effect of the defect engineering on these two-dimensional monolayer materials. Defect engineering leads to the discovery of potentially exotic properties that make the field of two-dimensional crystals fertile for future investigations and emerging technological applications with precisely tailored properties.

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We present an extensible Julia-based solver for the Euler equations that uses a summationby-parts (SBP) discretization on unstructured triangular grids. While SBP operators have been used for tensor-product discretizations for some time, they have only recently been extended to simplices. Here we investigate the accuracy and stability properties of simplexbased SBP discretizations of the Euler equations. Non-linear stabilization is a particular concern in this context, because SBP operators are nearly skew-symmetric. We consider an edge-based stabilization method, which has previously been used for advection-diffusionreaction problems and the Oseen equations, and apply it to the Euler equations. Additionally, we discuss how the development of our software has been facilitated by the use of Julia, a new, fast, dynamic programming language designed for technical computing. By taking advantage of Julia's unique capabilities, code that is both efficient and generic can be written, enhancing the extensibility of the solver.

This work focuses on multidimensional summation-by-parts (SBP) discretizations of linear elliptic operators with variable coefficients. We consider a general SBP discretization with dense simultaneous approximation terms (SATs), which serve as interior penalties to enforce boundary conditions and inter-element coupling in a weak sense. Through the analysis of adjoint consistency and stability, we present several conditions on the SAT penalties. Based on these conditions, we generalize the modified scheme of Bassi and Rebay (BR2) and the symmetric interior penalty Galerkin (SIPG) method to SBP-SAT discretizations. Numerical experiments are carried out on unstructured grids with triangular elements to verify the theoretical results.