Epitaxial Growth of 2D Materials on High-Index Substrate Surfaces

Recently, the successful synthesis of wafer-scale single-crystal graphene, hexagonal boron nitride (hBN), and MoS₂ on transition metal surfaces with step edges boosted the research interests in synthesizing wafer-scale 2D single crystals on high-index substrate surfaces. Here, using hBN growth on high-index Cu surfaces as an example, a systematic theoretical study to understand the epitaxial growth of 2D materials on various high-index surfaces is performed. It is revealed that hBN orientation on a high-index surface is highly dependent on the alignment of the step edges of the surface as well as the surface roughness. On an ideal high-index surface, well-aligned hBN islands can be easily achieved, whereas curved step edges on a rough surface can lead to the alignment of hBN along with different directions. This study shows that high-index surfaces with a large step density are robust for templating the epitaxial growth of 2D single crystals due to their large tolerance for surface roughness and provides a general guideline for the epitaxial growth of various 2D single crystals.     

Liquid Marble Patchwork on Super-Repellent Surface

Liquid marble (LM) is a droplet that is wrapped by hydrophobic solid particles, which behave as a non-wetting soft solid. Based on these properties, LM can be applied in fluidics and soft device applications. A wide variety of functional particles have been synthesized to form functional LMs. However, the formation of multifunctional LMs by integrating several types of functional particles is challenging. Here, a general strategy for the flexible patterning of functional particles on droplet surfaces in a patchwork-like design is reported. It is shown that LMs can switch their macroscopic behavior between a stable and active state on super-repellent surfaces in situ by jamming/unjamming the surface particles. Active LMs hydrostatically coalesce to form a self-sorted particle pattern on the droplet surface. With the support of LM handling robotics, on-demand cyclic activation–manipulation–coalescence–stabilization protocols by LMs with different sizes and particle types result in the reliable design of multi-faced LMs. Based on this concept, a single bi-functional LM is designed from two mono-functional LMs as an advanced droplet carrier.     

Education-driven research in CAD

We argue for a new research category, named education-driven research (EDR), which fills the gap between traditional field-specific research that is not concerned with educational objectives and research in education that focuses on fundamental teaching and learning principles and possibly on their customization to broad areas (such as mathematics or physics), but not to specific disciplines (such as CAD). The objective of EDR is to simplify the formulation of the underlying theoretical foundations and of specific tools and solutions in a specialized domain, so as to make them easy to understand and internalize. As such, EDR is a difficult and genuine research activity, which requires a deep understanding of the specific field and can rarely be carried out by generalists with primary expertise in broad education principles. We illustrate the concept of EDR with three examples in CAD: (1) the Split and Tweak subdivisions of a polygon and its use for generating curves, surfaces, and animations; (2) the construction of a topological partition of a plane induced by an arbitrary arrangement of edges; and (3) a romantic definition of the minimal and Hausdorff distances. These examples demonstrate the value of using analogies, of introducing evocative terminology, and of synthesizing the simplest fundamental building blocks. The intuitive understanding provided by EDR enables the students (and even the instructor) to better appreciate the limitations of a particular solution and to explore alternatives. In particular, in these examples, EDR has allowed the author to: (1) reduce the cost of evaluating a cubic B-spline curve; (2) develop a new subdivision curve that is better approximated by its control polygon than either a cubic B-spline or an interpolating 4-point subdivision curve; (3) discover how a circuit inclusion tree may be used for identifying the faces in an arrangement; and (4) rectify a common misconception about the computation of the Hausdorff error between triangle meshes. We invite the scientific community to encourage the development of EDR by publishing its results as genuine research contributions in peer-reviewed professional journals.     

Neural network systems to reproduce crash behavior of structural components

The use of neural networks as global approximation tool in crashworthiness problems is here investigated. Neural networks are not only asked to return some meaningful indices of the structural behavior but also to reproduce load-time curves during crash phenomena. To contain the number of examples required for the training process, parallel subsystems of small neural networks are designed. Design points for the training process are obtained by explicit finite element analyses performed by PAMCRASH. The settlement of the points in the design domain is defined using a maximum distance concept. The procedure is applied to different typical absorption structures made of aluminum alloy: riveted tubes, honeycomb structures, longitudinal keel beam and intersection elements of helicopter subfloors.     

Second-order accurate constraint formulation for subdivision finite element simulation of thin shells

We present a new method for enforcing boundary conditions within subdivision finite element simulations of thin shells. The proposed framework is demonstrated to be second-order accurate with respect to increasing refinement in the displacement and energy norm for simply supported, clamped, free and symmetric boundary conditions. Second-order accuracy on the boundary is consistent with the accuracy of subdivision-based approaches for the interior of a body. Our proposed framework is applicable to both triangular and quadrilateral refinement schemes, and does not impose any topological requirements upon the underlying subdivision control mesh. Several examples from an obstacle course of benchmark problems are used to demonstrate the convergence of the scheme. Copyright © 2004 John Wiley & Sons, Ltd.     

参数三次B样条曲线的一种整体光顺方法

本文在能量法的基础上，提出了一种新的目标函数，给出了参数三次Ｂ样条曲线的一种新的整体光顺方法。利用这种方法得到的曲线不仅具有较小的应变能，而且曲率变化比较均匀，具有很好的光顺效果。该方法能推广到对曲面的光顺。     

分形粗糙面的电磁散射－扩展边界条件

用扩展边界条件方法对分形粗糙良导体面及介质面的电磁散射问题进行了分析。用推广的Floquet模式，在分界面处将场分量用Fourier级数展开，根据边界条件及扩展边界条件得到了水平极化和垂直极化散射场的幅度分量的表达式。用其它近似方法（Kirchhoff和Rayleigh方法）及能量守恒准则验证了此方法的有效性。     

Signed line intercept count

Elements of surfaces that bound a phase (β) in a two phase mixture (α+β) may be classified as: (a) convex (++) if both principal curvatures are positive; (b) concave (? ?) if both are negative; and (c) saddle (+ ?) if one is positive and the other negative. This classification excludes the limiting cases for which one or both of the principal curvatures is zero. The traces of these surfaces that form the boundaries of the β areas on a representative two dimensional section may also be: (a) convex (+) if the local curvature is positive; or (b) concave (?) if it is negative. Line intercepts may be tabulated separately for intersections with convex (+) and concave (?) segments of boundary. This paper presents a derivation of fundamental stereological formulae that relate these counting measurements to three-dimensional geometric properties of the structure they sample.     

Adaptive generation of surfaces in volume data

A widespread approach to generating polygonal approximations of iso-surfaces or contour surfaces in volume data is the socalled marching-cubes algorithm. This algorithm, however, has the disadvantage that the number of polygonal chains generated is considerable. The splitting-box algorithm presented here reduces the number of polygonal chains by adapting their size to the shape of the surface. The resulting polygonal chains offer a wide spectrum for representing the contour surface. An exact representation is achieved by a new type of generic patches calculated from the polygonal chains. Approximations of different quality may be obtained by combining the algorithm generating the patches with simple triangulations.