Related papers: On discrete constant principal curvature surfaces
The advancements of nanomaterials or nanostructures have enabled the possibility of fabricating multifunctional materials that hold great promises in engineering applications. The carbon nanotube (CNT)-based nanostructure is one…
Locating and manipulating nano-sized objects to drive motion is a time and effort consuming task. Recent advances show that it is possible to generate motion without direct intervention, by embedding the source of motion in the system…
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the…
Careful research on different materials reveals that the material properties are mostly affected by the size of it. Material size down to nanometer scale exhibits some remarkable properties, resulting in unique physical and chemical…
We study curvatures of the groups of measure-preserving diffeomorphisms of non-orientable compact surfaces. For the cases of the Klein bottle and the real projective plane we compute curvatures, their asymptotics and the normalized Ricci…
Exploring various topological states (TS) and topological phase transitions (TPT) has attracted great attention in condensed matter physics. However, so far, there is rarely a typical material system that can be used as a platform to study…
Nanomaterials with core-shell architectures are prominent examples of strain-engineered materials, where material properties can be designed by fine-tuning the misfit strain at the interface. Here, we elucidate the full 3D atomic structure…
We survey our recent results on classifying complete constant mean curvature 1 (CMC-1) surfaces in hyperbolic 3-space with low total curvature. There are two natural notions of "total curvature"-- one is the total absolute curvature which…
Using concepts from integral geometry, we propose a definition for a local coarse-grained curvature tensor that is well-defined on polygonal surfaces. This coarse-grained curvature tensor shows fast convergence to the curvature tensor of…
We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly…
This paper presents an efficient approach for the conceptual design of architectural surfaces which are composed of triangular panels. In the free-form design of discrete architectural surfaces, the Gaussian curvature plays an important…
There are many non-trivial entire spacelike graphs with constant mean curvature $H$ (CMC $H$, for short) in the isotropic 3-space $\mathbb{I}^3$. In this paper, we show a value distribution theorem of Gaussian curvature of complete…
An infinite sheet of graphene lying above a perturbed ground plane is studied. The perturbation is a two dimensional ridge, and a bias voltage is applied between the graphene and the ground plane, resulting in a graphene nanoribbonlike…
In Euclidean 3-space endowed with a Cartesian reference system we consider a class of surfaces, called Delaunay tori, constructed by bending segments of Delaunay cylinders with neck-size $a$ and $n$ lobes along circumferences centered at…
In this note we prove that any closed graph manifold admitting a metric of non-positive sectional curvature (NPC-metric) has a finite cover, which is fibered over the circle. An explicit criterion to have a finite cover, which is fibered…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
Carbon nanotubes (CNT) hold enormous technological promise. It can only be harnessed if one controls in a practical way the CNT chirality, the feature of the tubular carbon topology that governs all the CNT properties---electronic, optical,…
Chemical vapor deposition (CVD) is a widely used technique to grow solid materials with accurate control of layer thickness and composition. Under mass-transport-limited conditions, the surface of thin films thus produced grows in an…
The frictional properties of individual carbon nanotubes (CNTs) are studied by sliding an atomic force microscopy tip across and along its principle axis. This direction-dependent frictional behavior is found to correlate strongly with the…