Related papers: On discrete constant principal curvature surfaces
Causal Dynamical Triangulations (CDT) is a non-perturbative lattice approach to quantum gravity where one assumes space-time foliation into spatial hyper-surfaces of fixed topology. Most of the CDT results were obtained for the spatial…
Dielectric properties of carbon nanotubes (CNT) are calculated with taking into account the deviation of carbon valence electrons from to be placed exactly on the CNT surface. The results show difference to the usually applied 2D electron…
Structure of the spin-orbit coupling varies from material to material and thus finding the correct spin-orbit coupling structure is an important step towards advanced spintronic applications. We show theoretically that the curvature in a…
In this paper, we characterize and classify the isoparametric hypersurfaces with constant principal curvatures in the product spaces $ \mathbb{Q}^{2}_{c_{1}} \times \mathbb{Q}^{2}_{c_{2}}$, where $\mathbb{Q}^{2}_{c_{i}}$ is a space form…
We use a multiscale procedure to derive a simple continuum model of multiwalled carbon nanotubes that takes into account both strong covalent bonds within graphene layers and weak bonds between atoms in different layers. The model predicts…
Self-assembly of ordered nanometer-scale patterns is interesting in itself, but its practical value depends on the ability to predict and control pattern formation. In this paper we demonstrate theoretically and numerically that engineering…
The focus in this paper is an analysis of existing state of the arts directed toward the development of the next generation of vibration damping systems. The research work concentrates on an investigation related to…
We study the discrete causal set geometry of a small causal diamond in a curved spacetime using the average abundance of k-element chains or total orders in the underlying causal set C. We begin by obtaining the first order curvature…
Carbon nanoribbons (CNRs) are graphene (planar) structures with large aspect ratio. Carbon nanobelts (CNBs) are small graphene nanoribbons rolled up into spiral-like structures, i. e., carbon nanoscrolls (CNSs) with large aspect ratio. In…
Generalized causal dynamical triangulations (generalized CDT) is a model of two-dimensional quantum gravity in which a limited number of spatial topology changes is allowed to occur. We solve the model at the discretized level using…
A novel method is presented which allows the characterization of diameter selective phenomena in SWCNTs. It is based on the transformation of fullerene peapod materials into double-wall carbon nanotubes and studying the diameter…
We investigate geometric invariants of cuspidal edges on focal surfaces of regular surface. In particular, we shall clarify the sign of the singular curvature at a cuspidal edge on a focal surface using singularities of parallel surface of…
Giving explicit parametrizations of discrete constant Gaussian curvature surfaces of revolution that are defined from an integrable systems approach, we study Ricci flow for discrete surfaces, and see how discrete surfaces of revolution…
We establish curvature inequalities and rigidity results for surfaces satisfying constant mean curvature type conditions in both Riemannian and Lorentzian geometry. In the Riemannian setting we study constant mean curvature (CMC) surfaces…
Mixtures of nanoparticles and polymer-like objects are encountered in many nanotechnological applications and biological systems. We study the behavior of grafted polymer layers decorated by nanoparticles that are attracted to the polymers…
The carbon nanostructures are perspective materials for the future applications. This has two reasons: first, the hexagonal atomic structure which enables a high molecular variability by placing different kinds of the defects and second,…
Carbon nanomembranes (CNMs) are nanometer-thin disordered carbon materials that are suitable for a range of applications, from energy generation and storage, through to water filtration. The structure-property relationships of these…
Constant mean curvature surfaces in $S^3$ can be studied via their associated family of flat connections. In the case of tori this approach has led to a deep understanding of the moduli space of all CMC tori. For compact CMC surfaces of…
We prove that singular minimal surfaces with constant Gauss curvature are planes, spheres and cylindrical surfaces. We also classify all singular minimal surfaces with a constant principal curvature and singular minimal surfaces with…
We study vector fields generating a local flow by automorphisms of a parabolic geometry with higher order fixed points. We develop general tools extending the techniques of [1], [2], and [3]. We apply these tools to almost Grassmannian,…