Related papers: On discrete constant principal curvature surfaces
Let M be a closed minimal hypersurface in 5-dimensional Euclidean sphere with constant nonnegative scalar curvature. We prove that, if the sum of the cubes of all principal curvatures and the number of distinct principal curvatures are…
We investigate curvature effects on geometric parameters, energetics and electronic structure of zigzag nanotubes with fully optimized geometries from first-principle calculations. The calculated curvature energies, which are inversely…
We give criteria for which a principal curvature becomes a bounded $C^\infty$-function at non-degenerate singular points of wave fronts by using geometric invariants. As applications, we study singularities of parallel surfaces and extended…
The electric polarizability and the spread of the total position tensors are used to characterize the metallic vs insulator nature of large (finite) systems. Finite clusters are usually treated within the open boundary condition formalism.…
A conservative primitive variable discrete exterior calculus (DEC) discretization of the Navier-Stokes equations is performed. An existing DEC method (Mohamed, M. S., Hirani, A. N., Samtaney, R. (2016). Discrete exterior calculus…
We study the fractal properties of the 2d discrete scale invariant (DSI) rough surfaces. The contour lines of these rough surfaces show clear DSI. In the appropriate limit the DSI surfaces converge to the scale invariant rough surfaces. The…
Coiled Carbon Nanotubes (CCNTs) are increasingly set to become a vital factor in the new generation of nanodevices and energy-absorbing materials due to their outstanding properties. In the following work, the multi-objective optimization…
By constructing an ODE through a kind of meromorphic 1-forms, we will give an explicit construction of a kind of conformal metrics of constant curvature on Riemann surfaces with singularities. As an application, we will classify constant…
The notion of discrete conformality proposed by Luo and Bobenko-Pinkall-Springborn on triangle meshes has rich mathematical theories and wide applications. Gu et al. proved that the discrete uniformizations approximate the continuous…
Recent advances in nanotechnology have provided new materials which have the potential to surpass copper and aluminum alloys in electrical conductivity, weight and ampacity [2-6]. Among these carbon nanotubes (CNTs) stand out due to their…
The last two decades, in particular, have witnessed a large volume of research revolving around structure-property correlation in Carbon based nanocomposites, synthesized by several methods.In the simplest of terms, the electronic…
We consider chirality related effects in optical, photogalvanic and electron-transport properties of carbon nanotubes. We show that these properties of chiral nanotubes are determined by terms in the electron effective Hamiltonian…
While one of the most promising applications of carbon nanotubes (CNTs) is to enhance polymer orientation and crystallization to achieve advanced carbon fibers, the successful realization of this goal has been hindered by the insufficient…
We study three-dimensional path geometries with nontrivial torsion of maximal rank. We introduce the notion of constant torsion and show that such path geometries are in one-to-one correspondence with certain cone structures modeled on…
In this review, we present our recent computational work on carbon-based nanostructured composites. These materials consist of carbon crystallites embedded in an amorphous carbon matrix and are modeled here through classical and…
Nanoscrolls consist of sheets rolled up into a papyrus-like form. Their open ends produce great radial flexibility, which can be exploited for a large variety of applications, from actuators to hydrogen storage. They have been successfully…
In the last three decades or so, we have witnessed an extraordinary progress in the research and technology of carbon-based nanomaterials. Among the peculiar highlights are the discoveries of fullerene, the carbon nanotubes and the…
Any ruled surface in Euclidean 3-space is described as a curve of unit dual vectors in the algebra of dual quaternions (=the even Clifford algebra of type (0,3,1)). Combining this classical framework and Singularity Theory, we characterize…
We start from a new theory (discussed earlier) in which the arena for physics is not spacetime, but its straightforward extension-the so called Clifford space ($C$-space), a manifold of points, lines, areas, etc..; physical quantities are…
In this paper, we introduce the discrete conformal structures on surfaces with boundary in an axiomatic approach, which ensures that the Poincar\'{e} dual of an ideally triangulated surface with boundary has a good geometric structure.Then…