Related papers: Curvature in conformal mappings of 2D lattices and…
A family of novel models of liquid on a 2D lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle…
We propose a family of modulated honeycomb lattices, a class of quasiperiodic tilings characterized by the metallic mean. These lattices consist of six distinct hexagonal prototiles with two edge lengths, $\ell$ and $s$, and can be regarded…
Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a…
To any metric spaces there is an associated metric profile. The rectifiability of the metric profile gives a good notion of curvature of a sub-Riemannian space. We shall say that a curvature class is the rectifiability class of the metric…
We report the magneto-transport properties of a two-dimensional electron gas in a modulation-doped AlGaAs/GaAs heterostructure subjected to a lateral potential with honeycomb geometry. Periodic oscillations of the magneto-resistance and a…
We study geometry of two-dimensional models of conformal space-time based on the group of Moebius transformation. The natural geometric invariants, called cycles, are used to linearise Moebius action. Conformal completion of the space-time…
We investigate theoretically globally nonuniform configurations of quantized-flux vortices in clean superconductors trapped by an external force field that induces a nonuniform vortex density profile. Using an extensive series of numerical…
The classical lattice dynamics of honeycomb lattices is studied in the harmonic approximation. Interactions between nearest neighbors are represented by springs connecting them. A short and necessary introduction of the lattice structure is…
The two-dimensional (2D) orientation field transform has been proved to be effective at enhancing 2D contours and curves in images by means of top-down processing. It, however, has no counterpart in three-dimensional (3D) images due to the…
When thermal energies are weak, two dimensional lamellar structures confined on a curved substrate display complex patterns arising from the competition between layer bending and compression in the presence of geometric constraints. We…
We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic…
I study the buckling transition under compression of a two-dimensional, hexagonal, regular elastic honeycomb. Under isotropic compression, the system buckles to a configuration consisting of a unit cell containing four of the original…
This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures,…
A new multifunctional 2D material is theoretically predicted based on systematic ab-initio calculations and model simulations for the honeycomb lattice of endohedral fullerene W@C28 molecules. It has structural bistability,…
The shape of liquid crystalline elastomers (LCEs) with spatial variation in the director orientation can be transformed by exposure to a stimulus. Here, informed by previously reported analytical treatments, we prepare complex spiral…
When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological…
The versatile technology of cold atoms confined in optical lattices allows the creation of a vast number of lattice geometries and interactions, providing a promising platform for emulating various lattice models. This opens the possibility…
Three-dimensional nanoarchitectures are widely used across various areas of physics, including spintronics, photonics, and superconductivity. In this regard, thin curved 3D membranes are especially interesting for applications in nano- and…
We present a two dimensional model describing the elastic behaviour of the wall of a curved blood vessel. The wall has a laminate structure consisting of several anisotropic layers of varying thickness and is assumed to be much smaller in…
We discuss a class of regions and conformal mappings which are useful in several problems of approximation theory, harmonic analysis and spectral theory.