Related papers: Curvature in conformal mappings of 2D lattices and…
A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry (Euclidean, hyperbolic, or spherical), each simplex has an…
The diverse quantization phenomena in 2D condensed-matter systems, being due to a uniform perpendicular magnetic field and the geometry-created lattice symmetries, are the focuses of this book. They cover the diversified magneto-electronic…
The ability of liquid interfaces to shape slender elastic structures provides powerful strategies to control the architecture of mechanical self assemblies. However, elastocapillarity-driven intelligent design remains unexplored in more…
Flat sheets encoded with patterns of contraction/elongation morph into curved surfaces. If the surfaces bear Gauss curvature, the resulting actuation can be strong and powerful. We deploy the Gauss-Bonnet theorem to deduce the Gauss…
The theoretical framework, which is built from the first-principles results, is successfully developed for investigating emergent two-dimensional (2D) materials, as it is clearly illustrated by carbon substitution in silicene. Computer…
Higher-order topological phase in 2-dimensional (2D) systems is characterized by in-gap corner states, which are hard to detect and utilize. We numerically investigate transport properties of topological corner states in 2D honeycomb…
We present a few ways of using conformal maps in the reconstruction of two-dimensional conductivities in electrical impedance tomography. First, by utilizing the Riemann mapping theorem, we can transform any simply connected domain of…
Recently, a new kind of two dimensional (2D) artificial electron lattice, i.e. molecule graphene, has drawn a lots of interest, where the metal surface electrons are transformed into a honeycomb lattice via absorbing a molecule lattice on…
Using first-principles plane-wave calculations systematic study of magnetic properties of doped two-dimensional honeycomb structures of III-V binary compounds have been conducted, either for magnetic or nonmagnetic dopants. Calculations…
A smooth curve $\gamma: [0,1] \to S^2$ is locally convex if its geodesic curvature is positive at every point. J. A. Little showed that the space of all locally positive curves $\gamma$ with $\gamma(0) = \gamma(1) = e_1$ and $\gamma'(0) =…
A combinatorial model of molecular conformational space that was previously developped (J. Gabarro-Arpa, Comp. Biol. and Chem. 27, (2003) 153-159), had the drawback that structures could not be properly embedded beacause it lacked explicit…
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate…
We developed a conformal map technique to analyze the attenuation of edge modes propagating along imperfect boundaries. In systems where the potential energy exhibits conformal invariance, the conformal transformation can straighten the…
The interest in two-dimensional and layered materials continues to expand, driven by the compelling properties of individual atomic layers that can be stacked and/or twisted into synthetic heterostructures. The plethora of electronic…
Computational methods for designing interactions between colloidal particles that induce self-assembly have received much attention for their promise to discover tailored materials. However, it often remains a challenge to translate…
Brain representations of curvature may be formed on the basis of either vision or touch. Experimental and theoretical work by the author and her colleagues has shown that the processing underlying such representations directly depends on…
An ability of various interatomic potentials to reproduce the properties of silicene (2D silicon) polymorphs were examined. Structural and mechanical properties of the flat (FS), low-buckled (LBS), trigonal dumbbell (TDS), honeycomb…
When used in bulk applications, mechanical metamaterials set forth a multiscale problem with many orders of magnitude in scale separation between the micro and macro scales. However, mechanical metamaterials fall outside conventional…
Inverse methods of statistical mechanics have facilitated the discovery of pair potentials that stabilize a wide variety of targeted lattices at zero temperature. However, such methods are complicated by the need to compare, within the…