Related papers: On the Sadowsky functional for anisotropic ribbons
Surface/edge energy is typically modeled as a continuous function of orientation, $\gamma({\bf n})$. We put forward a simple geometric argument that suggests this picture is inadequate for crystals with a non-Bravais lattice structure. In…
In semiconducting armchair graphene ribbons a chiral lattice deformation can induce pairs of topological gap states with opposite energies. Near the critical value of the deformation potential these kink and antikink states become almost…
We study a boundary value problem associated with a system of two second order differential equations with cubic nonlinearity which model a film of superconductor material subjected to a tangential magnetic field. We show that for an…
We calculate the electrical conductivity of a thin crystalline strip of atoms confined within a quasi one dimensional channel of fixed width. The conductivity shows anomalous behavior as the strip is deformed under tensile loading. Beyond a…
Athermal (i.e. zero-temperature) under-constrained systems are typically floppy, but they can be rigidified by the application of external strain, which is theoretically well understood. Here and in the companion paper, we extend this…
The superconducting state in a fully frustrated wire network with the dice lattice geometry is investigated in the vicinity of the transition temperature. Using Abrikosov's variational procedure, we write the Ginzburg-Landau free energy…
We develop an irregular lattice mass-spring-model (MSM) to simulate and study the deformation modes of a thin elastic ribbon as a function of applied end-to-end twist and tension. Our simulations reproduce all reported experimentally…
The present study explores the edge states in a finite-width graphene ribbon and a semi-infinite geometry subject to a perpendicular magnetic field and an in-plane electric field, applied perpendicular to a zigzag edge. To accomplish this,…
Elastic ribbons, slender structures whose length ($L$), width ($W$), and thickness ($b$) satisfy $L \gg W \gg b$, exhibit mechanical behaviors intermediate between one-dimensional rods ($L \gg W, b$) and two-dimensional plates ($L, W \gg…
We show that the conductivity tensor of a disordered two-dimensional electron gas becomes anisotropic in the presence of both Rashba and Dresselhaus spin-orbit interactions (SOI). This anisotropy is a mesoscopic effect and vanishes with…
We study the low energy spin excitations of zigzag graphene nanoribbons of varying width. We find their energy dispersion at small wave vector to be dominated by antiferromagnetic correlations between the ribbon's edges, in accrodance with…
We consider a family of cylindrical spacetimes endowed with angular momentum that are solutions to the vacuum Einstein equations outside the symmetry axis. This family was recently obtained by performing a complete gauge fixing adapted to…
We investigate the mechanics of two asymmetric ribbons bound at one end and pulled apart at the other ends. We characterize the elastic junction near the bonding and conceptualize it as a bending boundary layer. While the size of this…
Let $\Omega$ be an open subset of a Stein manifold $\Sigma$ and let $M$ be its boundary. It is well known that $M$ inherits a natural contact structure. In this paper we consider a family of variational functionals $F_\varepsilon$ defined…
Spin transport phenomena in solid materials suffer limitations from spin relaxation associated to disorder or lack of translational invariance. Ultracold atoms, free of that disorder, can provide a platform to observe phenomena beyond the…
We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…
We study the motion of a 1-D closed elastic string with bending and stretching energy immersed in a 2-D Stokes flow. In this paper we introduce the curve's tangent angle function and the stretching function to describe the deferent…
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is…
We have investigated, using effective mass approach (EMA), magnetic properties of a one-dimensional electron gas in graphene armchair ribbons when the electrons of occupy only the lowest conduction subband. We find that magnetic properties…
We establish small energy H\"{o}lder bounds for minimizers $u_\varepsilon$ of \[E_\varepsilon (u):=\int_\Omega W(\nabla u)+ \frac{1}{\varepsilon^2} \int_\Omega f(u),\] where $W$ is a positive definite quadratic form and the potential $f$…