Related papers: On the Sadowsky functional for anisotropic ribbons
We study the $\Gamma$-limit of sequences of variational problems for straight, transversely curved shallow shells, as the width of the planform $\varepsilon$ goes to zero. The energy is of von K\'arm\'an type for shallow shells under…
Graphene has many advantageous properties, but its lack of an electronic band gap makes this two dimensional material impractical for many nanoelectronic applications, for example field effect transistors. This problem can be circumvented…
We consider a family of three-dimensional stiffened plates whose dimensions are scaled through different powers of a small parameter $\varepsilon$. The plate and the stiffener are assumed to be linearly elastic, isotropic, and homogeneous.…
We derive, by means of Gamma-convergence, the equations of homogenized bending rod starting from $3D$ nonlinear elasticity equations. The main assumption is that the energy behaves like h^2 (after dividing by the order h^2 of vanishing…
We examine the spectrum and boundary energy in boundary sine-Gordon theory, based on our recent results on the complete spectrum predicted by closing the boundary bootstrap. We check the spectrum and the reflection factors against truncated…
We study the map from conductances to edge energies for harmonic functions on finite graphs with Dirichlet boundary conditions. We prove that for any compatible acyclic orientation and choice of energies there is a unique choice of…
A graphene nano-ribbon with armchair edges is known to have no edge state. However, if the nano-ribbon is in the quantum spin Hall (QSH) state, then there must be helical edge states. By folding a graphene ribbon to a ring and threading it…
The magneto-impedance (MI) in amorphous ribbon of nominal composition Fe73.5Nb3Cu1Si13.5B9 has been measured at 1MHz and at room temperature for different configurations of exciting a.c and biasing d.c. fields. A large drop in both…
We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative $L^2$-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic…
Electron transport in small graphene nanoribbons is studied by microwave emulation experiments and tight-binding calculations. In particular, it is investigated under which conditions a transport gap can be observed. Our experiments provide…
As shown in [15], under some structural assumptions, working on congested traffic problems in general and increasingly dense networks leads, at the limit by {\Gamma}-convergence, to continuous minimization problems posed on measures on…
We show that the elastic energy $E(\gamma)$ of a closed curve $\gamma$ has a minimizer among all plane simple regular closed curves of given enclosed area $A(\gamma)$, and that the minimum is attained for a circle. The proof is of a…
We study the $\Gamma$-convergence of a class of elastica-type energies defined on immersed planar curves and depending on a small positive parameter $\epsilon$. As $\epsilon\to 0^+$, sequences with equibounded energy develop concentration…
Gaussian deformation in graphene structures exhibits an interesting effect in which flower-shaped confinement states are observed in the deformed region [Carrillo-Bastos et al., Phys. Rev. B 90 041411 (2014)]. To exploit such a deformation…
We investigate the energy spectrum of single layer black phosphorene nanoribbons (BPN) by means of a low-energy expansion of a recently proposed tight-binding model that describes electron and hole bands close to the Fermi energy level.…
We investigate the statistical mechanics of long developable ribbons of finite width and very small thickness. The constraint of isometric deformations in these ribbon-like structures that follows from the geometric separation of scales…
In this paper we derive the one-dimensional bending-torsion equilibrium model modeling the junction of straight rods. The starting point is a three-dimensional nonlinear elasticity equilibrium problem written as a minimization problem for a…
Linearized elasticity models are derived, via Gamma-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the…
Electromagnetic plane waves, solutions to Maxwell's equations, are said to be `transverse' in vacuum. Namely, the waves' oscillatory electric and magnetic fields are confined within a plane transverse to the waves' propagation direction.…
We introduce a generalization of Mobius energy for knots to an energy functional for tubular neighbourhoods of closed inextensible curves. We prove the continuity of the energy and its boundedness for physically admissible tubes without…