Related papers: A REBO-potential-based model for graphene bending …
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…
On the basis of the Luttinger-Ward functional for interacting many-body systems given in terms of full Green's function $G$ and the bare interaction vertex $\Gamma^{(0)}$, we develop a novel Legendre transformation to express the grand…
Motivated by experiments on ion irradiated graphene, we compute the resistivity of graphene with dilute impurities. In the local moment regime we employ the perturbation theory up to third order in the exchange coupling to determine the…
We develop a model describing long-range atom-atom interactions in a two-dimensional periodic or a-periodic lattice of optical centers considering spectral and spatial broadening effects. Using both analytical and numerical Green's function…
For every $0 < s <3/4$, we study the asymptotic behavior of the $\varepsilon$-rescaled sum of the $s$-fractional Allen-Cahn energy and the squared $L^2$-norm of its first variation. We prove that the contribution of the first variation…
Atomic-scale engineering typically involves bottom-up approaches, leveraging parameters such as temperature, partial pressures, and chemical affinity to promote spontaneous arrangement of atoms. These parameters are applied globally,…
Suspended graphene samples are observed to be gently rippled rather than being flat. In [M. Friedrich, U. Stefanelli. Graphene ground states, arXiv:1802.05049], we have checked that this nonplanarity can be rigorously described within the…
We use non-perturbative renormalization group techniques to calculate the momentum dependence of thermal fluctuations of graphene, based on a self-consistent calculation of the momentum dependent elastic constants of a tethered membrane. We…
We study the effective elastic behavior of incompatibly prestrained plates, where the prestrain is independent of thickness as well as uniform through the thickness. We model such plates as three-dimensional elastic bodies with a prescribed…
First-principles calculations reported here illuminate the effects of the interfacial properties of $\alpha$-Al$_{2}$O$_{3}$ and graphene, with emphasis on the structural and electronic properties. Various contact interfaces and different…
We evaluate, by means of variational calculations, the bound state energy E_B of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential - e^2 / r . The trial wave function involves three variational…
The Wilsonian renormalization group (RG) properties of the conformal factor of the metric are profoundly altered by the fact that it has a wrong-sign kinetic term. The result is a novel perturbative continuum limit for quantum gravity,…
We study theoretically the Raman spectrum of the rotated double-layer graphene, consisting of two graphene layers rotated with respect to each other by an arbitrary angle \theta. We find a relatively simple dependence of the Raman G peak…
We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the…
A \Gamma-convergence result involving the elastic energy of a narrow inextensible ribbon is established. A non-dimensional form of the elastic energy is reduced to a one-dimensional integral over the centerline of the ribbon with the aspect…
Defect engineering via parallel cracks has been proposed as a route to tailor the fracture response of graphene. However, atomistic fracture predictions can be strongly sensitive to the interatomic potential. Here, we quantify the effect of…
We prove a homogenization theorem for a class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses of ergodicity and stationarity we prove that the $\Gamma$-limit of such energy is almost surely a…
We provide a novel sharp-interface analysis via Gamma-convergence for a non-local and non-homogeneous diffuse-interface model for phase transitions, featuring an interplay between a non-local interaction kernel and a spatially dependent…
The geometry of two-dimensional crystalline membranes dictates their mechanical, electronic and chemical properties. The local geometry of a surface is determined from the two invariants of the metric and the curvature tensors. Here we…
The wave equation describing the interaction of two electrons in graphene at arbitrary value of the Fermi energy $E_F$ is derived. For the solutions of this equation, we have found the explicit forms of the density and the current which…