13 citations · 23 across the 5 of their papers we have counts for
6 papers
On the Hierarchy of Scales in Modeling of Weakly Interacting Chains of Atoms
Dmitry Golovaty, J. Patrick Wilber
In the first part of this paper, we apply a well known discrete-to-continuum approach to a Frenkel-Kontorova-type model of an infinitely long one-dimensional chain of atoms weakly…
A Discrete-to-Continuum Model of Weakly Interacting Incommensurate Two-Dimensional Lattices: The hexagonal case
Malena I. Espanol, Dmitry Golovaty, J. Patrick Wilber
In this paper, we extend the discrete-to-continuum procedure we developed in our previous work to derive a continuum variational model for a hexagonal twisted bilayer material in w…
A Discrete-to-Continuum Model of Weakly Interacting Incommensurate Two-Dimensional Lattices
Malena I. Español, Dmitry Golovaty, J. Patrick Wilber
In this paper we propose a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The two lattices have sli…
A Discrete-to-Continuum Model of Weakly Interacting Incommensurate Chains
Malena Español, Dmitry Golovaty, J. Patrick Wilber
In this paper we use a formal discrete-to-continuum procedure to derive a continuum variational model for two chains of atoms with slightly incommensurate lattices. The chains repr…
Euler elastica as a -Limit of discrete bending energies of one-dimensional chains of atoms
Malena I. Espanol, Dmitry Golovaty, J. Patrick Wilber
This work is motivated by discrete-to-continuum modeling of the mechanics of a graphene sheet, which is a single-atom thick macromolecule of carbon atoms covalently bonded to form…
Buckling of Graphene Layers Supported by Rigid Substrates
J. Patrick Wilber
We formulate a nonlinear continuum model of a graphene sheet supported by a flat rigid substrate. The sheet is parallel to the substrate and loaded on a pair of opposite edges. A t…