scholarly journals Three Interactions of Holes in Two Dimensional Dimer Systems

10.37236/6353 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Tomack Gilmore
Keyword(s):  
Free Boundary ◽  
Half Plane ◽  
Triangular Lattice ◽  
Hexagonal Lattice ◽  
Side Length ◽  
Two Dimensional ◽  
Entire Plane ◽  
Fixed Boundary ◽  
Asymptotic Expressions ◽  
Electrostatic Phenomena

Consider the unit triangular lattice in the plane with origin $O$, drawn so that one of the sets of lattice lines is vertical. Let $l$ and $l'$ denote respectively the vertical and horizontal lines that intersect $O$. Suppose the plane contains a pair of triangular holes of side length two, distributed symmetrically with respect to $l$ and $l'$ and oriented so that both holes point toward the origin. In the following article rhombus tilings of three different regions of the plane are considered, namely: tilings of the entire plane; tilings of the half plane that lies to the left of $l$ (where $l$ is considered a free boundary, so unit rhombi are allowed to protrude halfway across it); and tilings of the half plane that lies just below the fixed boundary $l'$. Asymptotic expressions for the interactions of the triangular holes in these three different regions are obtained thus providing further evidence for Ciucu's ongoing program that seeks to draw parallels between gaps in dimer systems on the hexagonal lattice and certain electrostatic phenomena.

scholarly journals Two-dimensional iodine-monofluoride epitaxy on WSe2

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Yung-Chang Lin ◽  
Sungwoo Lee ◽  
Yueh-Chiang Yang ◽  
Po-Wen Chiu ◽  
Gun-Do Lee ◽  
...  
Keyword(s):  
Density Functional ◽  
Surface Passivation ◽  
Hexagonal Lattice ◽  
Chemical Vapor ◽  
Growth Promoter ◽  
Two Dimensional ◽  
Epitaxial Relationship ◽  
Chemical Vapor Deposition Growth ◽  
Scanning Transmission ◽  
Great Possibility

AbstractInterhalogen compounds (IHCs) are extremely reactive molecules used for halogenation, catalyst, selective etchant, and surface modification. Most of the IHCs are unstable at room temperature especially for the iodine-monofluoride (IF) whose structure is still unknown. Here we demonstrate an unambiguous observation of two-dimensional (2D) IF bilayer grown on the surface of WSe2 by using scanning transmission electron microscopy and electron energy loss spectroscopy. The bilayer IF shows a clear hexagonal lattice and robust epitaxial relationship with the WSe2 substrate. Despite the IF is known to sublimate at −14 °C and has never found as a solid form in the ambient condition, but surprisingly it is found stabilized on a suitable substrate and the stabilized structure is supported by a density functional theory. This 2D form of IHC is actually a byproduct during a chemical vapor deposition growth of WSe2 in the presence of alkali metal halides as a growth promoter and requires immediate surface passivation to sustain. This work points out a great possibility to produce 2D structures that are unexpected to be crystallized or cannot be obtained by a simple exfoliation but can be grown only on a certain substrate.

scholarly journals Connecting Networks for Two-Dimensional Butler Matrices Generating a Triangular Lattice of Beams

2021 ◽  
Vol 1 (2) ◽  
pp. 646-658
Author(s):  
NELSON J. G. FONSECA ◽  
SOPHIE-ABIGAEL GOMANNE ◽  
PILAR CASTILLO-TAPIA ◽  
OSCAR QUEVEDO-TERUEL ◽  
TAKASHI TOMURA ◽  
...  
Keyword(s):  
Triangular Lattice ◽  
Two Dimensional

Molecular Dynamics Simulations of Shock-Defect Interactions in Two-Dimensional Nonreactive Crystals

1992 ◽  
Vol 296 ◽  
Author(s):  
Robert S. Sinkovits ◽  
Lee Phillips ◽  
Elaine S. Oran ◽  
Jay P. Boris
Keyword(s):  
Molecular Dynamics ◽  
Hexagonal Lattice ◽  
Square Lattice ◽  
Two Dimensional ◽  
Connection Machine ◽  
Defect Sites ◽  
Principal Axes ◽  
Shock Motion ◽  
Defect Interactions ◽  
Dynamics Simulations

AbstractThe interactions of shocks with defects in two-dimensional square and hexagonal lattices of particles interacting through Lennard-Jones potentials are studied using molecular dynamics. In perfect lattices at zero temperature, shocks directed along one of the principal axes propagate through the crystal causing no permanent disruption. Vacancies, interstitials, and to a lesser degree, massive defects are all effective at converting directed shock motion into thermalized two-dimensional motion. Measures of lattice disruption quantitatively describe the effects of the different defects. The square lattice is unstable at nonzero temperatures, as shown by its tendency upon impact to reorganize into the lower-energy hexagonal state. This transition also occurs in the disordered region associated with the shock-defect interaction. The hexagonal lattice can be made arbitrarily stable even for shock-vacancy interactions through appropriate choice of potential parameters. In reactive crystals, these defect sites may be responsible for the onset of detonation. All calculations are performed using a program optimized for the massively parallel Connection Machine.

Interfacial crack in a two-dimensional hexagonal lattice

1994 ◽  
Vol 49 (1) ◽  
pp. 44-54 ◽  
Author(s):  
Robb Thomson ◽  
S. J. Zhou
Keyword(s):  
Hexagonal Lattice ◽  
Interfacial Crack ◽  
Two Dimensional

scholarly journals General up to next-nearest-neighbour elasticity of triangular lattices in three dimensions

2006 ◽  
Vol 462 (2073) ◽  
pp. 2695-2713 ◽  
Author(s):  
Cyril Dubus ◽  
Ken Sekimoto ◽  
Jean-Baptiste Fournier
Keyword(s):  
Blood Cell ◽  
Red Blood Cell ◽  
Triangular Lattice ◽  
Soft Matter ◽  
Rotational Symmetry ◽  
Three Dimensions ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Biological Physics ◽  
Crystalline System

We establish the most general form of the discrete elasticity of a two-dimensional triangular lattice embedded in three dimensions, taking into account up to next-nearest-neighbour interactions. Besides crystalline system, this is relevant to biological physics (e.g. red blood cell cytoskeleton) and soft matter (e.g. percolating gels, etc.). In order to correctly impose the rotational invariance of the bulk terms, it turns out to be necessary to take into account explicitly the elasticity associated with the vertices located at the edges of the lattice. We find that some terms that were suspected in the literature to violate rotational symmetry are, in fact, admissible.

Diffraction of a pulse by a resistive half-plane. I. Normal incidence

1960 ◽  
Vol 255 (1283) ◽  
pp. 538-549 ◽  
Keyword(s):  
Time Dependence ◽  
Half Plane ◽  
Wave Diffraction ◽  
Diffraction Problem ◽  
Normal Incidence ◽  
Step Function ◽  
Two Dimensional ◽  
Dynamic Similarity ◽  
Function Time ◽  
Dimensional Wave

The two-dimensional wave diffraction problem, acoustic or electromagnetic, in which a pulse of step-function time dependence is diffracted by a resistive half-plane is solved by assuming dynamic similarity in the solution.

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