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Homogenization of hexagonal lattices
"... (Communicated by Andrea Braides) Abstract. We characterize the macroscopic effective mechanical behavior of a graphene sheet modeled by a hexagonal lattice of elastic bars, using Γconvergence. 1. Introduction. We ..."
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(Communicated by Andrea Braides) Abstract. We characterize the macroscopic effective mechanical behavior of a graphene sheet modeled by a hexagonal lattice of elastic bars, using Γconvergence. 1. Introduction. We
Squishing dimers on the hexagon lattice
"... We describe an operation on dimer configurations on the hexagon lattice, called “squishing”, and use this operation to explain some of the properties of the DonaldsonThomas partition function for the orbifold C 3 /Z2 × Z2 (a certain fourvariable generating function for plane partitions which comes ..."
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We describe an operation on dimer configurations on the hexagon lattice, called “squishing”, and use this operation to explain some of the properties of the DonaldsonThomas partition function for the orbifold C 3 /Z2 × Z2 (a certain fourvariable generating function for plane partitions which
On sublattices of the hexagonal lattice
 DISCRETE MATHEMATICS
, 1997
"... How many sublattices of index N are there in the planar hexagonal lattice? Which of them are the best from the point of view of packing density, signaltonoise ratio, or energy? We answer the first question completely and give partial answers to the other questions. ..."
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Cited by 2 (0 self)
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How many sublattices of index N are there in the planar hexagonal lattice? Which of them are the best from the point of view of packing density, signaltonoise ratio, or energy? We answer the first question completely and give partial answers to the other questions.
DISTANCE COLORING OF THE HEXAGONAL LATTICE
"... Motivated by the frequency assignment problem we study the ddistant coloring of the vertices of an infinite plane hexagonal lattice H. Let d be a positive integer. A ddistant coloring of the lattice H is a coloring of the vertices of H such that each pair of vertices distance at most d apart have d ..."
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Motivated by the frequency assignment problem we study the ddistant coloring of the vertices of an infinite plane hexagonal lattice H. Let d be a positive integer. A ddistant coloring of the lattice H is a coloring of the vertices of H such that each pair of vertices distance at most d apart have
HEXAGONAL LATTICE POINTS ON CIRCLES
, 2005
"... We study the angular distribution of points in the hexagonal lattice (i.e., Z [ 1+ √ −3 2]) lying on a circle centered at the origin. We prove that the angles are equidistributed on average, and show that the discrepancy is quite small for almost all circles. Equidistribution on average is express ..."
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We study the angular distribution of points in the hexagonal lattice (i.e., Z [ 1+ √ −3 2]) lying on a circle centered at the origin. We prove that the angles are equidistributed on average, and show that the discrepancy is quite small for almost all circles. Equidistribution on average
On wellrounded sublattices of the hexagonal lattice
 Discr. Math
"... Abstract. We produce an explicit parameterization of wellrounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest signaltonoise ratio of wellrounded sublattices ..."
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Cited by 4 (3 self)
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Abstract. We produce an explicit parameterization of wellrounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest signaltonoise ratio of well
Bounds for the Connective Constant of the Hexagonal Lattice
, 2003
"... We give improved bounds for the connective constant of the hexagonal lattice. The lower bound is found by using Kesten’s method of irreducible bridges, and by determining generating functions for bridges on onedimensional lattices. The upper bound is obtained as the largest eigenvalue of a certain ..."
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We give improved bounds for the connective constant of the hexagonal lattice. The lower bound is found by using Kesten’s method of irreducible bridges, and by determining generating functions for bridges on onedimensional lattices. The upper bound is obtained as the largest eigenvalue of a certain
Coincidences of a Shifted Hexagonal Lattice and the Hexagonal Packing
"... A geometric study of twin and grain boundaries in crystals and quasicrystals is achieved via coincidence site lattices and coincidence site modules, respectively. Recently, coincidences of shifted lattices and multilattices (i.e. finite unions of shifted copies of a lattice) have been investigated. ..."
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. Here, we solve the coincidence problem for a shifted hexagonal lattice. This result allows us to analyze the coincidence isometries of the hexagonal packing by viewing the hexagonal packing as a multilattice.
HOMOGENISATION FOR HEXAGONAL LATTICES AND HONEYCOMB STRUCTURES
, 2014
"... An asymptotic scheme is generated that captures the motion of waves within discrete hexagonal and honeycomb lattices by creating continuum homogenised equations. The accuracy of these effective continuum medium equations in describing the frequencydependent anisotropy of the lattice structure is de ..."
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An asymptotic scheme is generated that captures the motion of waves within discrete hexagonal and honeycomb lattices by creating continuum homogenised equations. The accuracy of these effective continuum medium equations in describing the frequencydependent anisotropy of the lattice structure
Results 1  10
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38,422