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Analysis of an energy based atomistic/continuum approximation of a vacancy in the 2D triangular lattice

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Figure

Figure 1.Lattice and the computational domain with N = 12and two vacancies. The black disks denote the atoms belongingto the computational domain L, the white disks denote the atomsbelonging to L# \ L, and the vacancies are denoted by v and v′.
Figure 2. Example of a triangulationΩthe boundary of the atomistic region need not be aligned with T ch of the continuum regionc (shaded area), with nodes on ∂Ωc are such that the mesh can beextended periodically to a regular triangulation of Ω#c
Figure 3.The micro-triangulationNote that in Ωtension Ta (dotted lines) and the ex- Th of the macro-triangulation to the atomistic domain.a, Th coincides with Ta and has no hanging nodes.
Table 1. Numerically computed lower bounds on vacancy stabil-ity indices (rounded down to two significant digits) when V consistsof either single vacancies, or divacancies separated by “separationdistance”.
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