52 research outputs found
Melting behavior of ultrathin titanium nanowires
The thermal stability and melting behavior of ultrathin titanium nanowires
with multi-shell cylindrical structures are studied using molecular dynamic
simulation. The melting temperatures of titanium nanowires show remarkable
dependence on wire sizes and structures. For the nanowire thinner than 1.2 nm,
there is no clear characteristic of first-order phase transition during the
melting, implying a coexistence of solid and liquid phases due to finite size
effect. An interesting structural transformation from helical multi-shell
cylindrical to bulk-like rectangular is observed in the melting process of a
thicker hexagonal nanowire with 1.7 nm diameter.Comment: 4 pages, 4 figure
Eternal Domination in Grids
In the eternal domination game played on graphs, an attacker attacks a vertex at each turn and a team of guards must move a guard to the attacked vertex to defend it. The guards may only move to adjacent vertices on their turn. The goal is to determine the eternal domination number of a graph which is the minimum number of guards required to defend against an infinite sequence of attacks.This paper continues the study of the eternal domination game on strong grids . Cartesian grids have been vastly studied with tight bounds existing for small grids such as grids for . It was recently proven that where is the domination number of which lower bounds the eternal domination number [Lamprou et al., CIAC 2017]. We prove that, for all such that , (note that is the domination number of ). Our technique may be applied to other ``grid-like" graphs
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