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The nucleation and growth of point islands during submonolayer deposition ona one-dimensional substrate is simulated for critical island size $i=0,1,2,3$.The small and large size asymptotics for the gap size and capture zonedistributions (GSD and CZD) are studied. Comparisons to theoretical predictionsfrom fragmentation equation analyses are made, along with those from therecently proposed Generalised Wigner Surmise (GWS). We find that the simulationdata can be fully understood in the framework provided by the fragmentationequations, whilst highlighting the theoretical areas that require furtherdevelopment. The GWS works well for the small-size CZD behaviour, butcompletely fails to describe the large-size CZD asymptotics of theone-dimensional system.

Gap size and capture zone distributions in one-dimensional point island nucleation and growth simulations: asymptotics and models