Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scaling regimes for second layer nucleation   Nucleation on top of two-dimensional islands with step edge barriers is
investigated using scaling arguments. The nucleation rate is expressed in terms
of three basic time scales: The time interval between deposition events, the
residence time of atoms on the island, and the encounter time required for
$i^\ast + 1$ atoms forming a stable nucleus to meet. Application to the problem
of second-layer nucleation on growing first layer islands yields a sequence of
scaling regimes with different scaling exponents relating the critical island
size, at which nucleation takes place, to the diffusion and deposition rates.
Second layer nucleation is fluctuation-dominated, in the sense that the typical
number of atoms on the island is small compared to $i^\ast + 1$, when the first
layer island density exponent $\chi$ satisfies $\chi (i^\ast + 1) < 2$. The
upper critical nucleus size, above which the conventional mean-field theory of
second layer nucleation is valid, increases with decreasing dimensionality. In
the related case of nucleation on top of multilayer mounds
fluctuation-dominated and mean-field like regimes coexist for arbitrary values
of the critical nucleus size $i^\ast$.

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The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org