On the convergence to critical scaling profiles in submonolayer deposition models

Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael

http://hdl.handle.net/10400.2/7805

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Authors

Costa, Fernando Pestana da

Pinto, João Teixeira

Sasportes, Rafael

Abstract(s)

In this work we study the rate of convergence to similarity profiles in a mean field model for the deposition of a submonolayer of atoms in a crystal facet, when there is a critical minimal size $n\geq 2$ for the stability of the formed clusters. The work complements recently published related results by the same authors in which the rate of convergence was studied outside of a critical direction $x=\tau$ in the cluster size $x$ vs. time $\tau$ plane. In this paper we consider a different similarity variable, $\xi:= (x − \tau )/ \tau$ , corresponding to an inner expansion of that critical direction, and prove the convergence of solutions to a similarity profile $\Phi_{2,n}(\xi)$ when $x, \tau \to +\infty$ with $\xi$ fixed, as well as the rate at which the limit is approached.

Keywords

Dynamics of ODEs Submonolayer deposition models Asymptotic evaluation of integrals Convergence to scaling behavior Coagulation processes

URI

http://hdl.handle.net/10400.2/7805

Citation

Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael - On the convergence to critical scaling profiles in submonolayer deposition models. "Kinetic and Related Models" [Em linha]. ISSN 1937-5093 (Print) 1937-5077 (Online). Vol. 11, nº 6 (2018), p. 1359–1376