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arXiv · 1707.02529

On the convergence to critical scaling profiles in submonolayer deposition models

Fernando P. da Costa·João T. Pinto·Rafael Sasportes
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Abstract

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, $\xi := (x-\tau)/\sqrt{\tau}$, 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.

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BibTeXRIS

Fernando P. da Costa, João T. Pinto, Rafael Sasportes. 2017-07-09. On the convergence to critical scaling profiles in submonolayer deposition models. https://arxiv.org/abs/1707.02529

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