# Continuum description of profile scaling in nanostructure decay

Source: [Continuum description of profile scaling in nanostructure decay](<https://www.sota2.com/research/paper/68fa26142c2a3760193b6646>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T11:08:35.275Z

Authors: Dionisios Margetis, Michael J. Aziz, Howard A. Stone (2) \_\_INSTITUTION\_3\_\_ Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA USA; (2) Division of Engineering, Applied Sciences, Harvard University, Cambridge MA USA)

Published: 2003-06-04T03:45:17.000Z

## Abstract

The relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition is studied via a continuum approach that accounts for step energy g\_1 and step-step interaction energy g\_3\>0. For diffusion-limited kinetics, free-boundary and boundary-layer theories are used for self-similar shapes close to the growing facet. For long times and g\_3/g\_1 \< 1, (a) a universal equation is derived for the shape profile, (b) the layer thickness varies as (g\_3/g\_1)^{1/3}, (c) distinct solutions are found for different g\_3/\_1, and (d) for conical shapes, the profile peak scales as (g\_3/g\_1)^{-1/6}. These results compare favorably with kinetic simulations.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0306085>)

[PDF](<https://arxiv.org/pdf/cond-mat/0306085.pdf>)