Point island dynamics under fixed rate deposition

D. Allen; M. Grinfeld; R. Sasportes

doi:10.1016/j.jmaa.2018.12.018

Point island dynamics under fixed rate deposition

D. Allen, M. Grinfeld, R. Sasportes

Mathematics And Statistics

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Abstract

We consider the dynamics of point islands during submonolayer deposition, in which the fragmentation of subcritical size islands is allowed. To understand asymptotics of solutions, we use methods of centre manifold theory, and for globalisation, we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems. We also compare our results with those obtained by making the quasi-steady state assumption.

Original language	English
Pages (from-to)	1716-1728
Number of pages	13
Journal	Journal of Mathematical Analysis and Applications
Volume	472
Issue number	2
Early online date	11 Dec 2018
DOIs	https://doi.org/10.1016/j.jmaa.2018.12.018
Publication status	Published - 15 Apr 2019

Keywords

submonolayer deposition
centre manifold theory
compartmental systems
asymptotically autonomous dynamical systems

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10.1016/j.jmaa.2018.12.018

Allen-etal-JMAA-2018-Point-island-dynamics-under-fixed-rateAccepted author manuscript, 268 KBLicence: CC BY-NC-ND 4.0

Michael Grinfeld
- m.grinfeldstrath.acuk
Person: Academic

Cite this

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abstract = "We consider the dynamics of point islands during submonolayer deposition, in which the fragmentation of subcritical size islands is allowed. To understand asymptotics of solutions, we use methods of centre manifold theory, and for globalisation, we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems. We also compare our results with those obtained by making the quasi-steady state assumption.",

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AU - Grinfeld, M.

AU - Sasportes, R.

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N2 - We consider the dynamics of point islands during submonolayer deposition, in which the fragmentation of subcritical size islands is allowed. To understand asymptotics of solutions, we use methods of centre manifold theory, and for globalisation, we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems. We also compare our results with those obtained by making the quasi-steady state assumption.

AB - We consider the dynamics of point islands during submonolayer deposition, in which the fragmentation of subcritical size islands is allowed. To understand asymptotics of solutions, we use methods of centre manifold theory, and for globalisation, we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems. We also compare our results with those obtained by making the quasi-steady state assumption.

KW - submonolayer deposition

KW - centre manifold theory

KW - compartmental systems

KW - asymptotically autonomous dynamical systems

U2 - 10.1016/j.jmaa.2018.12.018

DO - 10.1016/j.jmaa.2018.12.018

M3 - Article

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

Point island dynamics under fixed rate deposition

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Michael Grinfeld

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