2008
DOI: 10.1103/physreve.78.021601
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Unified moving-boundary model with fluctuations for unstable diffusive growth

Abstract: We study a moving-boundary model of nonconserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Conspicuous examples are found in thin-film production by chemical vapor deposition and electrochemical deposition. The model also incorporates noise terms that account for fluctuations in the diffusive and attachment processes. A small-slope approximation allows us to derive effective interface evolution equations (IEEs) in which paramete… Show more

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Cited by 22 publications
(66 citation statements)
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“…Moreover, these results for the morphologically stable condition suggest that Eq. (1) is not Galilean invariant [8], as confirmed through the usual tilt transformation [3].…”
Section: Prl 102 256102 (2009) P H Y S I C a L R E V I E W L E T T Ementioning
confidence: 85%
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“…Moreover, these results for the morphologically stable condition suggest that Eq. (1) is not Galilean invariant [8], as confirmed through the usual tilt transformation [3].…”
Section: Prl 102 256102 (2009) P H Y S I C a L R E V I E W L E T T Ementioning
confidence: 85%
“…1 the evolution of the global surface roughness WðtÞ (root mean square fluctuation of the surface height) as computed from a numerical integration of Eq. (1) with ¼ 1, using the pseudospectral method described in [8,17]. As we see [inset of Fig.…”
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confidence: 98%
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“…Currently it is accepted that such a scheme underestimates both the KPZ nonlinearity and the effective coupling g [15,16]. Here we opt for a pseudo-spectral scheme that has been successfully used for the numerical integration of local [15,17] and non-local [18] stochastic equations featuring nonlinearities of the KPZ type. Details of this numerical method can be found e.g.…”
mentioning
confidence: 99%
“…It allows us to observe the change of geometry at the end of porous media whereas the actual mineral precipitation requires enormous amount of years to evolve. Although our mass transfer system is based on electrochemical ones, it can be apparently interpreted as one case of advectiondiffusion system without the electricity (Newman and Thomas-Alyea 2004;Nicoli et al 2008). In the electroneutral region which occupies most of the system, ion transfer is described by advection-diffusion equation with the apparent diffusion coefficient which represents that the effect of electric potential apparently disappears as a result of the interaction between migration and diffusion.…”
mentioning
confidence: 99%