Surface evolution of elastically stressed films under deposition by a diffuse interface model

Rätz, Andreas; Ribalta, Angel; Voigt, Axel

doi:10.1016/j.jcp.2005.09.013

Cited by 118 publications

(176 citation statements)

References 58 publications

(71 reference statements)

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“…We furthermore define the map 19) where ξ 1 is the largest intersection point of the two pressure functions as in (3.11), i.e. a point with , q max ).…”

Section: Behavior Of Solutions Onmentioning

confidence: 99%

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Instability of gravity wetting fronts for Richards equations with hysteresis

Schweizer¹

2012

Interfaces Free Bound.

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Abstract:We study the evolution of saturation profiles in a porous medium. When there is a more saturated medium on top of a less saturated medium, the effect of gravity is a downward motion of the liquid. While in experiments the effect of fingering can be observed, i.e. an instability of the planar front solution, it has been verified in different settings that the Richards equation with gravity has stable planar fronts.In the present work we analyze the Richards equation coupled to a play-type hysteresis model in the capillary pressure relation. Our result is that, in an appropriate geometry and with adequate initial and boundary conditions, the planar front solution is unstable. In particular, we find that the Richards equation with gravity and hysteresis does not define an L 1 -contraction.

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“…We furthermore define the map 19) where ξ 1 is the largest intersection point of the two pressure functions as in (3.11), i.e. a point with , q max ).…”

Section: Behavior Of Solutions Onmentioning

confidence: 99%

“…The numerical solution was obtained with the FEM toolbox AMDiS [29], which is applicable also to higher dimensional interface problems, see e.g. [19]. The project was partially funded by the Deutsche Forschungsgemeinschaft as SCHW 639/3-1.…”

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confidence: 99%

Instability of gravity wetting fronts for Richards equations with hysteresis

Schweizer¹

2012

Interfaces Free Bound.

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“…Here, Equations (1)- (3) are only approximated by assuming a finite thickness of the surface region of order . In the limit → 0 the original, sharp-interface problem can be recovered [141][142][143][144][145]. Phase-field approaches provide a robust numerical tool to solve surface evolution problems, and open the possibility to add more and more of the relevant phenomena in a consistent way.…”

Section: Comparison Of Computational Approachesmentioning

confidence: 99%

“…Approximations for surface diffusion based on this energy have been considered in Refs. [141,147,148]. The evolution law reads…”

Section: Diffuse-interface Approachmentioning

confidence: 99%

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Continuum modelling of semiconductor heteroepitaxy: an applied perspective

Bergamaschini

Salvalaglio

Backofen

et al. 2016

Advances in Physics: X

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Semiconductor heteroepitaxy involves a wealth of qualitatively different, competing phenomena. Examples include threedimensional island formation, injection of dislocations, mixing between film and substrate atoms. Their relative importance depends on the specific growth conditions, giving rise to a very complex scenario. The need for an optimal control over heteroepitaxial films and/or nanostructures is widespread: semiconductor epitaxy by molecular beam epitaxy or chemical vapour deposition is nowadays exploited also in industrial environments. Simulation models can be precious in limiting the parameter space to be sampled while aiming at films/nanostructures with the desired properties. In order to be appealing (and useful) to an applied audience, such models must yield predictions directly comparable with experimental data. This implies matching typical time scales and sizes, while offering a satisfactory description of the main physical driving forces. It is the aim of the present review to show that continuum models of semiconductor heteroepitaxy evolved significantly, providing a promising tool (even a working tool, in some cases) to comply with the above requirements. Several examples, spanning from the nanometre to the micron scale, are illustrated. Current limitations and future research directions are also discussed.

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Doubly degenerate diffuse interface models of surface diffusion

Salvalaglio

Voigt

Wise

2020

Math Methods in App Sciences

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We discuss two doubly degenerate Cahn–Hilliard (DDCH) models for isotropic surface diffusion. Degeneracy is introduced in both the mobility function and a restriction function associated to the chemical potential. Our computational results suggest that the restriction functions yield more accurate approximations of surface diffusion. We consider a slight generalization of a model that has appeared before, which is non‐variational, meaning there is no clear energy that is dissipated along the solution trajectories. We also introduce a new variational and, more precisely, energy dissipative model, which can be related to the generalized non‐variational model. For both models, we use formal matched asymptotics to show the convergence to the sharp‐interface limit of surface diffusion.

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Surface evolution of elastically stressed films under deposition by a diffuse interface model

Cited by 118 publications

References 58 publications

Instability of gravity wetting fronts for Richards equations with hysteresis

Instability of gravity wetting fronts for Richards equations with hysteresis

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

Doubly degenerate diffuse interface models of surface diffusion

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