Bubbles Interactions in the Cahn-Hilliard Equation

Calisto, H.; Clerc, Marcel G.; Rojas, R. G.; Tirapegui, E.

doi:10.1103/physrevlett.85.3805

Cited by 27 publications

(16 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Their wavelengths should increase with time and lead to the coarsening of the pattern. In Cahn–Hilliard dynamics, coarsening asymptotically leads to a decreasing number of domains of each phase 17. In the current case, coarsening should thus lead to a small number of grains corresponding to each crystal orientation.…”

Section: A Reaction–diffusion Model For Texture Evolution In An Adsormentioning

confidence: 84%

Reaction–diffusion approach to nanostructure formation and texture evolution in adsorbed monoatomic layers

Walgraef

2004

Int J of Quantum Chemistry

View full text Add to dashboard Cite

ABSTRACT:It is shown that coverage evolution, during atomic deposition on a substrate, may be described, on mesoscopic scales, by dynamical models of the reaction-diffusion type. The models combine reaction terms representing adsorptiondesorption processes and nonlinear diffusion terms of the Cahn-Hilliard type. The combination may lead, below a critical temperature, to the instability of uniform deposited layers. The instability induces to the formation of nanostructures that correspond to regular spatial variations of atomic coverage. Such models also may describe texture evolution during the deposition of polycrystalline films. In this case, grains with different orientations with respect to the substrate may coexist. Grains with lower surface energy usually dominate, except at high temperatures, where grains with faster lateral diffusion may override energetically favored ones. Furthermore, at sufficiently low temperatures, uniform grain distributions may become unstable versus regular spatial variations of grain orientations. The relevance of this approach to the deposition of Al or Cu on TiN or Ta substrates is discussed.

show abstract

Section: A Reaction–diffusion Model For Texture Evolution In An Adsormentioning

confidence: 84%

Reaction–diffusion approach to nanostructure formation and texture evolution in adsorbed monoatomic layers

Walgraef

2004

Int J of Quantum Chemistry

View full text Add to dashboard Cite

show abstract

“…This equation describes the dynamics of an interface between two symmetric states [55,56]. This model is well known for exhibiting a zigzag instability.…”

Section: Stability Of Localized Spotsmentioning

confidence: 96%

From localized spots to the formation of invaginated labyrinthine structures in a Swift–Hohenberg model

Bordeu

Clerc

Lefever

et al. 2015

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

“…An elegant approach to this problem has been presented recently for the one-dimensional Cahn-Hilliard equation in Calisto, Clerc, Rojas, and Tirapegui (2000). They show that, due to the conservative nature of the order parameter, the interaction between bubbles does not induce annihilation by recombination, as in systems with non conserved order parameters.…”

Section: Linear Stability and Nonlinear Analysismentioning

confidence: 98%