The evolution of a crystal surface: analysis of a one-dimensional step train connecting two facets in the ADL regime
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Publication:652396
DOI10.1016/j.physd.2011.07.016zbMath1233.82045OpenAlexW2072599949MaRDI QIDQ652396
Hala Al Hajj Shehadeh, Robert V. Kohn, Jonathan Weare
Publication date: 14 December 2011
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2011.07.016
Stefan problems, phase changes, etc. (80A22) Statistical mechanics of crystals (82D25) Crystals in solids (74N05)
Related Items (13)
Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces ⋮ Existence Theorems for a Crystal Surface Model Involving the $p$-Laplace Operator ⋮ Partial regularity for an exponential PDE in crystal surface models ⋮ Global strong solution with BV derivatives to singular solid-on-solid model with exponential nonlinearity ⋮ Gradient flow approach to an exponential thin film equation: global existence and latent singularity ⋮ Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model ⋮ Global existence and decay to equilibrium for some crystal surface models ⋮ Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface ⋮ A vicinal surface model for epitaxial growth with logarithmic free energy ⋮ Weak Solution of a Continuum Model For Vicinal Surface in The Attachment-Detachment-Limited Regime ⋮ From crystal steps to continuum laws: behavior near large facets in one dimension ⋮ Energy Scaling and Asymptotic Properties of Step Bunching in Epitaxial Growth with Elasticity Effects ⋮ Analytical Validation of a Continuum Model for the Evolution of a Crystal Surface in Multiple Space Dimensions
Cites Work
- A continuum description of the energetics and evolution of stepped surfaces in strained nanostructures
- Stability and dynamics of self-similarity in evolution equations
- From crystal steps to continuum laws: behavior near large facets in one dimension
- Derivation of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surface
- The role of self-similarity in singularities of partial differential equations
- Continuum Relaxation of Interacting Steps on Crystal Surfaces in $2+1$ Dimensions
- The growth of crystals and the equilibrium structure of their surfaces
- Continuum theory of epitaxial crystal growth. I.
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