An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt

DOI10.1016/0167-2789(95)00078-IzbMath0900.76696OpenAlexW2090178442WikidataQ58934261 ScholiaQ58934261MaRDI QIDQ1894230

David C. Sarocka, Andrew J. Bernoff

Publication date: 18 July 1995

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(95)00078-i

zbMATH Keywords

bifurcationperturbation expansionboundary layersolid-liquid interfacelong-wave theoryinstability radiusco-dimension two limitcritical growth radiusintrinsic coordinate systemnear-planar interfacesnear-spherical interfaces

Mathematics Subject Classification ID

Stefan problems, phase changes, etc. (80A22) Multiphase and multicomponent flows (76T99) Hydrodynamic stability (76E99)

Related Items

Symmetries and solutions to the thin film equations, Singularities in a modified Kuramoto-Sivashinsky equation describing interface motion for phase transition, Exhaustive Classification of the Invariant Solutions for a Specific Nonlinear Model Describing Near Planar and Marginally Long-Wave Unstable Interfaces for Phase Transition, Numerical approach to fractional blow-up equations with Atangana-Baleanu derivative in Riemann-Liouville sense, Phase field models for hypercooled solidification, Onset of superconductivity in decreasing fields for general domains, A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth, Large-amplitude solutions to the Sivashinsky and Riley-Davis equations for directional solidification, Effect of anisotropy on morphological instability in the freezing of a hypercooled melt

Cites Work

• Interfacial instabilities in directional solidification of dilute binary alloys: the Kuramoto-Sivashinsky equation
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Steady solutions of the Kuramoto-Sivashinsky equation
• On the weakly nonlinear evolution of a perturbed planar solid-liquid interface
• Stability of interfaces with velocity correction term
• Thermodynamically-consistent phase-field models for solidification
• Singularities in a modified Kuramoto-Sivashinsky equation describing interface motion for phase transition
• Back in the Saddle Again: A Computer Assisted Study of the Kuramoto–Sivashinsky Equation
• Evolution of Geometric Statistics
• On a free boundary problem associated with combustion and solidification
• Bifurcation to Rotating Waves in Equations with $O(2)$-Symmetry
• Kuramoto–Sivashinsky Dynamics on the Center–Unstable Manifold
• Unnamed Item
• Unnamed Item