Thin interface asymptotics for an energy/entropy approach to phase-field models with unequal conductivities

DOI10.1016/S0167-2789(00)00064-6zbMath0962.35175WikidataQ59445818 ScholiaQ59445818MaRDI QIDQ1586879

G. B. McFadden, Daniel M. Anderson, Adam A. Wheeler

Publication date: 13 June 2001

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

zbMATH Keywords

dendritic growthphase-field modelisothermal asymptoticssharp interface analysisthin interface analysis

Mathematics Subject Classification ID

Dynamics of phase boundaries in solids (74N20) Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics (82C24)

Related Items

PHASE-FIELD SIMULATIONS OF EUTECTIC SOLIDIFICATION USING AN ADAPTIVE FINITE ELEMENT METHOD, An adaptive mesh redistribution method for the incompressible mixture flows using phase-field model, A numerical procedure for solving 2D phase-field model problems, A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows, Unconditional stability and optimal error estimates of first order semi-implicit stabilized finite element method for two phase magnetohydrodynamic diffuse interface model, Optimal control and controllability of a phase field system with one control force, Phase transitions in materials with thermal memory, Improved phase-field models of melting and dissolution in multi-component flows, Phase transitions in materials with thermal memory and a Fourier term, Phase transitions in materials with thermal memory: The case of unequal conductivities, Analysis of a two-phase field model for the solidification of an alloy, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method

Cites Work

• Thermodynamically consistent models of phase-field type for the kinetics of phase transitions
• An analysis of a phase field model of a free boundary
• A mathematical model of dynamics of non-isothermal phase separation
• Continuum theory of thermally induced phase transitions based on an order parameter
• Thermodynamically-consistent phase-field models for solidification
• Dynamic solid-solid transitions with phase characterized by an order parameter
• Linking anisotropic sharp and diffuse surface motion laws via gradient flows
• A phase-field theory for solidification based on a general anisotropic sharp-interface theory with interfacial energy and entropy
• A phase-field model of solidification with convection
• Second-Order Phase Field Asymptotics for Unequal Conductivities
• On the notion of a ξ –vector and a stress tensor for a general class of anisotropic diffuse interface models
• Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations
• A ξ-vector formulation of anisotropic phase-field models: 3D asymptotics
• Directions in Condensed Matter Physics
• Unnamed Item
• Unnamed Item