Progress in modelling solidification microstructures in metals and alloys: dendrites and cells from 1700 to 2000
W Kurz, DJ Fisher, R Trivedi - International Materials …, 2019 - journals.sagepub.com
This is the first account of the history of our understanding of, and ability to model,
solidification microstructures. Its objective is to retrace the scientific steps made, from the …
solidification microstructures. Its objective is to retrace the scientific steps made, from the …
The cahn–hilliard equation
A Novick-Cohen - Handbook of differential equations: evolutionary …, 2008 - Elsevier
Publisher Summary This chapter focuses on the Cahn–Hilliard equation. In the context of the
Cahn–Hilliard equation, the two components could refer, for example, to a system with two …
Cahn–Hilliard equation, the two components could refer, for example, to a system with two …
[图书][B] Phase-field methods in materials science and engineering
N Provatas, K Elder - 2011 - books.google.com
This comprehensive and self-contained, one-stop source discusses phase-field
methodology in a fundamental way, explaining advanced numerical techniques for solving …
methodology in a fundamental way, explaining advanced numerical techniques for solving …
Thermodynamically-consistent phase-field models for solidification
SL Wang, RF Sekerka, AA Wheeler, BT Murray… - Physica D: Nonlinear …, 1993 - Elsevier
In an effort to unify the various phase-field models that have been used to study
solidification, we have developed a class of phase-field models for crystallization of a pure …
solidification, we have developed a class of phase-field models for crystallization of a pure …
Phase transitions and generalized motion by mean curvature
LC Evans, HM Soner… - Communications on Pure …, 1992 - Wiley Online Library
We study the limiting behavior of solutions to appropriately rescaled versions of the Allen‐
Cahn equation, a simplified model for dynamic phase transitions. We rigorously establish …
Cahn equation, a simplified model for dynamic phase transitions. We rigorously establish …
Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations
G Caginalp - Physical Review A, 1989 - APS
Using detailed asymptotic analyses of the dynamics of the phase-field model, we show that
the major sharp-interface models (Stefan, modified Stefan, Hele-Shaw, etc.) all arise as …
the major sharp-interface models (Stefan, modified Stefan, Hele-Shaw, etc.) all arise as …
Phase-field models for anisotropic interfaces
The inclusion of anisotropic surface free energy and anisotropic linear interface kinetics in
phase-field models is studied for the solidification of a pure material. The formulation is …
phase-field models is studied for the solidification of a pure material. The formulation is …
Efficient computation of dendritic microstructures using adaptive mesh refinement
We study dendritic microstructure evolution using an adaptive grid, finite element method
applied to a phase-field model. The computational complexity of our algorithm, per unit time …
applied to a phase-field model. The computational complexity of our algorithm, per unit time …
Adaptive mesh refinement computation of solidification microstructures using dynamic data structures
We study the evolution of solidification microstructures using a phase-field model computed
on an adaptive, finite element grid. We discuss the details of our algorithm and show that it …
on an adaptive, finite element grid. We discuss the details of our algorithm and show that it …
[PDF][PDF] Models for phase separation and their mathematics
PC Fife - 2000 - digital.library.txstate.edu
Models for phase separation and their mathematics Page 1 Electronic Journal of Differential
Equations, Vol. 2000(2000), No. 48, pp. 1–26. ISSN: 1072-6691. URL: http://ejde.math.swt.edu …
Equations, Vol. 2000(2000), No. 48, pp. 1–26. ISSN: 1072-6691. URL: http://ejde.math.swt.edu …