Rapid growth and critical behaviour in phase field models of solidification

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Rapid solidification fronts are studied using a phase field model. Unlike slow moving solutions which approximate the Mullins-Sekerka free boundary problem, different limiting behaviour is obtained for rapidly moving fronts. A time-dependent analysis is carried out for various cases and the leading order behaviour of solidification front solutions is derived to be one of several travelling wave problems. An analysis of these problems is conducted, leading to expressions for front speeds in certain limits. The dynamics leading to these travelling wave solutions is derived, and conclusions about stability are drawn. Finally, a discussion is made of the relationship to other solidification models.

Original languageEnglish (US)
Pages (from-to)39-56
Number of pages18
JournalEuropean Journal of Applied Mathematics
Volume12
Issue number1
DOIs
StatePublished - 2001
Externally publishedYes

Fingerprint

Phase Field Model
Solidification
Critical Behavior
Rapid solidification
Limiting Behavior
Free Boundary Problem
Traveling Wave Solutions
Traveling Wave
Approximate Solution

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Rapid growth and critical behaviour in phase field models of solidification. / Glasner, Karl B.

In: European Journal of Applied Mathematics, Vol. 12, No. 1, 2001, p. 39-56.

Research output: Contribution to journalArticle

@article{e1ece5a5b1de4c04bb5f1f923df08bfe,
title = "Rapid growth and critical behaviour in phase field models of solidification",
abstract = "Rapid solidification fronts are studied using a phase field model. Unlike slow moving solutions which approximate the Mullins-Sekerka free boundary problem, different limiting behaviour is obtained for rapidly moving fronts. A time-dependent analysis is carried out for various cases and the leading order behaviour of solidification front solutions is derived to be one of several travelling wave problems. An analysis of these problems is conducted, leading to expressions for front speeds in certain limits. The dynamics leading to these travelling wave solutions is derived, and conclusions about stability are drawn. Finally, a discussion is made of the relationship to other solidification models.",
author = "Glasner, {Karl B}",
year = "2001",
doi = "10.1017/S0956792501004351",
language = "English (US)",
volume = "12",
pages = "39--56",
journal = "European Journal of Applied Mathematics",
issn = "0956-7925",
publisher = "Cambridge University Press",
number = "1",

}

TY - JOUR

T1 - Rapid growth and critical behaviour in phase field models of solidification

AU - Glasner, Karl B

PY - 2001

Y1 - 2001

N2 - Rapid solidification fronts are studied using a phase field model. Unlike slow moving solutions which approximate the Mullins-Sekerka free boundary problem, different limiting behaviour is obtained for rapidly moving fronts. A time-dependent analysis is carried out for various cases and the leading order behaviour of solidification front solutions is derived to be one of several travelling wave problems. An analysis of these problems is conducted, leading to expressions for front speeds in certain limits. The dynamics leading to these travelling wave solutions is derived, and conclusions about stability are drawn. Finally, a discussion is made of the relationship to other solidification models.

AB - Rapid solidification fronts are studied using a phase field model. Unlike slow moving solutions which approximate the Mullins-Sekerka free boundary problem, different limiting behaviour is obtained for rapidly moving fronts. A time-dependent analysis is carried out for various cases and the leading order behaviour of solidification front solutions is derived to be one of several travelling wave problems. An analysis of these problems is conducted, leading to expressions for front speeds in certain limits. The dynamics leading to these travelling wave solutions is derived, and conclusions about stability are drawn. Finally, a discussion is made of the relationship to other solidification models.

UR - http://www.scopus.com/inward/record.url?scp=0035608336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035608336&partnerID=8YFLogxK

U2 - 10.1017/S0956792501004351

DO - 10.1017/S0956792501004351

M3 - Article

VL - 12

SP - 39

EP - 56

JO - European Journal of Applied Mathematics

JF - European Journal of Applied Mathematics

SN - 0956-7925

IS - 1

ER -