Evolution of flat crystallisation front in forced hydrodynamic flow - some explicit solutions

L. J. Cummings; K. Kornev

doi:10.1016/S0167-2789(98)00288-7

Evolution of flat crystallisation front in forced hydrodynamic flow - some explicit solutions

L. J. Cummings, K. Kornev

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We consider the two-dimensional solidification/melting (one problem being the time-reversal of the other) of dendrites in an imposed hydrodynamic flow with a stagnation point. Complex variable methods are used, and a new class of solutions is presented (neglecting surface effects at the interface). These solutions can exhibit the interesting phenomenon of transient singularity formation in the dendrite boundary; a cusp forms in the boundary, but then instantly smooths and the solution can be continued.

Original language	English (US)
Pages (from-to)	33-47
Number of pages	15
Journal	Physica D: Nonlinear Phenomena
Volume	127
Issue number	1-2
DOIs	https://doi.org/10.1016/S0167-2789(98)00288-7
State	Published - Mar 1 1999
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

Keywords

Crystallisation
Dendrite
Hydrodynamic flow
Melting

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10.1016/S0167-2789(98)00288-7

Cite this

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title = "Evolution of flat crystallisation front in forced hydrodynamic flow - some explicit solutions",

abstract = "We consider the two-dimensional solidification/melting (one problem being the time-reversal of the other) of dendrites in an imposed hydrodynamic flow with a stagnation point. Complex variable methods are used, and a new class of solutions is presented (neglecting surface effects at the interface). These solutions can exhibit the interesting phenomenon of transient singularity formation in the dendrite boundary; a cusp forms in the boundary, but then instantly smooths and the solution can be continued.",

keywords = "Crystallisation, Dendrite, Hydrodynamic flow, Melting",

author = "Cummings, {L. J.} and K. Kornev",

note = "Funding Information: The first author thanks the Israel Council for higher Education for a research grant, which was held at Technion, Haifa. ",

year = "1999",

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doi = "10.1016/S0167-2789(98)00288-7",

language = "English (US)",

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pages = "33--47",

journal = "Physica D: Nonlinear Phenomena",

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TY - JOUR

T1 - Evolution of flat crystallisation front in forced hydrodynamic flow - some explicit solutions

AU - Cummings, L. J.

AU - Kornev, K.

N1 - Funding Information: The first author thanks the Israel Council for higher Education for a research grant, which was held at Technion, Haifa.

PY - 1999/3/1

Y1 - 1999/3/1

N2 - We consider the two-dimensional solidification/melting (one problem being the time-reversal of the other) of dendrites in an imposed hydrodynamic flow with a stagnation point. Complex variable methods are used, and a new class of solutions is presented (neglecting surface effects at the interface). These solutions can exhibit the interesting phenomenon of transient singularity formation in the dendrite boundary; a cusp forms in the boundary, but then instantly smooths and the solution can be continued.

AB - We consider the two-dimensional solidification/melting (one problem being the time-reversal of the other) of dendrites in an imposed hydrodynamic flow with a stagnation point. Complex variable methods are used, and a new class of solutions is presented (neglecting surface effects at the interface). These solutions can exhibit the interesting phenomenon of transient singularity formation in the dendrite boundary; a cusp forms in the boundary, but then instantly smooths and the solution can be continued.

KW - Crystallisation

KW - Dendrite

KW - Hydrodynamic flow

KW - Melting

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UR - http://www.scopus.com/inward/citedby.url?scp=0033101408&partnerID=8YFLogxK

U2 - 10.1016/S0167-2789(98)00288-7

DO - 10.1016/S0167-2789(98)00288-7

M3 - Article

AN - SCOPUS:0033101408

SN - 0167-2789

VL - 127

SP - 33

EP - 47

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1-2

ER -

Evolution of flat crystallisation front in forced hydrodynamic flow - some explicit solutions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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