Concepts of modeling surface energy anisotropy in phase-field approaches

Abstract To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolu...
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Autor*in:	Tschukin, Oleg [verfasserIn] Silberzahn, Alexander Selzer, Michael Amos, Prince G. K. Schneider, Daniel Nestler, Britta

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	Phase field Anisotropy Allen–Cahn equation

Anmerkung:	© The Author(s) 2017

Übergeordnetes Werk:	Enthalten in: Geothermal Energy - Berlin : SpringerOpen, 2013, 5(2017), 1 vom: 11. Okt.
Übergeordnetes Werk:	volume:5 ; year:2017 ; number:1 ; day:11 ; month:10

Links:	Volltext

DOI / URN:	10.1186/s40517-017-0077-9

Katalog-ID:	SPR036566438

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520			\|a Abstract To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolution equations, considered in this work, are derived using the variational approach, and correspond to the conservative Allen–Cahn-type equation. For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models. Particularly, if the anisotropy becomes strong, the phase-field evolution equations become ill-posed. Thus, we present regularized phase-field models and discuss the corresponding simulation results. Furthermore, in the scope of the grain growth simulation, we extend the original two-phase models to multiphases.
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allfields	10.1186/s40517-017-0077-9 doi (DE-627)SPR036566438 (SPR)s40517-017-0077-9-e DE-627 ger DE-627 rakwb eng Tschukin, Oleg verfasserin aut Concepts of modeling surface energy anisotropy in phase-field approaches 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolution equations, considered in this work, are derived using the variational approach, and correspond to the conservative Allen–Cahn-type equation. For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models. Particularly, if the anisotropy becomes strong, the phase-field evolution equations become ill-posed. Thus, we present regularized phase-field models and discuss the corresponding simulation results. Furthermore, in the scope of the grain growth simulation, we extend the original two-phase models to multiphases. Phase field (dpeaa)DE-He213 Anisotropy (dpeaa)DE-He213 Allen–Cahn equation (dpeaa)DE-He213 Silberzahn, Alexander aut Selzer, Michael aut Amos, Prince G. K. aut Schneider, Daniel aut Nestler, Britta aut Enthalten in Geothermal Energy Berlin : SpringerOpen, 2013 5(2017), 1 vom: 11. Okt. (DE-627)749499893 (DE-600)2718871-1 2195-9706 nnns volume:5 year:2017 number:1 day:11 month:10 https://dx.doi.org/10.1186/s40517-017-0077-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2017 1 11 10
spelling	10.1186/s40517-017-0077-9 doi (DE-627)SPR036566438 (SPR)s40517-017-0077-9-e DE-627 ger DE-627 rakwb eng Tschukin, Oleg verfasserin aut Concepts of modeling surface energy anisotropy in phase-field approaches 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolution equations, considered in this work, are derived using the variational approach, and correspond to the conservative Allen–Cahn-type equation. For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models. Particularly, if the anisotropy becomes strong, the phase-field evolution equations become ill-posed. Thus, we present regularized phase-field models and discuss the corresponding simulation results. Furthermore, in the scope of the grain growth simulation, we extend the original two-phase models to multiphases. Phase field (dpeaa)DE-He213 Anisotropy (dpeaa)DE-He213 Allen–Cahn equation (dpeaa)DE-He213 Silberzahn, Alexander aut Selzer, Michael aut Amos, Prince G. K. aut Schneider, Daniel aut Nestler, Britta aut Enthalten in Geothermal Energy Berlin : SpringerOpen, 2013 5(2017), 1 vom: 11. Okt. (DE-627)749499893 (DE-600)2718871-1 2195-9706 nnns volume:5 year:2017 number:1 day:11 month:10 https://dx.doi.org/10.1186/s40517-017-0077-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2017 1 11 10
allfields_unstemmed	10.1186/s40517-017-0077-9 doi (DE-627)SPR036566438 (SPR)s40517-017-0077-9-e DE-627 ger DE-627 rakwb eng Tschukin, Oleg verfasserin aut Concepts of modeling surface energy anisotropy in phase-field approaches 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolution equations, considered in this work, are derived using the variational approach, and correspond to the conservative Allen–Cahn-type equation. For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models. Particularly, if the anisotropy becomes strong, the phase-field evolution equations become ill-posed. Thus, we present regularized phase-field models and discuss the corresponding simulation results. Furthermore, in the scope of the grain growth simulation, we extend the original two-phase models to multiphases. Phase field (dpeaa)DE-He213 Anisotropy (dpeaa)DE-He213 Allen–Cahn equation (dpeaa)DE-He213 Silberzahn, Alexander aut Selzer, Michael aut Amos, Prince G. K. aut Schneider, Daniel aut Nestler, Britta aut Enthalten in Geothermal Energy Berlin : SpringerOpen, 2013 5(2017), 1 vom: 11. Okt. (DE-627)749499893 (DE-600)2718871-1 2195-9706 nnns volume:5 year:2017 number:1 day:11 month:10 https://dx.doi.org/10.1186/s40517-017-0077-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2017 1 11 10
allfieldsGer	10.1186/s40517-017-0077-9 doi (DE-627)SPR036566438 (SPR)s40517-017-0077-9-e DE-627 ger DE-627 rakwb eng Tschukin, Oleg verfasserin aut Concepts of modeling surface energy anisotropy in phase-field approaches 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolution equations, considered in this work, are derived using the variational approach, and correspond to the conservative Allen–Cahn-type equation. For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models. Particularly, if the anisotropy becomes strong, the phase-field evolution equations become ill-posed. Thus, we present regularized phase-field models and discuss the corresponding simulation results. Furthermore, in the scope of the grain growth simulation, we extend the original two-phase models to multiphases. Phase field (dpeaa)DE-He213 Anisotropy (dpeaa)DE-He213 Allen–Cahn equation (dpeaa)DE-He213 Silberzahn, Alexander aut Selzer, Michael aut Amos, Prince G. K. aut Schneider, Daniel aut Nestler, Britta aut Enthalten in Geothermal Energy Berlin : SpringerOpen, 2013 5(2017), 1 vom: 11. Okt. (DE-627)749499893 (DE-600)2718871-1 2195-9706 nnns volume:5 year:2017 number:1 day:11 month:10 https://dx.doi.org/10.1186/s40517-017-0077-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2017 1 11 10
allfieldsSound	10.1186/s40517-017-0077-9 doi (DE-627)SPR036566438 (SPR)s40517-017-0077-9-e DE-627 ger DE-627 rakwb eng Tschukin, Oleg verfasserin aut Concepts of modeling surface energy anisotropy in phase-field approaches 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolution equations, considered in this work, are derived using the variational approach, and correspond to the conservative Allen–Cahn-type equation. For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models. Particularly, if the anisotropy becomes strong, the phase-field evolution equations become ill-posed. Thus, we present regularized phase-field models and discuss the corresponding simulation results. Furthermore, in the scope of the grain growth simulation, we extend the original two-phase models to multiphases. Phase field (dpeaa)DE-He213 Anisotropy (dpeaa)DE-He213 Allen–Cahn equation (dpeaa)DE-He213 Silberzahn, Alexander aut Selzer, Michael aut Amos, Prince G. K. aut Schneider, Daniel aut Nestler, Britta aut Enthalten in Geothermal Energy Berlin : SpringerOpen, 2013 5(2017), 1 vom: 11. Okt. (DE-627)749499893 (DE-600)2718871-1 2195-9706 nnns volume:5 year:2017 number:1 day:11 month:10 https://dx.doi.org/10.1186/s40517-017-0077-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2017 1 11 10
language	English
source	Enthalten in Geothermal Energy 5(2017), 1 vom: 11. Okt. volume:5 year:2017 number:1 day:11 month:10
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topic_facet	Phase field Anisotropy Allen–Cahn equation
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authorswithroles_txt_mv	Tschukin, Oleg @@aut@@ Silberzahn, Alexander @@aut@@ Selzer, Michael @@aut@@ Amos, Prince G. K. @@aut@@ Schneider, Daniel @@aut@@ Nestler, Britta @@aut@@
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author	Tschukin, Oleg
spellingShingle	Tschukin, Oleg misc Phase field misc Anisotropy misc Allen–Cahn equation Concepts of modeling surface energy anisotropy in phase-field approaches
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topic_title	Concepts of modeling surface energy anisotropy in phase-field approaches Phase field (dpeaa)DE-He213 Anisotropy (dpeaa)DE-He213 Allen–Cahn equation (dpeaa)DE-He213
topic	misc Phase field misc Anisotropy misc Allen–Cahn equation
topic_unstemmed	misc Phase field misc Anisotropy misc Allen–Cahn equation
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title	Concepts of modeling surface energy anisotropy in phase-field approaches
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title_full	Concepts of modeling surface energy anisotropy in phase-field approaches
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author_browse	Tschukin, Oleg Silberzahn, Alexander Selzer, Michael Amos, Prince G. K. Schneider, Daniel Nestler, Britta
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doi_str_mv	10.1186/s40517-017-0077-9
title_sort	concepts of modeling surface energy anisotropy in phase-field approaches
title_auth	Concepts of modeling surface energy anisotropy in phase-field approaches
abstract	Abstract To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolution equations, considered in this work, are derived using the variational approach, and correspond to the conservative Allen–Cahn-type equation. For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models. Particularly, if the anisotropy becomes strong, the phase-field evolution equations become ill-posed. Thus, we present regularized phase-field models and discuss the corresponding simulation results. Furthermore, in the scope of the grain growth simulation, we extend the original two-phase models to multiphases. © The Author(s) 2017
abstractGer	Abstract To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolution equations, considered in this work, are derived using the variational approach, and correspond to the conservative Allen–Cahn-type equation. For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models. Particularly, if the anisotropy becomes strong, the phase-field evolution equations become ill-posed. Thus, we present regularized phase-field models and discuss the corresponding simulation results. Furthermore, in the scope of the grain growth simulation, we extend the original two-phase models to multiphases. © The Author(s) 2017
abstract_unstemmed	Abstract To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolution equations, considered in this work, are derived using the variational approach, and correspond to the conservative Allen–Cahn-type equation. For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models. Particularly, if the anisotropy becomes strong, the phase-field evolution equations become ill-posed. Thus, we present regularized phase-field models and discuss the corresponding simulation results. Furthermore, in the scope of the grain growth simulation, we extend the original two-phase models to multiphases. © The Author(s) 2017
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title_short	Concepts of modeling surface energy anisotropy in phase-field approaches
url	https://dx.doi.org/10.1186/s40517-017-0077-9
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author2	Silberzahn, Alexander Selzer, Michael Amos, Prince G. K. Schneider, Daniel Nestler, Britta
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