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Two-dimensional Stefan problem using level set method

Cancer cell invasion across the surrounding tissues is driven by finger-like protrusions known as invadopodia. Plasma membrane of a cancer cell has the elastic characteristic that gives the idea to employ the knowledge of Stefan problem to solve the problem in cancer cell invasion. For this purpose,...

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Main Author:	Noor Azhuan, Nur Azura
Format:	Thesis
Language:	English
Published:	2017
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/86205/1/NurAzuraNoorMFS2017.pdf http://eprints.utm.my/id/eprint/86205/ http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:132421
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id	my.utm.86205
record_format	eprints
spelling	my.utm.862052020-08-30T09:07:49Z http://eprints.utm.my/id/eprint/86205/ Two-dimensional Stefan problem using level set method Noor Azhuan, Nur Azura QA Mathematics Cancer cell invasion across the surrounding tissues is driven by finger-like protrusions known as invadopodia. Plasma membrane of a cancer cell has the elastic characteristic that gives the idea to employ the knowledge of Stefan problem to solve the problem in cancer cell invasion. For this purpose, plasma membrane is treated as a free boundary interface. In fact, Stefan problem is a well-known free boundary problem that requires the solution of moving interface(s) as time proceeds along with the change in the temperature distribution. Hence, this study investigated twodimensional free boundary Stefan problem that focused on the solidification process. A mathematical model of solidification is first introduced by Chen et al. (1997) considering the jump of the temperature distribution fromthe liquid to the solid regions. The velocity concerning the movement of the interface is calculated by taking the first derivative of the temperature with respect to space. The model is solved numerically by using finite-difference of level set method [13]. Two algorithms of the level set method are presented in modelling and discretization parts, to handle the topology changes of Stefan problem, systematically. Results of the interface movement and temperature distribution are presented graphically and discussed in order to visualize the solidification process. 2017 Thesis NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/86205/1/NurAzuraNoorMFS2017.pdf Noor Azhuan, Nur Azura (2017) Two-dimensional Stefan problem using level set method. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science. http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:132421
institution	Universiti Teknologi Malaysia
building	UTM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Teknologi Malaysia
content_source	UTM Institutional Repository
url_provider	http://eprints.utm.my/
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Noor Azhuan, Nur Azura Two-dimensional Stefan problem using level set method
description	Cancer cell invasion across the surrounding tissues is driven by finger-like protrusions known as invadopodia. Plasma membrane of a cancer cell has the elastic characteristic that gives the idea to employ the knowledge of Stefan problem to solve the problem in cancer cell invasion. For this purpose, plasma membrane is treated as a free boundary interface. In fact, Stefan problem is a well-known free boundary problem that requires the solution of moving interface(s) as time proceeds along with the change in the temperature distribution. Hence, this study investigated twodimensional free boundary Stefan problem that focused on the solidification process. A mathematical model of solidification is first introduced by Chen et al. (1997) considering the jump of the temperature distribution fromthe liquid to the solid regions. The velocity concerning the movement of the interface is calculated by taking the first derivative of the temperature with respect to space. The model is solved numerically by using finite-difference of level set method [13]. Two algorithms of the level set method are presented in modelling and discretization parts, to handle the topology changes of Stefan problem, systematically. Results of the interface movement and temperature distribution are presented graphically and discussed in order to visualize the solidification process.
format	Thesis
author	Noor Azhuan, Nur Azura
author_facet	Noor Azhuan, Nur Azura
author_sort	Noor Azhuan, Nur Azura
title	Two-dimensional Stefan problem using level set method
title_short	Two-dimensional Stefan problem using level set method
title_full	Two-dimensional Stefan problem using level set method
title_fullStr	Two-dimensional Stefan problem using level set method
title_full_unstemmed	Two-dimensional Stefan problem using level set method
title_sort	two-dimensional stefan problem using level set method
publishDate	2017
url	http://eprints.utm.my/id/eprint/86205/1/NurAzuraNoorMFS2017.pdf http://eprints.utm.my/id/eprint/86205/ http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:132421
_version_	1677781145682444288
score	13.211869

Two-dimensional Stefan problem using level set method

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