Upper Bounds for Coarsening for the Deep Quench Obstacle Problem.
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| Title: | Upper Bounds for Coarsening for the Deep Quench Obstacle Problem. |
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| Authors: | Novick-Cohen, Amy1 amync@techunix.technion.ac.il |
| Source: | Journal of Statistical Physics. Oct2010, Vol. 141 Issue 1, p142-157. 16p. |
| Subjects: | Ostwald ripening, Phase separation method (Engineering), Low temperatures, Quantum theory, Metal quenching |
| Abstract: | The deep quench obstacle problem models phase separation at low temperatures. During phase separation, domains of high and low concentration are formed, then coarsen or grow in average size. Of interest is the time dependence of the dominant length scales of the system. Relying on recent results by Novick-Cohen and Shishkov (Discrete Contin. Dyn. Syst. B 25:251–272, ), we demonstrate upper bounds for coarsening for the deep quench obstacle problem, with either constant or degenerate mobility. For the case of constant mobility, we obtain upper bounds of the form t at early times as well as at times t for which $E(t)\le\frac{(1-\overline{u}^{2})}{4}$, where E( t) denotes the free energy. For the case of degenerate mobility, we get upper bounds of the form t or t at early times, depending on the value of E(0), as well as bounds of the form t whenever $E(t)\le\frac{(1-\overline{u}^{2})}{4}$. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 53505155 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Upper Bounds for Coarsening for the Deep Quench Obstacle Problem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Novick-Cohen%2C+Amy%22">Novick-Cohen, Amy</searchLink><relatesTo>1</relatesTo><i> amync@techunix.technion.ac.il</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Statistical+Physics%22">Journal of Statistical Physics</searchLink>. Oct2010, Vol. 141 Issue 1, p142-157. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Ostwald+ripening%22">Ostwald ripening</searchLink><br /><searchLink fieldCode="DE" term="%22Phase+separation+method+%28Engineering%29%22">Phase separation method (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Low+temperatures%22">Low temperatures</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+theory%22">Quantum theory</searchLink><br /><searchLink fieldCode="DE" term="%22Metal+quenching%22">Metal quenching</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The deep quench obstacle problem models phase separation at low temperatures. During phase separation, domains of high and low concentration are formed, then coarsen or grow in average size. Of interest is the time dependence of the dominant length scales of the system. Relying on recent results by Novick-Cohen and Shishkov (Discrete Contin. Dyn. Syst. B 25:251–272, ), we demonstrate upper bounds for coarsening for the deep quench obstacle problem, with either constant or degenerate mobility. For the case of constant mobility, we obtain upper bounds of the form t at early times as well as at times t for which $E(t)\le\frac{(1-\overline{u}^{2})}{4}$, where E( t) denotes the free energy. For the case of degenerate mobility, we get upper bounds of the form t or t at early times, depending on the value of E(0), as well as bounds of the form t whenever $E(t)\le\frac{(1-\overline{u}^{2})}{4}$. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10955-010-0040-7 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 142 Subjects: – SubjectFull: Ostwald ripening Type: general – SubjectFull: Phase separation method (Engineering) Type: general – SubjectFull: Low temperatures Type: general – SubjectFull: Quantum theory Type: general – SubjectFull: Metal quenching Type: general Titles: – TitleFull: Upper Bounds for Coarsening for the Deep Quench Obstacle Problem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Novick-Cohen, Amy IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2010 Type: published Y: 2010 Identifiers: – Type: issn-print Value: 00224715 Numbering: – Type: volume Value: 141 – Type: issue Value: 1 Titles: – TitleFull: Journal of Statistical Physics Type: main |
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