Dynamical model of oscillatory zoning in plagioclase with nonlinear partition relation
We present a nonlinear dynamical model for oscillatory zoning in plagioclase based on a simple isothermal constitutive undercooling mechanism. A phenomenological partitioning is introduced to relate the concentration of An in the melt at the interface with the concentration in the solid. The non‐lin...
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| Veröffentlicht in: | Geophysical research letters 1996-01, Vol.23 (1), p.17-20 |
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| container_title | Geophysical research letters |
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| creator | L'Heureux, Ivan Fowler, Anthony D. |
| description | We present a nonlinear dynamical model for oscillatory zoning in plagioclase based on a simple isothermal constitutive undercooling mechanism. A phenomenological partitioning is introduced to relate the concentration of An in the melt at the interface with the concentration in the solid. The non‐linearities in the model result from the coupling of the growth velocity with the local An concentration and from the boundary condition at the interface. The consideration of a nonlinear boundary condition is new and generalizes previous nonlinear growth models. It is shown that parameter values exist for which oscillatory solutions are possible via a Hopf bifurcation. As the system is driven further out of equilibrium, the model shows the development of chaotic solutions via a period‐doubling sequence. |
| doi_str_mv | 10.1029/95GL03327 |
| format | Article |
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A phenomenological partitioning is introduced to relate the concentration of An in the melt at the interface with the concentration in the solid. The non‐linearities in the model result from the coupling of the growth velocity with the local An concentration and from the boundary condition at the interface. The consideration of a nonlinear boundary condition is new and generalizes previous nonlinear growth models. It is shown that parameter values exist for which oscillatory solutions are possible via a Hopf bifurcation. As the system is driven further out of equilibrium, the model shows the development of chaotic solutions via a period‐doubling sequence.</description><identifier>ISSN: 0094-8276</identifier><identifier>EISSN: 1944-8007</identifier><identifier>DOI: 10.1029/95GL03327</identifier><identifier>CODEN: GPRLAJ</identifier><language>eng</language><publisher>Washington, DC: Blackwell Publishing Ltd</publisher><subject>Boundary conditions ; Earth sciences ; Earth, ocean, space ; Exact sciences and technology ; Geochemistry ; Hopf bifurcation ; Mathematical models ; Melts ; Mineralogy ; Nonlinearity ; Plagioclase ; Silicates ; Soil and rock geochemistry ; Supercooling ; Zoning</subject><ispartof>Geophysical research letters, 1996-01, Vol.23 (1), p.17-20</ispartof><rights>Copyright 1996 by the American Geophysical Union.</rights><rights>1996 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a3890-26ba829ac3e15243d17b41031ffe4ae730f6f42a24da760a73d870cdf3ded1243</citedby><cites>FETCH-LOGICAL-a3890-26ba829ac3e15243d17b41031ffe4ae730f6f42a24da760a73d870cdf3ded1243</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1029%2F95GL03327$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1029%2F95GL03327$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,4009,27902,27903,27904,45553,45554</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=2951625$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>L'Heureux, Ivan</creatorcontrib><creatorcontrib>Fowler, Anthony D.</creatorcontrib><title>Dynamical model of oscillatory zoning in plagioclase with nonlinear partition relation</title><title>Geophysical research letters</title><addtitle>Geophys. 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As the system is driven further out of equilibrium, the model shows the development of chaotic solutions via a period‐doubling sequence.</description><subject>Boundary conditions</subject><subject>Earth sciences</subject><subject>Earth, ocean, space</subject><subject>Exact sciences and technology</subject><subject>Geochemistry</subject><subject>Hopf bifurcation</subject><subject>Mathematical models</subject><subject>Melts</subject><subject>Mineralogy</subject><subject>Nonlinearity</subject><subject>Plagioclase</subject><subject>Silicates</subject><subject>Soil and rock geochemistry</subject><subject>Supercooling</subject><subject>Zoning</subject><issn>0094-8276</issn><issn>1944-8007</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1996</creationdate><recordtype>article</recordtype><recordid>eNp1kLFOIzEURa0VSATYgj9wQcEWA8_2zHimRCwJoAgUxEJpPWZs1ruOHexBIXw9RonSUb1bnHP1dAk5YnDKgLdnbTWZghBc_iAj1pZl0QDIHTICaHPmst4j-yn9AwABgo3I4--Vx7nt0NF56LWjwdCQOuscDiGu6Efw1r9Q6-nC4YsNncOk6dIOf6kP3lmvMdIFxsEONngadfZyOCS7Bl3SPzf3gPwZXz5cXBXTu8n1xfm0QNG0UPD6GRveYic0q3gpeiafS5YfM0aXqKUAU5uSIy97lDWgFH0joeuN6HXPsnBATta9ixhe33Qa1NymTufvvQ5vSbFKMGANMJHRX2u0iyGlqI1aRDvHuFIM1Nd2artdZo83tZjyNCai72zaCrytWM2rjJ2usaV1evV9n5rcT5umhCwUa8GmQb9vBYz_VS2FrNTT7USJm_HDuBIzNROfZ3-LQQ</recordid><startdate>19960101</startdate><enddate>19960101</enddate><creator>L'Heureux, Ivan</creator><creator>Fowler, Anthony D.</creator><general>Blackwell Publishing Ltd</general><general>American Geophysical Union</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>19960101</creationdate><title>Dynamical model of oscillatory zoning in plagioclase with nonlinear partition relation</title><author>L'Heureux, Ivan ; Fowler, Anthony D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a3890-26ba829ac3e15243d17b41031ffe4ae730f6f42a24da760a73d870cdf3ded1243</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1996</creationdate><topic>Boundary conditions</topic><topic>Earth sciences</topic><topic>Earth, ocean, space</topic><topic>Exact sciences and technology</topic><topic>Geochemistry</topic><topic>Hopf bifurcation</topic><topic>Mathematical models</topic><topic>Melts</topic><topic>Mineralogy</topic><topic>Nonlinearity</topic><topic>Plagioclase</topic><topic>Silicates</topic><topic>Soil and rock geochemistry</topic><topic>Supercooling</topic><topic>Zoning</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>L'Heureux, Ivan</creatorcontrib><creatorcontrib>Fowler, Anthony D.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Geophysical research letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>L'Heureux, Ivan</au><au>Fowler, Anthony D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamical model of oscillatory zoning in plagioclase with nonlinear partition relation</atitle><jtitle>Geophysical research letters</jtitle><addtitle>Geophys. Res. Lett</addtitle><date>1996-01-01</date><risdate>1996</risdate><volume>23</volume><issue>1</issue><spage>17</spage><epage>20</epage><pages>17-20</pages><issn>0094-8276</issn><eissn>1944-8007</eissn><coden>GPRLAJ</coden><abstract>We present a nonlinear dynamical model for oscillatory zoning in plagioclase based on a simple isothermal constitutive undercooling mechanism. A phenomenological partitioning is introduced to relate the concentration of An in the melt at the interface with the concentration in the solid. The non‐linearities in the model result from the coupling of the growth velocity with the local An concentration and from the boundary condition at the interface. The consideration of a nonlinear boundary condition is new and generalizes previous nonlinear growth models. It is shown that parameter values exist for which oscillatory solutions are possible via a Hopf bifurcation. As the system is driven further out of equilibrium, the model shows the development of chaotic solutions via a period‐doubling sequence.</abstract><cop>Washington, DC</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1029/95GL03327</doi><tpages>4</tpages></addata></record> |
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| ispartof | Geophysical research letters, 1996-01, Vol.23 (1), p.17-20 |
| issn | 0094-8276 1944-8007 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1531018013 |
| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Boundary conditions Earth sciences Earth, ocean, space Exact sciences and technology Geochemistry Hopf bifurcation Mathematical models Melts Mineralogy Nonlinearity Plagioclase Silicates Soil and rock geochemistry Supercooling Zoning |
| title | Dynamical model of oscillatory zoning in plagioclase with nonlinear partition relation |
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