A Stable Self-Similar Singularity of Evaporating Drops: Ellipsoidal Collapse to a Point
Abstract We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follo...
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| Autor*in: |
Fontelos, Marco A. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2014 |
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| Übergeordnetes Werk: |
Enthalten in: Archive for rational mechanics and analysis - Springer Berlin Heidelberg, 1957, 217(2014), 2 vom: 16. Dez., Seite 373-411 |
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| Übergeordnetes Werk: |
volume:217 ; year:2014 ; number:2 ; day:16 ; month:12 ; pages:373-411 |
| Links: |
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| DOI / URN: |
10.1007/s00205-014-0834-x |
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| 520 | |a Abstract We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape. | ||
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10.1007/s00205-014-0834-x doi (DE-627)OLC2056424142 (DE-He213)s00205-014-0834-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Fontelos, Marco A. verfasserin aut A Stable Self-Similar Singularity of Evaporating Drops: Ellipsoidal Collapse to a Point 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape. Spherical Harmonic Free Boundary Problem Spherical Coordinate System Spherical Harmonic Expansion Vector Spherical Harmonic Hong, Seok Hyun aut Hwang, Hyung Ju aut Enthalten in Archive for rational mechanics and analysis Springer Berlin Heidelberg, 1957 217(2014), 2 vom: 16. Dez., Seite 373-411 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:217 year:2014 number:2 day:16 month:12 pages:373-411 https://doi.org/10.1007/s00205-014-0834-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_65 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4323 GBV_ILN_4700 AR 217 2014 2 16 12 373-411 |
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10.1007/s00205-014-0834-x doi (DE-627)OLC2056424142 (DE-He213)s00205-014-0834-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Fontelos, Marco A. verfasserin aut A Stable Self-Similar Singularity of Evaporating Drops: Ellipsoidal Collapse to a Point 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape. Spherical Harmonic Free Boundary Problem Spherical Coordinate System Spherical Harmonic Expansion Vector Spherical Harmonic Hong, Seok Hyun aut Hwang, Hyung Ju aut Enthalten in Archive for rational mechanics and analysis Springer Berlin Heidelberg, 1957 217(2014), 2 vom: 16. Dez., Seite 373-411 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:217 year:2014 number:2 day:16 month:12 pages:373-411 https://doi.org/10.1007/s00205-014-0834-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_65 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4323 GBV_ILN_4700 AR 217 2014 2 16 12 373-411 |
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10.1007/s00205-014-0834-x doi (DE-627)OLC2056424142 (DE-He213)s00205-014-0834-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Fontelos, Marco A. verfasserin aut A Stable Self-Similar Singularity of Evaporating Drops: Ellipsoidal Collapse to a Point 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape. Spherical Harmonic Free Boundary Problem Spherical Coordinate System Spherical Harmonic Expansion Vector Spherical Harmonic Hong, Seok Hyun aut Hwang, Hyung Ju aut Enthalten in Archive for rational mechanics and analysis Springer Berlin Heidelberg, 1957 217(2014), 2 vom: 16. Dez., Seite 373-411 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:217 year:2014 number:2 day:16 month:12 pages:373-411 https://doi.org/10.1007/s00205-014-0834-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_65 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4323 GBV_ILN_4700 AR 217 2014 2 16 12 373-411 |
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10.1007/s00205-014-0834-x doi (DE-627)OLC2056424142 (DE-He213)s00205-014-0834-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Fontelos, Marco A. verfasserin aut A Stable Self-Similar Singularity of Evaporating Drops: Ellipsoidal Collapse to a Point 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape. Spherical Harmonic Free Boundary Problem Spherical Coordinate System Spherical Harmonic Expansion Vector Spherical Harmonic Hong, Seok Hyun aut Hwang, Hyung Ju aut Enthalten in Archive for rational mechanics and analysis Springer Berlin Heidelberg, 1957 217(2014), 2 vom: 16. Dez., Seite 373-411 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:217 year:2014 number:2 day:16 month:12 pages:373-411 https://doi.org/10.1007/s00205-014-0834-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_65 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4323 GBV_ILN_4700 AR 217 2014 2 16 12 373-411 |
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10.1007/s00205-014-0834-x doi (DE-627)OLC2056424142 (DE-He213)s00205-014-0834-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Fontelos, Marco A. verfasserin aut A Stable Self-Similar Singularity of Evaporating Drops: Ellipsoidal Collapse to a Point 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape. Spherical Harmonic Free Boundary Problem Spherical Coordinate System Spherical Harmonic Expansion Vector Spherical Harmonic Hong, Seok Hyun aut Hwang, Hyung Ju aut Enthalten in Archive for rational mechanics and analysis Springer Berlin Heidelberg, 1957 217(2014), 2 vom: 16. Dez., Seite 373-411 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:217 year:2014 number:2 day:16 month:12 pages:373-411 https://doi.org/10.1007/s00205-014-0834-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_65 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4323 GBV_ILN_4700 AR 217 2014 2 16 12 373-411 |
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Fontelos, Marco A. Hong, Seok Hyun Hwang, Hyung Ju |
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a stable self-similar singularity of evaporating drops: ellipsoidal collapse to a point |
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A Stable Self-Similar Singularity of Evaporating Drops: Ellipsoidal Collapse to a Point |
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Abstract We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape. © Springer-Verlag Berlin Heidelberg 2014 |
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Abstract We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape. © Springer-Verlag Berlin Heidelberg 2014 |
| abstract_unstemmed |
Abstract We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape. © Springer-Verlag Berlin Heidelberg 2014 |
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A Stable Self-Similar Singularity of Evaporating Drops: Ellipsoidal Collapse to a Point |
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