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Volumn 93, Issue 3-4, 1998, Pages 725-776

Axisymmetric surface diffusion: Dynamics and stability of self-similar pinchoff

Author keywords

Linear stability; Pinchoff; Similarity solution; Surface diffusion

Indexed keywords


EID: 0039992070     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000033251.81126.af     Document Type: Article
Times cited : (127)

References (68)
  • 1
    • 0000147123 scopus 로고
    • Mean curvature flow through singularities for surfaces of rotation
    • Steven Altschuler, Sigurd B. Angenent, and Yoshikazu Giga, Mean curvature flow through singularities for surfaces of rotation, J. Geom. Anal. 5(3):293-358 (1995).
    • (1995) J. Geom. Anal. , vol.5 , Issue.3 , pp. 293-358
    • Altschuler, S.1    Angenent, S.B.2    Giga, Y.3
  • 2
    • 0029674544 scopus 로고    scopus 로고
    • Stable and unstable singularities in the unforced Hele-Shaw cell
    • Robert Almgren, Andrea L. Bertozzi, and Michael P. Brenner, Stable and unstable singularities in the unforced Hele-Shaw cell, Phys. Fl. 8(6):1356-1370 (1996).
    • (1996) Phys. Fl. , vol.8 , Issue.6 , pp. 1356-1370
    • Almgren, R.1    Bertozzi, A.L.2    Brenner, M.P.3
  • 6
    • 0040573839 scopus 로고
    • Singularities in a modified Kuramoto Sivashinsky equation describing interface motion for phase transition
    • A. J. Bernoff and A. L. Bertozzi, Singularities in a modified Kuramoto Sivashinsky equation describing interface motion for phase transition, Physica D 85(3):375-404 (1995).
    • (1995) Physica D , vol.85 , Issue.3 , pp. 375-404
    • Bernoff, A.J.1    Bertozzi, A.L.2
  • 7
    • 0002854269 scopus 로고
    • Singularities and similarities in interface flow
    • Applied Mathematical Sciences, L. Sirovich, ed. Springer-Verlag, New York
    • Andrea L. Bertozzi, Michael P. Brenner, Todd F. Dupont, and Leo P. Kadanoff, Singularities and similarities in interface flow, in Trends and Perspectives in Applied Mathematics, Vol. 100, Applied Mathematical Sciences, L. Sirovich, ed. (Springer-Verlag, New York, 1994), pp. 155-208.
    • (1994) Trends and Perspectives in Applied Mathematics , vol.100 , pp. 155-208
    • Bertozzi, A.L.1    Brenner, M.P.2    Dupont, T.F.3    Kadanoff, L.P.4
  • 9
    • 0040250418 scopus 로고
    • Loss and gain of regularity in a lubrication equation for thin viscous films
    • Pitman Research Notes in Mathematics Series, J. I. Diaz, M. A. Herrero, A. Linan, and J. L. Vazquez, eds. Longman House, Proceedings of the International Colloquium on Free Boundary Problems, Toledo, Spain, June 1993
    • A. L. Bertozzi, Loss and gain of regularity in a lubrication equation for thin viscous films, in Free Boundary Problems. Theory and Applications, Vol. 323, Pitman Research Notes in Mathematics Series, J. I. Diaz, M. A. Herrero, A. Linan, and J. L. Vazquez, eds. (Longman House, 1995), pp. 72-85. Proceedings of the International Colloquium on Free Boundary Problems, Toledo, Spain, June 1993.
    • (1995) Free Boundary Problems. Theory and Applications , vol.323 , pp. 72-85
    • Bertozzi, A.L.1
  • 10
    • 0030169093 scopus 로고    scopus 로고
    • Symmetric singularity formation in lubrication-type equations for interface motion
    • Andrea L. Bertozzi, Symmetric singularity formation in lubrication-type equations for interface motion, SIAM J. Applied Math. 56(3):681-714 (1996).
    • (1996) SIAM J. Applied Math. , vol.56 , Issue.3 , pp. 681-714
    • Bertozzi, A.L.1
  • 11
    • 0001195672 scopus 로고    scopus 로고
    • Breaking threads, similarity solutions and the number 0.0304
    • M. P. Brenner, J. R. Lister, and H. A. Stone, Breaking threads, similarity solutions and the number 0.0304, Phys. Fluids 8:2827-2836 (1996).
    • (1996) Phys. Fluids , vol.8 , pp. 2827-2836
    • Brenner, M.P.1    Lister, J.R.2    Stone, H.A.3
  • 13
    • 0032368532 scopus 로고    scopus 로고
    • Long-wave instabilities and saturation in thin film equations
    • A. L. Bertozzi and M. C. Pugh, Long-wave instabilities and saturation in thin film equations, Comm. Pure Appl. Math. LI:625-661 (1998).
    • (1998) Comm. Pure Appl. Math. , vol.LI , pp. 625-661
    • Bertozzi, A.L.1    Pugh, M.C.2
  • 14
    • 0040844889 scopus 로고
    • The use of Delaunay curves for the wetting of axisymmetric bodies
    • P. Basa, J. C. Schon, and P. Salamon, The use of Delaunay curves for the wetting of axisymmetric bodies, Quarterly Appl. Math. 52(1):1-22 (1994).
    • (1994) Quarterly Appl. Math. , vol.52 , Issue.1 , pp. 1-22
    • Basa, P.1    Schon, J.C.2    Salamon, P.3
  • 15
    • 0028741491 scopus 로고
    • An integrable fourth-order nonlinear evolution equation applied to thermal grooving of metal surfaces
    • P. Broadbridge and P. Tritscher, An integrable fourth-order nonlinear evolution equation applied to thermal grooving of metal surfaces, IMA J. Appl. Math. 53(3):249-265 (1994).
    • (1994) IMA J. Appl. Math. , vol.53 , Issue.3 , pp. 249-265
    • Broadbridge, P.1    Tritscher, P.2
  • 16
    • 0004139504 scopus 로고
    • Addison-Wesley Pub. Co., Reading, MA
    • Eugene Butkov, Mathematical Physics (Addison-Wesley Pub. Co., Reading, MA, 1968).
    • (1968) Mathematical Physics
    • Butkov, E.1
  • 18
    • 0030488511 scopus 로고    scopus 로고
    • The Cahn-Hilliard equation with a concentration dependent mobility: Motion by minus the Laplacian of the mean curvature
    • J. W. Cahn, C. M. Elliott, and A. Novick-Cohen, The Cahn-Hilliard equation with a concentration dependent mobility: Motion by minus the Laplacian of the mean curvature, European J. Appl. Math. 7(3):287-301 (1996).
    • (1996) European J. Appl. Math. , vol.7 , Issue.3 , pp. 287-301
    • Cahn, J.W.1    Elliott, C.M.2    Novick-Cohen, A.3
  • 19
    • 0000695499 scopus 로고
    • Stability of cylindrical bodies in the theory of surface diffusion
    • B. D. Coleman, R. S. Falk, and M. Moakher, Stability of cylindrical bodies in the theory of surface diffusion, Physica D 89(1-2):123-135 (1995).
    • (1995) Physica D , vol.89 , Issue.1-2 , pp. 123-135
    • Coleman, B.D.1    Falk, R.S.2    Moakher, M.3
  • 20
    • 0000522499 scopus 로고    scopus 로고
    • Space-time finite element methods for surface diffusion with application to the theory of the stability of cylinders
    • B. D. Coleman, R. S. Falk, and M. Moakher, Space-time finite element methods for surface diffusion with application to the theory of the stability of cylinders, SIAM J. Sci. Comput. 17(6):1434-1448 (1996).
    • (1996) SIAM J. Sci. Comput. , vol.17 , Issue.6 , pp. 1434-1448
    • Coleman, B.D.1    Falk, R.S.2    Moakher, M.3
  • 21
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • Yun Gang Chen, Yoshikazu Giga, and Shun'ichi Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom. 33(3):749-786 (1991).
    • (1991) J. Differential Geom. , vol.33 , Issue.3 , pp. 749-786
    • Chen, Y.G.1    Giga, Y.2    Goto, S.3
  • 22
    • 12044252828 scopus 로고
    • Pattern formation outside of equilibrium
    • M. C. Cross and P. C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65(3):854-1112 (1993).
    • (1993) Rev. Mod. Phys. , vol.65 , Issue.3 , pp. 854-1112
    • Cross, M.C.1    Hohenberg, P.C.2
  • 23
    • 0031171948 scopus 로고    scopus 로고
    • Dynamics of inviscid capillary breakup: Collapse and pinchoff of a film bridge
    • Y.-J. Chen and P. H. Steen, Dynamics of inviscid capillary breakup: Collapse and pinchoff of a film bridge, J. Fluid Mechanics 341:245-267 (1997).
    • (1997) J. Fluid Mechanics , vol.341 , pp. 245-267
    • Chen, Y.-J.1    Steen, P.H.2
  • 24
    • 0028409294 scopus 로고
    • Surface motion by surface diffusion
    • J. W. Cahn and J. E. Taylor, Surface motion by surface diffusion, Acta Metall. Mater. 42(4):1045-1063 (1994).
    • (1994) Acta Metall. Mater. , vol.42 , Issue.4 , pp. 1045-1063
    • Cahn, J.W.1    Taylor, J.E.2
  • 25
    • 0001510439 scopus 로고
    • Sur la surface de revolution dont la courbure moyenne est constante
    • C. E. Delaunay, Sur la surface de revolution dont la courbure moyenne est constante, J. Math. Pures Appl. 6:309-320 (1841).
    • (1841) J. Math. Pures Appl. , vol.6 , pp. 309-320
    • Delaunay, C.E.1
  • 26
    • 0001007002 scopus 로고
    • Finitetime singularity formation in Hele-Shaw systems
    • Todd F. Dupont, Raymond E Goldstein, Leo P. Kadanoff, and Su-Min Zhou, Finitetime singularity formation in Hele-Shaw systems, Phys. Rev. E 47(6): 4182-4196 (1993).
    • (1993) Phys. Rev. E , vol.47 , Issue.6 , pp. 4182-4196
    • Dupont, T.F.1    Goldstein, R.E.2    Kadanoff, L.P.3    Zhou, S.-M.4
  • 27
    • 0025448930 scopus 로고
    • Evolution of geometric statistics
    • Donald A. Drew. Evolution of geometric statistics, SIAM J. Appl. Math. 50(3):649-666 (1990).
    • (1990) SIAM J. Appl. Math. , vol.50 , Issue.3 , pp. 649-666
    • Drew, D.A.1
  • 28
    • 0030526461 scopus 로고    scopus 로고
    • On the Cahn-Hilliard equation with degenerate mobility
    • Charles M. Elliott and Harald Garcke, On the Cahn-Hilliard equation with degenerate mobility, SIAM J. Math. Anal. 27(2):404-423 (1996).
    • (1996) SIAM J. Math. Anal. , vol.27 , Issue.2 , pp. 404-423
    • Elliott, C.M.1    Garcke, H.2
  • 29
    • 0001238859 scopus 로고    scopus 로고
    • Existence results for diffusive surface motion laws
    • Charles M. Elliott and Harald Gareke. Existence results for diffusive surface motion laws, Adv. Math. Sci. Appl. 7(1):467-490 (1997).
    • (1997) Adv. Math. Sci. Appl. , vol.7 , Issue.1 , pp. 467-490
    • Elliott, C.M.1    Gareke, H.2
  • 30
    • 12044255149 scopus 로고
    • Universal pinching of 3D axisymmetric free surface flow
    • Jens Eggers, Universal pinching of 3D axisymmetric free surface flow, Phys. Rev. Lett. 71:3458 (1993).
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 3458
    • Eggers, J.1
  • 31
    • 0001641702 scopus 로고    scopus 로고
    • Coalescence of spheres by surface diffusion
    • Jens Eggers, Coalescence of spheres by surface diffusion, Phys. Rev. Lett. 80(12):2634-2637 (1998).
    • (1998) Phys. Rev. Lett. , vol.80 , Issue.12 , pp. 2634-2637
    • Eggers, J.1
  • 33
    • 0032379074 scopus 로고    scopus 로고
    • The surface diffusion flow for immersed hypersurfaces
    • Joachim Escher, Uwe F. Mayer, and Gieri Simonett, The surface diffusion flow for immersed hypersurfaces (1998). To appear in SIAM J Math. Anal.
    • (1998) SIAM J Math. Anal.
    • Escher, J.1    Mayer, U.F.2    Simonett, G.3
  • 34
    • 84972518016 scopus 로고
    • Motion of level sets by mean curvature. I
    • L. C. Evans and J. Spruck, Motion of level sets by mean curvature. I, J. Differential Geom. 33(3):635-681 (1991).
    • (1991) J. Differential Geom. , vol.33 , Issue.3 , pp. 635-681
    • Evans, L.C.1    Spruck, J.2
  • 37
    • 0002756704 scopus 로고
    • On the volume infimum for liquid bridges
    • R. Finn and T. I. Vogel, On the volume infimum for liquid bridges, Z. Anal. Anwendungen 11(1):3-23 (1992).
    • (1992) Z. Anal. Anwendungen , vol.11 , Issue.1 , pp. 3-23
    • Finn, R.1    Vogel, T.I.2
  • 38
    • 0031537321 scopus 로고    scopus 로고
    • Gyroids of constant mean curvature
    • Karsten Grosse-Brauckmann, Gyroids of constant mean curvature, Experimental Mathematics 6(1):33-50 (1997).
    • (1997) Experimental Mathematics , vol.6 , Issue.1 , pp. 33-50
    • Grosse-Brauckmann, K.1
  • 39
    • 0000332576 scopus 로고
    • Characterizing blowup using similarity variables
    • Yoshikazu Giga and Robert V. Kohn, Characterizing blowup using similarity variables, Indiana Univ. Math. J. 36(1):1-40 (1987).
    • (1987) Indiana Univ. Math. J. , vol.36 , Issue.1 , pp. 1-40
    • Giga, Y.1    Kohn, R.V.2
  • 40
    • 0000489919 scopus 로고
    • Topology transitions and singularities in viscous flows
    • Raymond E. Goldstein, Adriana I. Pesci, and Michael J. Shelley, Topology transitions and singularities in viscous flows, Phys. Rev. Lett. 70(20):3043-3046 (1993).
    • (1993) Phys. Rev. Lett. , vol.70 , Issue.20 , pp. 3043-3046
    • Goldstein, R.E.1    Pesci, A.I.2    Shelley, M.J.3
  • 42
    • 0002431632 scopus 로고
    • Surface diffusion as a motivation for sintering
    • Chapter 8, W. E. Kingston, ed. McGraw-Hill
    • C. Herring, Surface diffusion as a motivation for sintering, in The Physics of Powder Metallurgy, Chapter 8, W. E. Kingston, ed. (McGraw-Hill, 1951), pp. 143-179.
    • (1951) The Physics of Powder Metallurgy , pp. 143-179
    • Herring, C.1
  • 44
    • 84972527004 scopus 로고
    • Asymptotic behavior for singularities of the mean curvature flow
    • Gerhard Huisken, Asymptotic behavior for singularities of the mean curvature flow, J. Differential Geom. 31(1):285-299 (1990).
    • (1990) J. Differential Geom. , vol.31 , Issue.1 , pp. 285-299
    • Huisken, G.1
  • 45
    • 0009181042 scopus 로고    scopus 로고
    • Singularities and blowups
    • September
    • Leo P. Kadanoff, Singularities and blowups, Physics Today, p. 11, September 1997.
    • (1997) Physics Today , pp. 11
    • Kadanoff, L.P.1
  • 46
    • 0024716995 scopus 로고
    • Two-dimensional finite difference analysis of shape instabilities in plates
    • [ LC89] J. K. Lee and T. H. Courtney, Two-dimensional finite difference analysis of shape instabilities in plates, Metall. Trans. A 20:1385-1394 (1989).
    • (1989) Metall. Trans. A , vol.20 , pp. 1385-1394
    • Lee, J.K.1    Courtney, T.H.2
  • 48
    • 0040250416 scopus 로고
    • A model for capillary induced instabilities in directionally solidified eutectic alloys
    • J. L. Walter et al., ed. Ginn Custom Publishing, Lexington, MA
    • T. F. Marinas and R. F. Sekerka, A model for capillary induced instabilities in directionally solidified eutectic alloys, in Conference on In Situ Composites-III, J. L. Walter et al., ed. (Ginn Custom Publishing, Lexington, MA, 1979), pp. 86-96.
    • (1979) Conference on In Situ Composites-III , pp. 86-96
    • Marinas, T.F.1    Sekerka, R.F.2
  • 49
    • 21544450961 scopus 로고
    • Theory of thermal grooving
    • W. W. Mullins, Theory of thermal grooving, J. Appl. Phys. 28(3):333-339 (1957).
    • (1957) J. Appl. Phys. , vol.28 , Issue.3 , pp. 333-339
    • Mullins, W.W.1
  • 50
    • 21544475638 scopus 로고
    • Flattening of a nearly plane solid surface due to capillarity
    • W. Mullins, Flattening of a nearly plane solid surface due to capillarity, J. Appl. Phys. 30(1):77-83 (1959).
    • (1959) J. Appl. Phys. , vol.30 , Issue.1 , pp. 77-83
    • Mullins, W.1
  • 51
    • 0029360183 scopus 로고
    • Mass transport at interfaces in single component systems
    • W. W. Mullins, Mass transport at interfaces in single component systems, Metall. Trans. A 26:1917-1929 (1995).
    • (1995) Metall. Trans. A , vol.26 , pp. 1917-1929
    • Mullins, W.W.1
  • 53
    • 36849118851 scopus 로고
    • Morphological changes of a surface of revolution due to capillarity-induced surface diffusion
    • F. A. Nichols and W. W. Mullins, Morphological changes of a surface of revolution due to capillarity-induced surface diffusion, J. Appl. Phys. 36(6): 1826-1835 (1965).
    • (1965) J. Appl. Phys. , vol.36 , Issue.6 , pp. 1826-1835
    • Nichols, F.A.1    Mullins, W.W.2
  • 54
    • 0000955407 scopus 로고
    • Surface- (interface-) and volume-diffusion contributions to morphological changes driven by capillarity
    • F. A. Nichols and W. W. Mullins, Surface- (interface-) and volume-diffusion contributions to morphological changes driven by capillarity, Trans. Metall. Soc. AIME 233:1840-1847 (1965).
    • (1965) Trans. Metall. Soc. AIME , vol.233 , pp. 1840-1847
    • Nichols, F.A.1    Mullins, W.W.2
  • 56
    • 0000999835 scopus 로고
    • An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt
    • David C. Sarocka and Andrew J. Bernoff, An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt, Physica D 85(3): 348-374 (1995).
    • (1995) Physica D , vol.85 , Issue.3 , pp. 348-374
    • Sarocka, D.C.1    Bernoff, A.J.2
  • 58
    • 0001283493 scopus 로고
    • Singularities and uniqueness of cylindrically symmetric surfaces moving by mean curvature
    • H. M. Soner and P. E. Souganidis, Singularities and uniqueness of cylindrically symmetric surfaces moving by mean curvature, Comm. Partial Differential Equations 18(5-6):859-894 (1993).
    • (1993) Comm. Partial Differential Equations , vol.18 , Issue.5-6 , pp. 859-894
    • Soner, H.M.1    Souganidis, P.E.2
  • 59
    • 21844495223 scopus 로고
    • Linking anisotropic sharp and diffuse surface motion laws via gradient flows
    • J. E. Taylor and J. W. Cahn, Linking anisotropic sharp and diffuse surface motion laws via gradient flows, J. Stat. Phys. 77(1-2):183-197 (1994).
    • (1994) J. Stat. Phys. , vol.77 , Issue.1-2 , pp. 183-197
    • Taylor, J.E.1    Cahn, J.W.2
  • 60
    • 0023366145 scopus 로고
    • Stability of a liquid drop trapped between two parallel planes
    • Thomas I. Vogel, Stability of a liquid drop trapped between two parallel planes, SIAM J. Appl. Math. 47(3):516-525 (1987).
    • (1987) SIAM J. Appl. Math. , vol.47 , Issue.3 , pp. 516-525
    • Vogel, T.I.1
  • 61
    • 0000611933 scopus 로고
    • Stability of a liquid drop trapped between two parallel planes, II. General contact angles
    • Thomas I. Vogel, Stability of a liquid drop trapped between two parallel planes, II. General contact angles, SIAM J. Appl. Math. 49(4):1009-1028 (1989).
    • (1989) SIAM J. Appl. Math. , vol.49 , Issue.4 , pp. 1009-1028
    • Vogel, T.I.1
  • 62
    • 0003577381 scopus 로고
    • Graduate Tezts in Mathematics Springer-Verlag, New York/Berlin, Corrected reprint of the 1971 edition
    • Frank W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Vol. 94, Graduate Tezts in Mathematics (Springer-Verlag, New York/Berlin, 1983). Corrected reprint of the 1971 edition.
    • (1983) Foundations of Differentiable Manifolds and Lie Groups , vol.94
    • Warner, F.W.1
  • 63
    • 0031282918 scopus 로고    scopus 로고
    • Invariant manifolds for parabolic partial differential equations on unbounded domains
    • C. Eugene Wayne, Invariant manifolds for parabolic partial differential equations on unbounded domains, Arch. Rational Mach. Anal. 138(3):279-306 (1997).
    • (1997) Arch. Rational Mach. Anal. , vol.138 , Issue.3 , pp. 279-306
    • Wayne, C.E.1
  • 64
    • 0006144178 scopus 로고    scopus 로고
    • Self-similar asymptotics for linear and nonlinear diffusion equations
    • T. P. Witelski and A. J. Bernoff, Self-similar asymptotics for linear and nonlinear diffusion equations, Studies in Applied Mathematics 100(2):153-193 (1998).
    • (1998) Studies in Applied Mathematics , vol.100 , Issue.2 , pp. 153-193
    • Witelski, T.P.1    Bernoff, A.J.2
  • 65
    • 0031169802 scopus 로고    scopus 로고
    • Capillarity driven motion of solid film wedges
    • H. Wong, M. J. Miksis, and S. H. Davis, Capillarity driven motion of solid film wedges, Acta Mater. 45(6):2477-2484 (1997).
    • (1997) Acta Mater. , vol.45 , Issue.6 , pp. 2477-2484
    • Wong, H.1    Miksis, M.J.2    Davis, S.H.3
  • 66
    • 0032485949 scopus 로고    scopus 로고
    • Universal pinch off of rods by capillarity-driven surface diffusion (1998)
    • H. Wong, M. J. Miksis, P. W. Voorhees, and S. H. Davis, Universal pinch off of rods by capillarity-driven surface diffusion (1998). Scripta Mater. 39(1):55-60 (1998).
    • (1998) Scripta Mater. , vol.39 , Issue.1 , pp. 55-60
    • Wong, H.1    Miksis, M.J.2    Voorhees, P.W.3    Davis, S.H.4
  • 67
    • 0038528137 scopus 로고    scopus 로고
    • Capillary instabilities of a catenoidal hole in a soild film
    • H. Wong, P. W. Voorhees, M. J. Miksis, and S. H. Davis, Capillary instabilities of a catenoidal hole in a soild film, J. Appl. Phys. 81(9):6091-6099 (1997).
    • (1997) J. Appl. Phys. , vol.81 , Issue.9 , pp. 6091-6099
    • Wong, H.1    Voorhees, P.W.2    Miksis, M.J.3    Davis, S.H.4
  • 68
    • 0040593911 scopus 로고
    • On the volume infimum for liquid bridges
    • L. Zhou, On the volume infimum for liquid bridges, Z. Anal. Anwendungen 12(4):629642 (1993).
    • (1993) Z. Anal. Anwendungen , vol.12 , Issue.4 , pp. 629642
    • Zhou, L.1


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