메뉴 건너뛰기




Volumn 240, Issue 7, 2011, Pages 675-693

Curvature driven flow of bi-layer interfaces

Author keywords

CanhamHelfrich energy; Functionalized Cahn Hilliard energy; Geometric evolution; Network formation

Indexed keywords

PHASE INTERFACES;

EID: 79951508407     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2010.11.016     Document Type: Article
Times cited : (59)

References (37)
  • 1
    • 6344246453 scopus 로고    scopus 로고
    • Fibriallar structure of Nafion: Matching Fourier and real space studies of corresponding films and solutions
    • L. Rubatat, G. Gebel, O. Diat, Fibriallar structure of Nafion: matching Fourier and real space studies of corresponding films and solutions, Macromolecules, 2004, 77727783.
    • (2004) Macromolecules , pp. 7772-7783
    • Rubatat, L.1    Gebel, G.2    Diat, O.3
  • 2
    • 68249140118 scopus 로고    scopus 로고
    • PEM fuel cells: A mathematical overview
    • K. Promislow, and B. Wetton PEM fuel cells: a mathematical overview SIAM J. Math. Anal. 70 2009 369 409
    • (2009) SIAM J. Math. Anal. , vol.70 , pp. 369-409
    • Promislow, K.1    Wetton, B.2
  • 4
    • 70350484189 scopus 로고    scopus 로고
    • "Plastic" solar cells: Self-assembly of bulk heterojunction nanomaterials by spontaneous phase separation
    • J. Peet, A. Heeger, and G. Bazan "Plastic" solar cells: self-assembly of bulk heterojunction nanomaterials by spontaneous phase separation Acc. Chem. Res. 42 2009 1700 1708
    • (2009) Acc. Chem. Res. , vol.42 , pp. 1700-1708
    • Peet, J.1    Heeger, A.2    Bazan, G.3
  • 6
    • 0014709498 scopus 로고
    • Minimum energy of bending as a possible explanation of biconcave shape of human red blood cell
    • P. Canham Minimum energy of bending as a possible explanation of biconcave shape of human red blood cell J. Theoret. Biol. 26 1970 61 81
    • (1970) J. Theoret. Biol. , vol.26 , pp. 61-81
    • Canham, P.1
  • 7
    • 84943997802 scopus 로고
    • Elastic properties of lipid bilayerstheory and possible experiments
    • W. Helfrich Elastic properties of lipid bilayerstheory and possible experiments Z. Nat.forsch. C 28 1973 693 703
    • (1973) Z. Nat.forsch. C , vol.28 , pp. 693-703
    • Helfrich, W.1
  • 8
    • 0036627609 scopus 로고    scopus 로고
    • Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: Interface-controlled evolution, phase transitions, epitaxial growth of elastic films
    • DOI 10.1007/s002050200193
    • M. Gurtin, and M. Jabbour Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: interface-controlled evolution, phase transitions, epitaxial growth of elastic films Arch. Ration. Mech. Anal. 163 2002 171 208 (Pubitemid 36185866)
    • (2002) Archive for Rational Mechanics and Analysis , vol.163 , Issue.3 , pp. 171-208
    • Gurtin, M.E.1    Jabbour, M.E.2
  • 9
    • 0036822243 scopus 로고    scopus 로고
    • The geometry of soft materials: A primer
    • DOI 10.1103/RevModPhys.74.953
    • Randall Kamien The geometry of soft materials: a primer Rev. Modern Phys. 74 2002 953 971 (Pubitemid 36116694)
    • (2002) Reviews of Modern Physics , vol.74 , Issue.4 , pp. 953-971
    • Kamien, R.D.1
  • 10
    • 0035615741 scopus 로고    scopus 로고
    • An Eulerian description of fluids containing visco-elastic particles
    • Chun Liu, and Noel Walkington An Eulerian description of fluids containing visco-elastic particles Arch. Ration. Mech. Anal. 159 2001 229 252
    • (2001) Arch. Ration. Mech. Anal. , vol.159 , pp. 229-252
    • Liu, C.1    Walkington, N.2
  • 11
    • 29144520935 scopus 로고    scopus 로고
    • Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
    • DOI 10.1016/j.jcp.2005.07.020, PII S0021999105003566
    • Qiang Du, Chun Liu, and Xiaoqiang Wang Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions J. Comput. Phys. 212 2006 757 777 (Pubitemid 41799946)
    • (2006) Journal of Computational Physics , vol.212 , Issue.2 , pp. 757-777
    • Du, Q.1    Liu, C.2    Wang, X.3
  • 12
    • 33746012315 scopus 로고
    • Free energy of a nonuniform system. I. Interfacial energy
    • J.W. Cahn, and J.E. Hilliard Free energy of a nonuniform system. I. Interfacial energy J. Chem. Phys. 28 1958 258 267
    • (1958) J. Chem. Phys. , vol.28 , pp. 258-267
    • Cahn, J.W.1    Hilliard, J.E.2
  • 13
    • 0001410452 scopus 로고
    • Front migration in the nonlinear Cahn-Hilliard equation
    • R.L. Pego Front migration in the nonlinear Cahn-Hilliard equation Proc. R. Soc. Lond. Ser. A 422 1989 261 278
    • (1989) Proc. R. Soc. Lond. Ser. A , vol.422 , pp. 261-278
    • Pego, R.L.1
  • 14
    • 21844492512 scopus 로고
    • Convergence of the Cahn-Hilliard equation to the HeleShaw model
    • N. Alikakos, P. Bates, and X. Chen Convergence of the Cahn-Hilliard equation to the HeleShaw model Arch. Ration. Mech. Anal. 128 1994 165 205
    • (1994) Arch. Ration. Mech. Anal. , vol.128 , pp. 165-205
    • Alikakos, N.1    Bates, P.2    Chen, X.3
  • 15
    • 0000161576 scopus 로고
    • Geometrical evolution of developed interfaces
    • P. de Mottoni, and M. Schatzman Geometrical evolution of developed interfaces Trans. Amer. Math. Soc. 347 1995 1533 1589
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 1533-1589
    • De Mottoni, P.1    Schatzman, M.2
  • 16
    • 34250109116 scopus 로고
    • The gradient theory of phase transitions and the minimal interface criterion
    • L. Modica The gradient theory of phase transitions and the minimal interface criterion Arch. Ration. Mech. Anal. 98 1987 123 142
    • (1987) Arch. Ration. Mech. Anal. , vol.98 , pp. 123-142
    • Modica, L.1
  • 17
    • 34250095380 scopus 로고
    • The effect of a singular perturbation on nonconvex variational problems
    • P. Sternberg The effect of a singular perturbation on nonconvex variational problems Arch. Ration. Mech. Anal. 101 1988 209 260
    • (1988) Arch. Ration. Mech. Anal. , vol.101 , pp. 209-260
    • Sternberg, P.1
  • 18
    • 0020124370 scopus 로고
    • Ion transport and clustering in Nafion perfluorinated membranes
    • William Hsu, and Timothy Gierke Ion transport and clustering in Nafion perfluorinated membranes J. Membr. Sci. 13 1983 307 326
    • (1983) J. Membr. Sci. , vol.13 , pp. 307-326
    • Hsu, W.1    Gierke, T.2
  • 19
    • 33746622999 scopus 로고    scopus 로고
    • Undulated cylinders of charged diblock copolymers
    • DOI 10.1140/epje/i2006-10025-1
    • G.M. Grason, and C.D. Santangelo Undulated cylinders of charged diblock copolymers Eur. Phys. J. E 20 2006 335 346 (Pubitemid 44157699)
    • (2006) European Physical Journal E , vol.20 , Issue.3 , pp. 335-346
    • Grason, G.M.1    Santangelo, C.D.2
  • 20
    • 66549093474 scopus 로고    scopus 로고
    • Effect of molecular weight on hydrated morphologies of the short-side-chain perfluorosulfonic acid membrane
    • Dongsheng Wu, Stephen Paddison, and James Elliott Effect of molecular weight on hydrated morphologies of the short-side-chain perfluorosulfonic acid membrane Macromolecules 42 2009 3358 3367
    • (2009) Macromolecules , vol.42 , pp. 3358-3367
    • Wu, D.1    Paddison, S.2    Elliott, J.3
  • 21
    • 7544235790 scopus 로고    scopus 로고
    • Transport in proton conductors for fuel-cell applications: Simulations, elementary reactions, and phenomenology
    • Klaus-Dieter Kreuer, Stephen J. Paddison, Eckhard Spohr, and Micheal Schuster Transport in proton conductors for fuel-cell applications: simulations, elementary reactions, and phenomenology Chem. Rev. 104 2004 4637 4678
    • (2004) Chem. Rev. , vol.104 , pp. 4637-4678
    • Kreuer, K.-D.1    Paddison, S.J.2    Spohr, E.3    Schuster, M.4
  • 22
    • 37649025930 scopus 로고    scopus 로고
    • Parallel cylindrical water nanochannels in Nafion fuel cell membranes
    • K. Schmidt-Rohr, and Q. Chen Parallel cylindrical water nanochannels in Nafion fuel cell membranes Nat. Mater. 7 2008 75 83
    • (2008) Nat. Mater. , vol.7 , pp. 75-83
    • Schmidt-Rohr, K.1    Chen, Q.2
  • 24
    • 75749155894 scopus 로고    scopus 로고
    • Path-dependent morphologies in oil/water/diblock copolymer mixtures
    • Sangwoo Lee, Manickam A. Arunagirinathan, and Frank S. Bates Path-dependent morphologies in oil/water/diblock copolymer mixtures Langmuir 26 2010 1707 1715
    • (2010) Langmuir , vol.26 , pp. 1707-1715
    • Lee, S.1    Arunagirinathan, M.A.2    Bates, F.S.3
  • 26
    • 6944232936 scopus 로고
    • Correlation between structural and interfacial properties of amphillic systems
    • G. Gompper, and M. Schick Correlation between structural and interfacial properties of amphillic systems Phys. Rev. Lett. 65 1990 1116 1119
    • (1990) Phys. Rev. Lett. , vol.65 , pp. 1116-1119
    • Gompper, G.1    Schick, M.2
  • 27
    • 33749607402 scopus 로고    scopus 로고
    • On a modified conjecture of de Giorgi
    • Matthias Rger, and Reiner Schtzle On a modified conjecture of De Giorgi Math. Z. 254 2006 675 714
    • (2006) Math. Z. , vol.254 , pp. 675-714
    • Rger, M.1    Schtzle, R.2
  • 28
    • 77958411749 scopus 로고
    • Nonlocal reactiondiffusion equations and nucleation
    • J. Rubinstein, and P. Sternberg Nonlocal reactiondiffusion equations and nucleation IMA J. Appl. Math. 48 1992 249 264
    • (1992) IMA J. Appl. Math. , vol.48 , pp. 249-264
    • Rubinstein, J.1    Sternberg, P.2
  • 29
    • 0000073994 scopus 로고    scopus 로고
    • Exponentially small splitting of heteroclinic orbits: From the rapidly forced pendulum to discrete solitons
    • P.G. Kevrekidis, C.K.R.T. Jones, and T. Kapitula Exponentially small splitting of heteroclinic orbits: from the rapidly forced pendulum to discrete solitons Phys. Lett. A 269 2000 1357 1377
    • (2000) Phys. Lett. A , vol.269 , pp. 1357-1377
    • Kevrekidis, P.G.1    Jones, C.K.R.T.2    Kapitula, T.3
  • 30
    • 0034258264 scopus 로고    scopus 로고
    • Gluing unstable fronts and backs together can produce stable pulses
    • Bjorn Sandstede, and Arnd Scheel Gluing unstable fronts and backs together can produce stable pulses Nonlinearity 13 2000 233 277
    • (2000) Nonlinearity , vol.13 , pp. 233-277
    • Sandstede, B.1    Scheel, A.2
  • 31
    • 1642310541 scopus 로고    scopus 로고
    • Consequences of nonergodicity in aqueous binary PEO-PB micellar dispersions
    • Sumeet Jain, and Frank Bates Consequences of nonergodicity in aqueous binary PEO-PB micellar dispersions Macromolecules 37 2004 1511 1523
    • (2004) Macromolecules , vol.37 , pp. 1511-1523
    • Jain, S.1    Bates, F.2
  • 32
    • 0037453427 scopus 로고    scopus 로고
    • On the origins of morphological complexity in block copolymer surfactants
    • DOI 10.1126/science.1082193
    • Sumeet Jain, and Frank Bates On the origins of morphological complexity in block copolymer surfactants Science 300 2003 460 464 (Pubitemid 36444321)
    • (2003) Science , vol.300 , Issue.5618 , pp. 460-464
    • Jain, S.1    Bates, F.S.2
  • 33
    • 0542363944 scopus 로고
    • Spectrum for the AllenCahn, Cahn-Hilliard, and phase-field equations for generic interfaces
    • Xinfu Chen Spectrum for the AllenCahn, Cahn-Hilliard, and phase-field equations for generic interfaces Comm. Partial Differential Equations 19 1994 1371 1395
    • (1994) Comm. Partial Differential Equations , vol.19 , pp. 1371-1395
    • Chen, X.1
  • 34
    • 79951516208 scopus 로고    scopus 로고
    • Stability indices for constrained self-adjoint operators
    • (in press)
    • Todd Kapitula, Keith Promislow, Stability indices for constrained self-adjoint operators, Proc. Amer. Math. Soc. (in press).
    • Proc. Amer. Math. Soc.
    • Kapitula, T.1    Promislow, K.2
  • 36
    • 0036435355 scopus 로고    scopus 로고
    • A renormalization method for modulational stability of quasi-steady patterns in dispersive systems
    • K. Promislow A renormalization method for modulational stability of quasi-steady patterns in dispersive systems SIAM J. Math. Anal. 33 6 2002 1455 1482
    • (2002) SIAM J. Math. Anal. , vol.33 , Issue.6 , pp. 1455-1482
    • Promislow, K.1
  • 37
    • 19944370883 scopus 로고    scopus 로고
    • Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators
    • DOI 10.1016/j.physd.2005.04.015, PII S0167278905001594
    • R. Moore, and K. Promislow Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators Physica D 206 2005 62 81 (Pubitemid 40753411)
    • (2005) Physica D: Nonlinear Phenomena , vol.206 , Issue.1-2 , pp. 62-81
    • Moore, R.O.1    Promislow, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.