-
Previous Article
Multiplicative ergodic theorem on flag bundles of semi-simple Lie groups
- DCDS Home
- This Issue
- Next Article
Critical points of functionalized Lagrangians
1. | Department of Mathematics, Michigan State University, East Lansing, MI, 48824 |
2. | Nico Holding LLC, 222 W. Adams Street, Chicago, IL, 60606, United States |
References:
[1] |
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial energy,, J. Chem. Phys., 28 (1958), 258. Google Scholar |
[2] |
P. Canham, Minimum energy of bending as a possible explanation of biconcave shape of human red blood cell,, J. Theor. Biol., 26 (1970), 61.
doi: 10.1016/S0022-5193(70)80032-7. |
[3] |
E. Crossland, M. Kamperman, M. Nedelcu, C. Ducati, U. Wiesner, D. Smilgies, G. Toombes, M. Hillmyer, S. Ludwigs, U. Steiner and H. Snaith, A Bicontinuous double gyroid hybrid solar cell,, Nano Letters, 9 (2009), 2807.
doi: 10.1021/nl803174p. |
[4] |
Qiang Du, Chun Liu, Rolf Ryham and Xiaoqiang Wang, A phase field formulation of the Willmore problem,, Nonlinearity, 18 (2005), 1249.
|
[5] |
L. C. Evans, "Partial Differential Equations,", American Mathematical Society, (2000).
|
[6] |
N. Gavish, G. Hayrapetyan, K. Promislow and L. Yang, Curvature driven flow of bi-layer interfaces,, Physica D, 240 (2011), 675.
doi: 10.1016/j.physd.2010.11.016. |
[7] |
G. Gompper and M. Schick, Correlation between structural and interfacial properties of amphillic systems,, Phys. Rev. Lett., 65 (1990), 1116.
doi: 10.1103/PhysRevLett.65.1116. |
[8] |
W. Helfrich, Elastic properties of lipid bilayers - theory and possible experiments,, Zeitshcrift fur naturforschung C, 28 (1973), 693. Google Scholar |
[9] |
William Hsu and Timothy Gierke, Ion transport and clustering in Nafion perfluorinated membranes,, J. Membrane Science, 13 (1983), 307.
doi: 10.1016/S0376-7388(00)81563-X. |
[10] |
Kun-Mu Lee, Chih-Yu Hsu, Wei-Hao Chiu, Meng-Chin Tsui, Yung-Liang Tung, Song-Yeu Tsai and Kuo-Chuan Ho, Dye-sensitized solar cells with mirco-porous TiO$_2$ electrode and gel polymer electrolytes prepared by in situ cross-link reaction,, Solar Energy Materials & Solar cells, 93 (2009), 2003. Google Scholar |
[11] |
Roger Moser, A higher order asymptotic problem related to phase transition,, SIAM Journal Math. Anal., 37 (2005), 712.
doi: 10.1016/j.ijpharm.2004.11.015. |
[12] |
L. Modica, The gradient theory of phase transitions and the minimal interface criterion,, Arch. Rational. Mech. Anal., 98 (1987), 123.
|
[13] |
J. Peet, A. Heeger and G. Bazan, "Plastic'' Solar cells: Self-assembly of bulk hetrojunction nanomaterials by spontaneous phase separation,, Accounts of Chemical Research, 42 (2009), 1700.
doi: 10.1016/j.ssc.2008.12.019. |
[14] |
K. Promislow and B. Wetton, PEM fuel cells: A mathematical overview,, SIAM Math. Analysis, 70 (2009), 369.
|
[15] |
Matthias Röger and Reiner Schätzle, On a modified conjecture of De Giorgi,, Math. Z., 254 (2006), 675.
|
[16] |
L. Rubatat, G. Gebel and O. Diat, Fibriallar structure of Nafion: Matching Fourier and real space studies of corresponding films and solutions,, Macromolecules, 2004 (): 7772. Google Scholar |
[17] |
U. Schwarz and G. Gompper, Bicontinuous surfaces in self-assembled amphiphilic systems,, in, 600 (2002), 107. Google Scholar |
[18] |
P. Sternberg, The effect of a singular perturbation on nonconvex variational problems,, Arch. Rational Mech. Anal., 101 (1988), 209.
|
[19] |
M. Struwe, "Variational Methods,", Springer-Verlag, (1990).
|
show all references
References:
[1] |
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial energy,, J. Chem. Phys., 28 (1958), 258. Google Scholar |
[2] |
P. Canham, Minimum energy of bending as a possible explanation of biconcave shape of human red blood cell,, J. Theor. Biol., 26 (1970), 61.
doi: 10.1016/S0022-5193(70)80032-7. |
[3] |
E. Crossland, M. Kamperman, M. Nedelcu, C. Ducati, U. Wiesner, D. Smilgies, G. Toombes, M. Hillmyer, S. Ludwigs, U. Steiner and H. Snaith, A Bicontinuous double gyroid hybrid solar cell,, Nano Letters, 9 (2009), 2807.
doi: 10.1021/nl803174p. |
[4] |
Qiang Du, Chun Liu, Rolf Ryham and Xiaoqiang Wang, A phase field formulation of the Willmore problem,, Nonlinearity, 18 (2005), 1249.
|
[5] |
L. C. Evans, "Partial Differential Equations,", American Mathematical Society, (2000).
|
[6] |
N. Gavish, G. Hayrapetyan, K. Promislow and L. Yang, Curvature driven flow of bi-layer interfaces,, Physica D, 240 (2011), 675.
doi: 10.1016/j.physd.2010.11.016. |
[7] |
G. Gompper and M. Schick, Correlation between structural and interfacial properties of amphillic systems,, Phys. Rev. Lett., 65 (1990), 1116.
doi: 10.1103/PhysRevLett.65.1116. |
[8] |
W. Helfrich, Elastic properties of lipid bilayers - theory and possible experiments,, Zeitshcrift fur naturforschung C, 28 (1973), 693. Google Scholar |
[9] |
William Hsu and Timothy Gierke, Ion transport and clustering in Nafion perfluorinated membranes,, J. Membrane Science, 13 (1983), 307.
doi: 10.1016/S0376-7388(00)81563-X. |
[10] |
Kun-Mu Lee, Chih-Yu Hsu, Wei-Hao Chiu, Meng-Chin Tsui, Yung-Liang Tung, Song-Yeu Tsai and Kuo-Chuan Ho, Dye-sensitized solar cells with mirco-porous TiO$_2$ electrode and gel polymer electrolytes prepared by in situ cross-link reaction,, Solar Energy Materials & Solar cells, 93 (2009), 2003. Google Scholar |
[11] |
Roger Moser, A higher order asymptotic problem related to phase transition,, SIAM Journal Math. Anal., 37 (2005), 712.
doi: 10.1016/j.ijpharm.2004.11.015. |
[12] |
L. Modica, The gradient theory of phase transitions and the minimal interface criterion,, Arch. Rational. Mech. Anal., 98 (1987), 123.
|
[13] |
J. Peet, A. Heeger and G. Bazan, "Plastic'' Solar cells: Self-assembly of bulk hetrojunction nanomaterials by spontaneous phase separation,, Accounts of Chemical Research, 42 (2009), 1700.
doi: 10.1016/j.ssc.2008.12.019. |
[14] |
K. Promislow and B. Wetton, PEM fuel cells: A mathematical overview,, SIAM Math. Analysis, 70 (2009), 369.
|
[15] |
Matthias Röger and Reiner Schätzle, On a modified conjecture of De Giorgi,, Math. Z., 254 (2006), 675.
|
[16] |
L. Rubatat, G. Gebel and O. Diat, Fibriallar structure of Nafion: Matching Fourier and real space studies of corresponding films and solutions,, Macromolecules, 2004 (): 7772. Google Scholar |
[17] |
U. Schwarz and G. Gompper, Bicontinuous surfaces in self-assembled amphiphilic systems,, in, 600 (2002), 107. Google Scholar |
[18] |
P. Sternberg, The effect of a singular perturbation on nonconvex variational problems,, Arch. Rational Mech. Anal., 101 (1988), 209.
|
[19] |
M. Struwe, "Variational Methods,", Springer-Verlag, (1990).
|
[1] |
Yuri Chekanov, Felix Schlenk. Notes on monotone Lagrangian twist tori. Electronic Research Announcements, 2010, 17: 104-121. doi: 10.3934/era.2010.17.104 |
[2] |
Sergi Simon. Linearised higher variational equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4827-4854. doi: 10.3934/dcds.2014.34.4827 |
[3] |
Antonio Rieser. A topological approach to spectral clustering. Foundations of Data Science, 2021 doi: 10.3934/fods.2021005 |
[4] |
Shanshan Chen, Junping Shi, Guohong Zhang. Spatial pattern formation in activator-inhibitor models with nonlocal dispersal. Discrete & Continuous Dynamical Systems - B, 2021, 26 (4) : 1843-1866. doi: 10.3934/dcdsb.2020042 |
[5] |
Murat Uzunca, Ayşe Sarıaydın-Filibelioǧlu. Adaptive discontinuous galerkin finite elements for advective Allen-Cahn equation. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 269-281. doi: 10.3934/naco.2020025 |
[6] |
Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1717-1746. doi: 10.3934/dcdss.2020451 |
[7] |
Christopher Bose, Rua Murray. Minimum 'energy' approximations of invariant measures for nonsingular transformations. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 597-615. doi: 10.3934/dcds.2006.14.597 |
[8] |
Xue-Ping Luo, Yi-Bin Xiao, Wei Li. Strict feasibility of variational inclusion problems in reflexive Banach spaces. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2495-2502. doi: 10.3934/jimo.2019065 |
[9] |
Charles Amorim, Miguel Loayza, Marko A. Rojas-Medar. The nonstationary flows of micropolar fluids with thermal convection: An iterative approach. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2509-2535. doi: 10.3934/dcdsb.2020193 |
[10] |
Livia Betz, Irwin Yousept. Optimal control of elliptic variational inequalities with bounded and unbounded operators. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021009 |
[11] |
Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367 |
[12] |
Jingni Guo, Junxiang Xu, Zhenggang He, Wei Liao. Research on cascading failure modes and attack strategies of multimodal transport network. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2020159 |
[13] |
Andrey Kovtanyuk, Alexander Chebotarev, Nikolai Botkin, Varvara Turova, Irina Sidorenko, Renée Lampe. Modeling the pressure distribution in a spatially averaged cerebral capillary network. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021016 |
[14] |
Guido De Philippis, Antonio De Rosa, Jonas Hirsch. The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals. Discrete & Continuous Dynamical Systems - A, 2019, 39 (12) : 7031-7056. doi: 10.3934/dcds.2019243 |
[15] |
Tomáš Roubíček. An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 867-893. doi: 10.3934/dcdss.2017044 |
[16] |
Zhi-Min Chen, Philip A. Wilson. Stability of oscillatory gravity wave trains with energy dissipation and Benjamin-Feir instability. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2329-2341. doi: 10.3934/dcdsb.2012.17.2329 |
[17] |
Reza Lotfi, Yahia Zare Mehrjerdi, Mir Saman Pishvaee, Ahmad Sadeghieh, Gerhard-Wilhelm Weber. A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 221-253. doi: 10.3934/naco.2020023 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]