-
1
-
-
78751619232
-
Morphology of surfaces in mesoscopic polymers, surfactants, electrons, or reaction-diffusion systems: Methods, simulations, and measurements
-
AKSIMENTIEV, A., FIALKOWSKI, M., & HOLYST, R. Morphology of surfaces in mesoscopic polymers, surfactants, electrons, or reaction-diffusion systems: methods, simulations, and measurements. Adv. Chem. Phys. 121 (2002), 141-239.
-
(2002)
Adv. Chem. Phys.
, vol.121
, pp. 141-239
-
-
Aksimentiev, A.1
Fialkowski, M.2
Holyst, R.3
-
3
-
-
0012520952
-
A new approach to variational problems with multiple scales
-
Zbl 1021.49012 MR 1823420
-
ALBERTI, G., & MÜLLER, S. A new approach to variational problems with multiple scales. Comm. Pure Appl. Math. 54 (2001), 761-825. Zbl 1021.49012 MR 1823420
-
(2001)
Comm. Pure Appl. Math.
, vol.54
, pp. 761-825
-
-
Alberti, G.1
Müller, S.2
-
4
-
-
0000092187
-
Periodic surfaces of prescribed mean curvature
-
ANDERSON, D., DAVIS, H., SCRIVEN, L., & NITSCHE, J. C. Periodic surfaces of prescribed mean curvature. Adv. Chem. Phys. 77 (1990), 337.
-
(1990)
Adv. Chem. Phys.
, vol.77
, pp. 337
-
-
Anderson, D.1
Davis, H.2
Scriven, L.3
Nitsche, J.C.4
-
5
-
-
0023829056
-
Minimal surfaces and structures: From inorganic and metal crystals to cell membranes and biopolymers
-
ANDERSSON, S., HYDE, S. T., LARSSON, K., & LIDIN, S. Minimal surfaces and structures: from inorganic and metal crystals to cell membranes and biopolymers. Chem. Rev. 88 (1988), 221-242.
-
(1988)
Chem. Rev.
, vol.88
, pp. 221-242
-
-
Andersson, S.1
Hyde, S.T.2
Larsson, K.3
Lidin, S.4
-
6
-
-
0348046829
-
Block copolymers - Designer soft materials
-
BATES, F. S., & FREDRICKSON, G. H. Block copolymers - designer soft materials. Physics Today 52 (1999), no. 2, 32-38.
-
(1999)
Physics Today
, vol.52
, Issue.2
, pp. 32-38
-
-
Bates, F.S.1
Fredrickson, G.H.2
-
7
-
-
17144426836
-
Γ-convergence for beginners
-
Oxford Univ. Press Zbl pre01865939 MR 1968440
-
BRAIDES, A. Γ-convergence for Beginners. Oxford Lecture Ser. Math. Appl. 22, Oxford Univ. Press (2002). Zbl pre01865939 MR 1968440
-
(2002)
Oxford Lecture Ser. Math. Appl.
, vol.22
-
-
Braides, A.1
-
8
-
-
11744273384
-
The surface evolver
-
Software available at
-
BRAKKE, K. The surface evolver. Experiment. Math. 1 (1992), 141-165. Software available at: http://www.susqu.edu/facstaff/b/brakke/evolver/evolver. html.
-
(1992)
Experiment. Math.
, vol.1
, pp. 141-165
-
-
Brakke, K.1
-
9
-
-
33746012315
-
Free energy of a nonuniform system I. Interfacial Free Energy
-
CAHN, J. W., & HILLIARD, J. E. Free energy of a nonuniform system I. Interfacial Free 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
-
10
-
-
0000410819
-
Scaling laws in microphase separation of diblock copolymers
-
Zbl 1023.82015 MR 1852942
-
CHOKSI, R. Scaling laws in microphase separation of diblock copolymers. J. Nonlinear Sci. 11 (2001), 223-236. Zbl 1023.82015 MR 1852942
-
(2001)
J. Nonlinear Sci.
, vol.11
, pp. 223-236
-
-
Choksi, R.1
-
11
-
-
0346801867
-
On a derivation of a density functional theory for microphase separation of diblock copolymers
-
Zbl 1034.82037 MR 2012976
-
CHOKSI, R., & REN, X. On a derivation of a density functional theory for microphase separation of diblock copolymers. J. Statist. Phys. 113 (2003), 151-176. Zbl 1034.82037 MR 2012976
-
(2003)
J. Statist. Phys.
, vol.113
, pp. 151-176
-
-
Choksi, R.1
Ren, X.2
-
12
-
-
36248952676
-
On the first and second variations of a nonlocal isoperimetric problem
-
to appear
-
CHOKSI, R., & STERNBERG, P. On the first and second variations of a nonlocal isoperimetric problem. J. Reine Angew. Math., to appear.
-
J. Reine Angew. Math.
-
-
Choksi, R.1
Sternberg, P.2
-
14
-
-
42749102046
-
Ripening of porous media
-
DAVIDOVITCH, B., ERTAS, D., & HALSEY, T. C. Ripening of porous media. Phys. Rev. E 70 (2004), 031609.
-
(2004)
Phys. Rev. E
, vol.70
, pp. 031609
-
-
Davidovitch, B.1
Ertas, D.2
Halsey, T.C.3
-
15
-
-
3142523730
-
Reaction-limited sintering in nearly saturated environments
-
DAVIDOVITCH, B., ERTAS, D., & HALSEY, T. C. Reaction-limited sintering in nearly saturated environments. Philos. Mag. 84 (2004), 1937.
-
(2004)
Philos. Mag.
, vol.84
, pp. 1937
-
-
Davidovitch, B.1
Ertas, D.2
Halsey, T.C.3
-
16
-
-
0003418232
-
-
Springer, New York Zbl 0874.49001 MR 0257325
-
FEDERER, H. Geometric Measure Theory. Springer, New York (1969). Zbl 0874.49001 MR 0257325
-
(1969)
Geometric Measure Theory
-
-
Federer, H.1
-
17
-
-
54749104300
-
Models for phase separation and their mathematics
-
Zbl 0957.35062 MR 1772733
-
FIFE, P. Models for phase separation and their mathematics. Electron. J. Differential Equations 2000, no. 48, 1-26. Zbl 0957.35062 MR 1772733
-
Electron. J. Differential Equations
, vol.2000
, Issue.48
, pp. 1-26
-
-
Fife, P.1
-
18
-
-
0003174115
-
Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation
-
Zbl 0890.35043 MR 1429160
-
FIFE, P., KIELHÖFER, H., MAIER-PAAPE, S., & WANNER, T. Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation. Phys. D 100 (1997), 257-278. Zbl 0890.35043 MR 1429160
-
(1997)
Phys. D
, vol.100
, pp. 257-278
-
-
Fife, P.1
Kielhöfer, H.2
Maier-Paape, S.3
Wanner, T.4
-
19
-
-
0028767777
-
Complex phase behavior of polyisoprene-polystyrene diblock copolymers near the order-disorder transition
-
FÖRSTER S., KHANDPUR, K., ZHAO, J., BATES, F., HAMLEY, I., RYAN, J., & BRAS, W. Complex phase behavior of polyisoprene-polystyrene diblock copolymers near the order-disorder transition. Macromolecules 27 (1994), 6922-6935.
-
(1994)
Macromolecules
, vol.27
, pp. 6922-6935
-
-
Förster, S.1
Khandpur, K.2
Zhao, J.3
Bates, F.4
Hamley, I.5
Ryan, J.6
Bras, W.7
-
21
-
-
0002246356
-
On the regularity of boundaries of sets minimizing perimeter with a volume constraint
-
Zbl 0486.49024 MR 0684753
-
GONZALEZ, E., MASSARI, U., & TAMANINI, I. On the regularity of boundaries of sets minimizing perimeter with a volume constraint. Indiana Univ. Math. J. 32 (1983), 25-37. Zbl 0486.49024 MR 0684753
-
(1983)
Indiana Univ. Math. J.
, vol.32
, pp. 25-37
-
-
Gonzalez, E.1
Massari, U.2
Tamanini, I.3
-
22
-
-
0001220422
-
Stable constant mean curvature surfaces minimize area
-
Zbl 0878.49026 MR 1432843
-
GROSSE-BRAUCKMANN, K. Stable constant mean curvature surfaces minimize area. Pacific J. Math. 175 (1997), 527-534. Zbl 0878.49026 MR 1432843
-
(1997)
Pacific J. Math.
, vol.175
, pp. 527-534
-
-
Grosse-Brauckmann, K.1
-
23
-
-
0031537321
-
Gyroids of constant mean curvature
-
Zbl 0898.53010 MR 1464580
-
GROSSE-BRAUCKMANN, K. Gyroids of constant mean curvature. Experiment. Math. 6 (1997), 33-50. Zbl 0898.53010 MR 1464580
-
(1997)
Experiment. Math.
, vol.6
, pp. 33-50
-
-
Grosse-Brauckmann, K.1
-
26
-
-
0021853508
-
On a theory of phase transitions with interfacial energy
-
MR 0768066
-
GURTIN, M. On a theory of phase transitions with interfacial energy. Arch. Ration. Mech. Anal. 87 (1985), no. 3, 187-212. MR 0768066
-
(1985)
Arch. Ration. Mech. Anal.
, vol.87
, Issue.3
, pp. 187-212
-
-
Gurtin, M.1
-
27
-
-
0001031874
-
Gitterperiodische Punktmengen und Isoperimetrie
-
Zbl 0248.52012 MR 0324550
-
HADWIGER, H. Gitterperiodische Punktmengen und Isoperimetrie. Monatsh. Math. 76 (1972), 410-418. Zbl 0248.52012 MR 0324550
-
(1972)
Monatsh. Math.
, vol.76
, pp. 410-418
-
-
Hadwiger, H.1
-
28
-
-
0028461343
-
The gyroid: A new equilibrium morphology in weakly segregated diblock copolymers
-
HAJDUK, D. A. ET AL. The gyroid: a new equilibrium morphology in weakly segregated diblock copolymers. Macromolecules 27 (1994), 4063-4075.
-
(1994)
Macromolecules
, vol.27
, pp. 4063-4075
-
-
Hajduk, D.A.1
-
29
-
-
2142834706
-
The periodic isoperimetric problem
-
Zbl 1046.52002 MR 2031051
-
HAUSWIRTH, L., PEREZ, J., ROMON, P., & ROS, A. The periodic isoperimetric problem. Trans. Amer. Math. Soc. 356 (2004), 2025-2047. Zbl 1046.52002 MR 2031051
-
(2004)
Trans. Amer. Math. Soc.
, vol.356
, pp. 2025-2047
-
-
Hauswirth, L.1
Perez, J.2
Romon, P.3
Ros, A.4
-
30
-
-
0029854260
-
A new turn for Archimedes
-
HOFFMAN, D. A new turn for Archimedes. Nature 384 (1996), 28-29.
-
(1996)
Nature
, vol.384
, pp. 28-29
-
-
Hoffman, D.1
-
31
-
-
0033449295
-
The isoperimetric problem on surfaces
-
Zbl 1003.52011 MR 1699261
-
HOWARDS, H., HUTCHINGS, M., & MORGAN, F. The isoperimetric problem on surfaces. Amer. Math. Monthly 106 (1999), 430-439. Zbl 1003.52011 MR 1699261
-
(1999)
Amer. Math. Monthly
, vol.106
, pp. 430-439
-
-
Howards, H.1
Hutchings, M.2
Morgan, F.3
-
32
-
-
0010598327
-
Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory
-
Zbl 1070.49026 MR 1803974
-
HUTCHINSON, J., & TONEGAWA, Y. Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory. Calc. Var. Partial Differential Equations 10 (2000), 49-84. Zbl 1070.49026 MR 1803974
-
(2000)
Calc. Var. Partial Differential Equations
, vol.10
, pp. 49-84
-
-
Hutchinson, J.1
Tonegawa, Y.2
-
33
-
-
0001162145
-
The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions
-
Zbl 0687.53010 MR 1003093
-
KARCHER, H. The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions. Manuscripta Math. 64 (1989), 291-357. Zbl 0687.53010 MR 1003093
-
(1989)
Manuscripta Math.
, vol.64
, pp. 291-357
-
-
Karcher, H.1
-
34
-
-
27844439674
-
-
Transl. Math. Monogr. 221, Amer. Math. Soc. Zbl 1042.53001 MR 2013507
-
KENMOTSU, K. Surfaces with Constant Mean Curvature. Transl. Math. Monogr. 221, Amer. Math. Soc. (2003). Zbl 1042.53001 MR 2013507
-
(2003)
Surfaces with Constant Mean Curvature
-
-
Kenmotsu, K.1
-
35
-
-
84975988204
-
Local minimisers and singular perturbations
-
Zbl 0676.49011 MR 0985990
-
KOHN, R. V., & STERNBERG, P. Local minimisers and singular perturbations. Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), 69-94. Zbl 0676.49011 MR 0985990
-
(1989)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.111
, pp. 69-94
-
-
Kohn, R.V.1
Sternberg, P.2
-
36
-
-
34250109116
-
The gradient theory of phase transitions and the minimal interface criterion
-
Zbl 0616.76004 MR 0866718
-
MODICA, L. The gradient theory of phase transitions and the minimal interface criterion. Arch. Ration. Mech. Anal. 98 (1987), 123-142. Zbl 0616.76004 MR 0866718
-
(1987)
Arch. Ration. Mech. Anal.
, vol.98
, pp. 123-142
-
-
Modica, L.1
-
37
-
-
0000359194
-
--convergenza
-
Zbl 0356.49008 MR 0445362
-
-- convergenza. Boll. Un. Mat. Ital. (5) 14 (1977), 285-299. Zbl 0356.49008 MR 0445362
-
(1977)
Boll. Un. Mat. Ital.
, vol.14
, Issue.5
, pp. 285-299
-
-
Modica, L.1
Mortola, S.2
-
38
-
-
0000390068
-
Singular perturbations as a selection criterion for periodic minimizing sequences
-
Zbl 0821.49015 MR 1261722
-
MÜLLER, S. Singular perturbations as a selection criterion for periodic minimizing sequences. Calc. Var. 1 (1993), 169-204. Zbl 0821.49015 MR 1261722
-
(1993)
Calc. Var.
, vol.1
, pp. 169-204
-
-
Müller, S.1
-
39
-
-
41349101280
-
Theory of domain patterns in systems with long-range interactions of Coulomb type
-
MR 1953930
-
MURATOV, C. B. Theory of domain patterns in systems with long-range interactions of Coulomb type. Phys. Rev. E 66 (2002), 066108. MR 1953930
-
(2002)
Phys. Rev. E
, vol.66
, pp. 066108
-
-
Muratov, C.B.1
-
40
-
-
0002733111
-
Some mathematical aspects of the micro-phase separation in diblock copolymers
-
MR 1334695
-
NISHIURA, Y., & OHNISHI, I. Some mathematical aspects of the micro-phase separation in diblock copolymers. Phys. D 84 (1995), 31-39. MR 1334695
-
(1995)
Phys. D
, vol.84
, pp. 31-39
-
-
Nishiura, Y.1
Ohnishi, I.2
-
42
-
-
0000482598
-
Equilibrium morphology of block copolymer melts
-
OHTA, T., & KAWASAKI, K. Equilibrium morphology of block copolymer melts. Macromolecules 19 (1986), 2621-2632.
-
(1986)
Macromolecules
, vol.19
, pp. 2621-2632
-
-
Ohta, T.1
Kawasaki, K.2
-
43
-
-
0034347328
-
On the multiplicity of solutions of two nonlocal variational problems
-
Zbl 0973.49007 MR 1752422
-
REN, X., & WEI, J. On the multiplicity of solutions of two nonlocal variational problems. SIAM J. Math. Anal. 31 (2000), 909-924. Zbl 0973.49007 MR 1752422
-
(2000)
SIAM J. Math. Anal.
, vol.31
, pp. 909-924
-
-
Ren, X.1
Wei, J.2
-
44
-
-
84978800888
-
On energy minimizers of the diblock copolymer problem
-
Zbl 1031.49035 MR 1980472
-
REN, X., & WEI, J. On energy minimizers of the diblock copolymer problem. Interfaces Free Bound. 5 (2003), 193-238. Zbl 1031.49035 MR 1980472
-
(2003)
Interfaces Free Bound.
, vol.5
, pp. 193-238
-
-
Ren, X.1
Wei, J.2
-
45
-
-
33644939600
-
Wriggled lamellar solutions and their stability in the diblock copolymer problem
-
MR 2176111
-
REN, X., & WEI, J. Wriggled lamellar solutions and their stability in the diblock copolymer problem. SIAM J. Math. Anal. 37 (2005), 455-489. MR 2176111
-
(2005)
SIAM J. Math. Anal.
, vol.37
, pp. 455-489
-
-
Ren, X.1
Wei, J.2
-
46
-
-
22544461938
-
Stability of spot and ring solutions of the diblock copolymer equation
-
Zbl 1064.82040 MR 2098120
-
REN, X., & WEI, J. Stability of spot and ring solutions of the diblock copolymer equation. J. Math. Phys. 45 (2004), 4106-4133. Zbl 1064.82040 MR 2098120
-
(2004)
J. Math. Phys.
, vol.45
, pp. 4106-4133
-
-
Ren, X.1
Wei, J.2
-
47
-
-
0036813973
-
Concentrically layered energy equilibria of the diblock copolymer problem
-
Zbl 1010.82041 MR 1939157
-
REN, X., & WEI, J. Concentrically layered energy equilibria of the diblock copolymer problem. Europ. J. Appl. Math. 13 (2002), 479-496. Zbl 1010.82041 MR 1939157
-
(2002)
Europ. J. Appl. Math.
, vol.13
, pp. 479-496
-
-
Ren, X.1
Wei, J.2
-
48
-
-
51249163412
-
Stable constant mean curvature tori and the isoperimetric problem in three space forms
-
Zbl 0760.53037 MR 1161286
-
RITORE M., & ROS, A. Stable constant mean curvature tori and the isoperimetric problem in three space forms. Comment. Math. Helvet. 67 (1992), 293-305. Zbl 0760.53037 MR 1161286
-
(1992)
Comment. Math. Helvet.
, vol.67
, pp. 293-305
-
-
Ritore, M.1
Ros, A.2
-
49
-
-
8644240623
-
-
Proceedings from the Clay Mathematics Institute Summer School, MSRI, Berkeley, CA. Available at
-
ROS, A. The isoperimetric problem. Proceedings from the Clay Mathematics Institute Summer School, MSRI, Berkeley, CA. Available at www.ugr.es/~aros.
-
The Isoperimetric Problem
-
-
Ros, A.1
-
50
-
-
0000049028
-
Schwarz' P and D surfaces are stable
-
Zbl 0747.53010 MR 1245555
-
ROSS, M. Schwarz' P and D surfaces are stable. Differential Geom. Appl. 2 (1992), 179-195. Zbl 0747.53010 MR 1245555
-
(1992)
Differential Geom. Appl.
, vol.2
, pp. 179-195
-
-
Ross, M.1
-
51
-
-
33750006083
-
-
The Scientific Graphics Project
-
The Scientific Graphics Project. http://www.msri.org/publications/sgp/ SGP/indexc.html
-
-
-
-
52
-
-
0004096780
-
-
Proc. Centre Math. Anal. Austral. Nat. Univ. 3 Zbl 0546.49019 MR 0756417
-
SIMON, L. Lectures on Geometric Measure Theory. Proc. Centre Math. Anal. Austral. Nat. Univ. 3 (1983). Zbl 0546.49019 MR 0756417
-
(1983)
Lectures on Geometric Measure Theory
-
-
Simon, L.1
-
53
-
-
34250095380
-
The effect of a singular perturbation on nonconvex variational problems
-
Zbl 0647.49021 MR 0930124
-
STERNBERG, P. The effect of a singular perturbation on nonconvex variational problems. Arch. Ration. Mech. Anal. 101 (1988), 209-260. Zbl 0647.49021 MR 0930124
-
(1988)
Arch. Ration. Mech. Anal.
, vol.101
, pp. 209-260
-
-
Sternberg, P.1
-
54
-
-
0032370858
-
Connectivity of phase boundaries in strictly convex domains
-
Zbl 0911.49025 MR 1620498
-
STERNBERG, P., & ZUMBRUN, K. Connectivity of phase boundaries in strictly convex domains. Arch. Ration. Mech. Anal. 141 (1998), 375-400. Zbl 0911.49025 MR 1620498
-
(1998)
Arch. Ration. Mech. Anal.
, vol.141
, pp. 375-400
-
-
Sternberg, P.1
Zumbrun, K.2
-
55
-
-
0036335523
-
Double gyroid morphology in a gradient system with nonlocal effects
-
TERAMOTO, T., & NISHIURA, Y. Double gyroid morphology in a gradient system with nonlocal effects. J. Phys. Soc. Japan 71 (2002), 1611-1614.
-
(2002)
J. Phys. Soc. Japan
, vol.71
, pp. 1611-1614
-
-
Teramoto, T.1
Nishiura, Y.2
-
56
-
-
0024057538
-
Periodic area-minimizing surfaces in block copolymers
-
THOMAS, E., ANDERSON, D. M., HENKEE, C. S., & HOFFMAN, D. Periodic area-minimizing surfaces in block copolymers. Nature 334 (1988), 598-601.
-
(1988)
Nature
, vol.334
, pp. 598-601
-
-
Thomas, E.1
Anderson, D.M.2
Henkee, C.S.3
Hoffman, D.4
-
57
-
-
0037119540
-
Phase field model with a variable chemical potential
-
Zbl 1013.35070 MR 1926927
-
TONEGAWA, Y. Phase field model with a variable chemical potential. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), 993-1019. Zbl 1013.35070 MR 1926927
-
(2002)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.132
, pp. 993-1019
-
-
Tonegawa, Y.1
-
58
-
-
33744932727
-
A diffused interface whose chemical potential lies in a Sobolev space
-
MR 2185866
-
TONEGAWA, Y. A diffused interface whose chemical potential lies in a Sobolev space. Ann. Scuola Norm. Sup. Pisa 4 (2005), 487-510. MR 2185866
-
(2005)
Ann. Scuola Norm. Sup. Pisa
, vol.4
, pp. 487-510
-
-
Tonegawa, Y.1
-
59
-
-
0041008860
-
A strong minimax property of nondegenerate submanifolds
-
Zbl 0808.49037 MR 1305283
-
WHITE, B. A strong minimax property of nondegenerate submanifolds. J. Reine Angew. Math. 457 (1994), 203-218. Zbl 0808.49037 MR 1305283
-
(1994)
J. Reine Angew. Math.
, vol.457
, pp. 203-218
-
-
White, B.1
|