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An application of the modular function in nonlocal variational problems
被引:48
作者
:
Chen, Xinfu
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
Chen, Xinfu
[
1
]
Oshita, Yoshihito
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
Oshita, Yoshihito
机构
:
[1]
Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
[2]
Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan
来源
:
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
|
2007年
/ 186卷
/ 01期
关键词
:
D O I
:
10.1007/s00205-007-0050-z
中图分类号
:
O29 [应用数学];
学科分类号
:
070104 ;
摘要
:
Using the modular function and its invariance under the action of a modular group and an heuristic reduction of a mathematical model, we present a mathematical account of a hexagonal pattern selection observed in di-block copolymer melts.
引用
收藏
页码:109 / 132
页数:24
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A new approach to variational problems with multiple scales
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[J].
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,
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(07)
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[Anonymous], INTERFACES FREE BOUN
[3]
CELL DYNAMIC SYSTEM APPROACH TO BLOCK COPOLYMERS
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0
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0
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UNIV ILLINOIS, BECKMAN INST, URBANA, IL 61801 USA
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BAHIANA, M
OONO, Y
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UNIV ILLINOIS, BECKMAN INST, URBANA, IL 61801 USA
UNIV ILLINOIS, BECKMAN INST, URBANA, IL 61801 USA
OONO, Y
[J].
PHYSICAL REVIEW A,
1990,
41
(12):
: 6763
-
6771
[4]
Block copolymers - Designer soft materials
Bates, FS
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0
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Univ Minnesota, Minneapolis, MN 55455 USA
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[J].
PHYSICS TODAY,
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(02)
: 32
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[5]
Periodicity and uniqueness of global minimizers of an energy functional containing a long-range interaction
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Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
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[J].
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: 1299
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On the derivation of a density functional theory for microphase separation of diblock copolymers
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Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada
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[J].
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Univ Utah, Dept Math, Salt Lake City, UT 84112 USA
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[J].
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KAWAI, H
[J].
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1980,
13
(05)
: 1237
-
1247
[10]
ORDERED STRUCTURE IN BLOCK POLYMER-SOLUTIONS .4. SCALING RULES ON SIZE OF FLUCTUATIONS WITH BLOCK MOLECULAR-WEIGHT, CONCENTRATION, AND TEMPERATURE IN SEGREGATION AND HOMOGENEOUS REGIMES
HASHIMOTO, T
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SHIBAYAMA, M
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KAWAI, H
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0
引用数:
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[J].
MACROMOLECULES,
1983,
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(07)
: 1093
-
1101
←
1
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3
→
共 24 条
[1]
A new approach to variational problems with multiple scales
论文数:
引用数:
h-index:
机构:
Alberti, G
Müller, S
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy
Müller, S
[J].
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,
2001,
54
(07)
: 761
-
825
[2]
[Anonymous], INTERFACES FREE BOUN
[3]
CELL DYNAMIC SYSTEM APPROACH TO BLOCK COPOLYMERS
BAHIANA, M
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV ILLINOIS, BECKMAN INST, URBANA, IL 61801 USA
UNIV ILLINOIS, BECKMAN INST, URBANA, IL 61801 USA
BAHIANA, M
OONO, Y
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV ILLINOIS, BECKMAN INST, URBANA, IL 61801 USA
UNIV ILLINOIS, BECKMAN INST, URBANA, IL 61801 USA
OONO, Y
[J].
PHYSICAL REVIEW A,
1990,
41
(12):
: 6763
-
6771
[4]
Block copolymers - Designer soft materials
Bates, FS
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Minnesota, Minneapolis, MN 55455 USA
Univ Minnesota, Minneapolis, MN 55455 USA
Bates, FS
Fredrickson, GH
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Minnesota, Minneapolis, MN 55455 USA
Fredrickson, GH
[J].
PHYSICS TODAY,
1999,
52
(02)
: 32
-
38
[5]
Periodicity and uniqueness of global minimizers of an energy functional containing a long-range interaction
Chen, XF
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
Chen, XF
Oshita, Y
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
Oshita, Y
[J].
SIAM JOURNAL ON MATHEMATICAL ANALYSIS,
2005,
37
(04)
: 1299
-
1332
[6]
On the derivation of a density functional theory for microphase separation of diblock copolymers
Choksi, R
论文数:
0
引用数:
0
h-index:
0
机构:
Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada
Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada
Choksi, R
Ren, XF
论文数:
0
引用数:
0
h-index:
0
机构:
Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada
Ren, XF
[J].
JOURNAL OF STATISTICAL PHYSICS,
2003,
113
(1-2)
: 151
-
176
[7]
The Nishiura-Ohnishi free boundary problem in the 1D case
Fife, PC
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Utah, Dept Math, Salt Lake City, UT 84112 USA
Fife, PC
Hilhorst, D
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Utah, Dept Math, Salt Lake City, UT 84112 USA
Hilhorst, D
[J].
SIAM JOURNAL ON MATHEMATICAL ANALYSIS,
2001,
33
(03)
: 589
-
606
[8]
Hamley I.W., 1999, PHYS BLOCK COPOLYMER
[9]
DOMAIN-BOUNDARY STRUCTURE OF STYRENE-ISOPRENE BLOCK CO-POLYMER FILMS CAST FROM SOLUTION .4. MOLECULAR-WEIGHT DEPENDENCE OF LAMELLAR MICRODOMAINS
HASHIMOTO, T
论文数:
0
引用数:
0
h-index:
0
HASHIMOTO, T
SHIBAYAMA, M
论文数:
0
引用数:
0
h-index:
0
SHIBAYAMA, M
KAWAI, H
论文数:
0
引用数:
0
h-index:
0
KAWAI, H
[J].
MACROMOLECULES,
1980,
13
(05)
: 1237
-
1247
[10]
ORDERED STRUCTURE IN BLOCK POLYMER-SOLUTIONS .4. SCALING RULES ON SIZE OF FLUCTUATIONS WITH BLOCK MOLECULAR-WEIGHT, CONCENTRATION, AND TEMPERATURE IN SEGREGATION AND HOMOGENEOUS REGIMES
HASHIMOTO, T
论文数:
0
引用数:
0
h-index:
0
HASHIMOTO, T
SHIBAYAMA, M
论文数:
0
引用数:
0
h-index:
0
SHIBAYAMA, M
KAWAI, H
论文数:
0
引用数:
0
h-index:
0
KAWAI, H
[J].
MACROMOLECULES,
1983,
16
(07)
: 1093
-
1101
←
1
2
3
→