-
1
-
-
4243401801
-
-
10.1103/PhysRevLett.4.380
-
Y. Nambu, Phys. Rev. Lett. 4, 380 (1960). 10.1103/PhysRevLett.4.380
-
(1960)
Phys. Rev. Lett.
, vol.4
, pp. 380
-
-
Nambu, Y.1
-
2
-
-
51649206572
-
-
10.1007/BF02812722
-
J. Goldstone, Nuovo Cimento 19, 154 (1961). 10.1007/BF02812722
-
(1961)
Nuovo Cimento
, vol.19
, pp. 154
-
-
Goldstone, J.1
-
3
-
-
36149017798
-
-
10.1103/PhysRev.130.439
-
P. W. Anderson, Phys. Rev. 130, 439 (1963). 10.1103/PhysRev.130.439
-
(1963)
Phys. Rev.
, vol.130
, pp. 439
-
-
Anderson, P.W.1
-
4
-
-
36049056789
-
-
10.1103/PhysRev.155.1554
-
T. W. B. Kibble, Phys. Rev. 155, 1554 (1967). 10.1103/PhysRev.155.1554
-
(1967)
Phys. Rev.
, vol.155
, pp. 1554
-
-
Kibble, T.W.B.1
-
5
-
-
50549200528
-
-
10.1016/0031-9163(64)91136-9;
-
P. W. Higgs, Phys. Lett. 12, 132 (1964) 10.1016/0031-9163(64)91136-9
-
(1964)
Phys. Lett.
, vol.12
, pp. 132
-
-
Higgs, P.W.1
-
6
-
-
33845890179
-
-
10.1103/PhysRevLett.13.508
-
P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964). 10.1103/PhysRevLett.13.508
-
(1964)
Phys. Rev. Lett.
, vol.13
, pp. 508
-
-
Higgs, P.W.1
-
7
-
-
84971301149
-
-
10.1111/j.1749-6632.1949.tb27296.x
-
L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949). 10.1111/j.1749-6632. 1949.tb27296.x
-
(1949)
Ann. N.Y. Acad. Sci.
, vol.51
, pp. 627
-
-
Onsager, L.1
-
8
-
-
0015331929
-
-
10.1016/0038-1098(72)90186-X
-
P.-G. de Gennes, Solid State Commun. 10, 753 (1972). 10.1016/0038- 1098(72)90186-X
-
(1972)
Solid State Commun.
, vol.10
, pp. 753
-
-
De Gennes, P.-G.1
-
12
-
-
71449120087
-
-
Ph.D. thesis, University of California Santa Barbara
-
A. Hexemer, Ph.D. thesis, University of California Santa Barbara, 2007.
-
(2007)
-
-
Hexemer, A.1
-
18
-
-
0038709956
-
-
10.1103/PhysRevB.24.363;
-
D. R. Nelson and J. Toner, Phys. Rev. B 24, 363 (1981) 10.1103/PhysRevB.24.363
-
(1981)
Phys. Rev. B
, vol.24
, pp. 363
-
-
Nelson, D.R.1
Toner, J.2
-
19
-
-
0001234419
-
-
10.1103/PhysRevA.27.1157;
-
J. Toner, Phys. Rev. A 27, 1157 (1983) 10.1103/PhysRevA.27.1157
-
(1983)
Phys. Rev. A
, vol.27
, pp. 1157
-
-
Toner, J.1
-
23
-
-
0034225686
-
-
10.1103/PhysRevE.62.658;
-
B. Pansu, E. Grelet, M.-H. Li, and H. T. Nguyen, Phys. Rev. E 62, 658 (2000) 10.1103/PhysRevE.62.658
-
(2000)
Phys. Rev. e
, vol.62
, pp. 658
-
-
Pansu, B.1
Grelet, E.2
Li, M.-H.3
Nguyen, H.T.4
-
24
-
-
0035938066
-
-
10.1103/PhysRevLett.86.3791;
-
E. Grelet, B. Pansu, M.-H. Li, and H. T. Nguyen, Phys. Rev. Lett. 86, 3791 (2001) 10.1103/PhysRevLett.86.3791
-
(2001)
Phys. Rev. Lett.
, vol.86
, pp. 3791
-
-
Grelet, E.1
Pansu, B.2
Li, M.-H.3
Nguyen, H.T.4
-
27
-
-
18544400071
-
-
10.1103/PhysRevE.68.041703
-
B. A. DiDonna and R. D. Kamien, Phys. Rev. E 68, 041703 (2003). 10.1103/PhysRevE.68.041703
-
(2003)
Phys. Rev. e
, vol.68
, pp. 041703
-
-
Didonna, B.A.1
Kamien, R.D.2
-
30
-
-
34547239319
-
Geometric theory of columnar phases on curved substrates
-
DOI 10.1103/PhysRevLett.99.017801
-
C. D. Santangelo, V. Vitelli, R. D. Kamien, and D. R. Nelson, Phys. Rev. Lett. 99, 017801 (2007). 10.1103/PhysRevLett.99.017801 (Pubitemid 47150485)
-
(2007)
Physical Review Letters
, vol.99
, Issue.1
, pp. 017801
-
-
Santangelo, C.D.1
Vitelli, V.2
Kamien, R.D.3
Nelson, D.R.4
-
31
-
-
40549103816
-
Formation of new morphologies of surfactant-inorganic-water systems under spherical confinements
-
DOI 10.1021/jp710840b
-
X. R. Zhang, D. P. Cao, and W. C. Wang, J. Phys. Chem. C 112, 2943 (2008). 10.1021/jp710840b (Pubitemid 351362322)
-
(2008)
Journal of Physical Chemistry C
, vol.112
, Issue.8
, pp. 2943-2948
-
-
Zhang, X.1
Cao, D.2
Wang, W.3
-
32
-
-
33747616908
-
Crystallography on curved surfaces
-
DOI 10.1073/pnas.0602755103
-
V. Vitelli, J. Lucks, and D. R. Nelson, Proc. Natl. Acad. Sci. U.S.A. 103, 12323 (2006). 10.1073/pnas.0602755103 (Pubitemid 44267258)
-
(2006)
Proceedings of the National Academy of Sciences of the United States of America
, vol.103
, Issue.33
, pp. 12323-12328
-
-
Vitelli, V.1
Lucks, J.B.2
Nelson, D.R.3
-
33
-
-
0034289652
-
Interacting topological defects on frozen topographies
-
DOI 10.1103/PhysRevB.62.8738
-
M. J. Bowick, D. R. Nelson, and A. Travesset, Phys. Rev. B 62, 8738 (2000). 10.1103/PhysRevB.62.8738 (Pubitemid 32367337)
-
(2000)
Physical Review B - Condensed Matter and Materials Physics
, vol.62
, Issue.13
, pp. 8738-8751
-
-
Bowick, M.J.1
Nelson, D.R.2
Travesset, A.3
-
35
-
-
53449094240
-
-
10.1103/PhysRevLett.101.147801
-
X. Xing, Phys. Rev. Lett. 101, 147801 (2008). 10.1103/PhysRevLett.101. 147801
-
(2008)
Phys. Rev. Lett.
, vol.101
, pp. 147801
-
-
Xing, X.1
-
36
-
-
61349085998
-
-
10.1007/s10955-009-9681-9
-
X. Xing, J. Stat. Phys. 134, 487 (2009). 10.1007/s10955-009-9681-9
-
(2009)
J. Stat. Phys.
, vol.134
, pp. 487
-
-
Xing, X.1
-
37
-
-
33947642483
-
Self-consistent field theory simulations of block copolymer assembly on a sphere
-
DOI 10.1103/PhysRevE.75.031802
-
T. L. Chantawansri, A. W. Bosse, A. Hexemer, H. D. Ceniceros, C. J. García-Cervera, E. J. Kramer, and G. H. Fredrickson, Phys. Rev. E 75, 031802 (2007). 10.1103/PhysRevE.75.031802 (Pubitemid 46492316)
-
(2007)
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
, vol.75
, Issue.3
, pp. 031802
-
-
Chantawansri, T.L.1
Bosse, A.W.2
Hexemer, A.3
Ceniceros, H.D.4
Garcia-Cervera, C.J.5
Kramer, E.J.6
Fredrickson, G.H.7
-
38
-
-
33748639260
-
Self-assembled pattern formation of block copolymers on the surface of the sphere using self-consistent field theory
-
DOI 10.1140/epje/i2006-10035-y
-
J. F. Li, J. Fan, H. D. Zhang, F. Qiu, P. Tang, and Y. L. Yang, Eur. Phys. J. E 20, 449 (2006). 10.1140/epje/i2006-10035-y (Pubitemid 44386805)
-
(2006)
European Physical Journal E
, vol.20
, Issue.4
, pp. 449-457
-
-
Li, J.F.1
Fan, J.2
Zhang, H.D.3
Qiu, F.4
Tang, P.5
Yang, Y.L.6
-
39
-
-
37649027298
-
-
10.1103/PhysRevE.67.036206
-
P. C. Matthews, Phys. Rev. E 67, 036206 (2003). 10.1103/PhysRevE.67. 036206
-
(2003)
Phys. Rev. e
, vol.67
, pp. 036206
-
-
Matthews, P.C.1
-
42
-
-
38749152414
-
Patterning on nonplanar substrates: Flexible honeycomb films from a range of self-assembling star copolymers
-
DOI 10.1021/la702495p
-
L. A. Connal, R. Vestberg, P. A. Gurr, C. J. Hawker, and G. G. Qiao, Langmuir 24, 556 (2008). 10.1021/la702495p (Pubitemid 351177551)
-
(2008)
Langmuir
, vol.24
, Issue.2
, pp. 556-562
-
-
Connal, L.A.1
Vestberg, R.2
Gurr, P.A.3
Hawker, C.J.4
Qiao, G.G.5
-
43
-
-
33646028588
-
-
10.1007/BF01646487
-
S. Coleman, Commun. Math. Phys. 31, 259 (1973). 10.1007/BF01646487
-
(1973)
Commun. Math. Phys.
, vol.31
, pp. 259
-
-
Coleman, S.1
-
46
-
-
71449124148
-
-
More precisely, suppose γi (s,t) describes a family of geodesics, one for each t, where γi (s,0) is parametrized by arc length. Then ξi ≡t γi (s,t) t=0 is a Jacobi field, measuring the density of nearby geodesics, and satisfies the equation d2 ξi /d s2 =-K ξi when ξi is perpendicular to the tangent of γi. Equation (8) follows from Section 5-5 of Ref. for more details.
-
More precisely, suppose γi (s,t) describes a family of geodesics, one for each t, where γi (s,0) is parametrized by arc length. Then ξi ≡t γi (s,t) t=0 is a Jacobi field, measuring the density of nearby geodesics, and satisfies the equation d2 ξi /d s2 =-K ξi when ξi is perpendicular to the tangent of γi. Equation (8) follows from Section 5-5 of Ref. for more details.
-
-
-
-
47
-
-
0003724744
-
-
2nd ed. (Butterworth, Oxford
-
L. D. Landau, L. P. Pitaevskii, and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Butterworth, Oxford, 1984).
-
(1984)
Electrodynamics of Continuous Media
-
-
Landau, L.D.1
Pitaevskii, L.P.2
Lifshitz, E.M.3
-
48
-
-
22144488651
-
-
Springer, New York
-
P. Schneider, C. Kochanek, J. Wambsganss, and G. Meylan, Gravitational Lensing: Strong, Weak and Micro (Springer, New York, 2006).
-
(2006)
Gravitational Lensing: Strong, Weak and Micro
-
-
Schneider, P.1
Kochanek, C.2
Wambsganss, J.3
Meylan, G.4
-
51
-
-
0003867976
-
-
See, e.g., Cambridge University Press, Cambridge
-
See, e.g., D. R. Nelson, Defects and Geometry in Condensed Matter Physics (Cambridge University Press, Cambridge, 2002), Chap..
-
(2002)
Defects and Geometry in Condensed Matter Physics
-
-
Nelson, D.R.1
-
55
-
-
0036822243
-
The geometry of soft materials: A primer
-
DOI 10.1103/RevModPhys.74.953
-
R. D. Kamien, Rev. Mod. Phys. 74, 953 (2002). 10.1103/RevModPhys.74.953 (Pubitemid 36116694)
-
(2002)
Reviews of Modern Physics
, vol.74
, Issue.4
, pp. 953-971
-
-
Kamien, R.D.1
-
56
-
-
42749105028
-
Anomalous coupling between topological defects and curvature
-
DOI 10.1103/PhysRevLett.93.215301, 215301
-
V. Vitelli and A. M. Turner, Phys. Rev. Lett. 93, 215301 (2004). 10.1103/PhysRevLett.93.215301 (Pubitemid 40011392)
-
(2004)
Physical Review Letters
, vol.93
, Issue.21
, pp. 2153011-2153014
-
-
Vitelli, V.1
Turner, A.M.2
-
57
-
-
34547674516
-
-
10.1103/PhysRevB.76.054106
-
L. Giomi and M. J. Bowick, Phys. Rev. B 76, 054106 (2007). 10.1103/PhysRevB.76.054106
-
(2007)
Phys. Rev. B
, vol.76
, pp. 054106
-
-
Giomi, L.1
Bowick, M.J.2
-
59
-
-
0039388961
-
-
10.1088/0022-3719/17/30/019
-
S. Sachdev and D. R. Nelson, J. Phys. C 17, 5473 (1984). 10.1088/0022-3719/17/30/019
-
(1984)
J. Phys. C
, vol.17
, pp. 5473
-
-
Sachdev, S.1
Nelson, D.R.2
-
60
-
-
34247580877
-
Stress focusing in elastic sheets
-
DOI 10.1103/RevModPhys.79.643
-
T. Witten, Rev. Mod. Phys. 79, 643 (2007). 10.1103/RevModPhys.79.643 (Pubitemid 46677004)
-
(2007)
Reviews of Modern Physics
, vol.79
, Issue.2
, pp. 643-675
-
-
Witten, T.A.1
-
61
-
-
0346111990
-
-
10.1021/nl0202096;
-
D. R. Nelson, Nano Lett. 2, 1125 (2002) 10.1021/nl0202096
-
(2002)
Nano Lett.
, vol.2
, pp. 1125
-
-
Nelson, D.R.1
-
62
-
-
0000621083
-
-
see also 10.1051/jp2:1992133
-
see also T. C. Lubensky and J. Prost, J. Phys. II 2, 371 (1992). 10.1051/jp2:1992133
-
(1992)
J. Phys. II
, vol.2
, pp. 371
-
-
Lubensky, T.C.1
Prost, J.2
-
65
-
-
0004190360
-
-
See, for instance, Princeton University Press, Princeton, NJ
-
See, for instance, J. Milnor, Morse Theory (Princeton University Press, Princeton, NJ, 1969), p. 100.
-
(1969)
Morse Theory
, pp. 100
-
-
Milnor, J.1
-
66
-
-
63149118554
-
-
10.1103/PhysRevE.79.031701
-
L. R. Gómez and D. A. Vega, Phys. Rev. E 79, 031701 (2009). 10.1103/PhysRevE.79.031701
-
(2009)
Phys. Rev. e
, vol.79
, pp. 031701
-
-
Gómez, L.R.1
Vega, D.A.2
|