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Models for higher algebroids
The emergence of torsion in the continuum limit of distributed edge-dislocations
1. | Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel, Israel |
References:
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I. Agricola and C. Thier, The geodesics of metric connections with vectorial torsion,, Ann. Global Anal. Geom., 26 (2004), 321.
doi: 10.1023/B:AGAG.0000047509.63818.4f. |
[2] |
B. Bilby, R. Bullough and E. Smith, Continuous distributions of dislocations: A new application of the methods of Non-Riemannian geometry,, Proc. Roy. Soc. A, 231 (1955), 263.
doi: 10.1098/rspa.1955.0171. |
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B. Bilby and E. Smith, Continuous distributions of dislocations. III,, Proc. Roy. Soc. Edin. A, 236 (1956), 481.
doi: 10.1098/rspa.1956.0150. |
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M. Do Carmo, Riemannian Geometry,, Birkhäuser, (1992).
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D. J. H. Garling, Inequalities: A Journey into Linear Analysis,, Cambridge University Press, (2007).
doi: 10.1017/CBO9780511755217. |
[6] |
J. Guven, J. Hanna, O. Kahraman and M. Müller, Dipoles in thin sheets,, Eur. Phys. J. E, 36 (2013).
doi: 10.1140/epje/i2013-13106-0. |
[7] |
J. Heinonen, Lectures on Lipschitz Analysis,, Jyväskylän Yliopistopaino, (2005).
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[8] |
K. Kondo, Geometry of elastic deformation and incompatibility,, in Memoirs of the Unifying Study of the Basic Problems in Engineering Science by Means of Geometry (ed. K. Kondo), 1 (1955), 5. Google Scholar |
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E. Kroner, The Physics of Defects,, in Les Houches Summer School Proceedings (eds. R. Balian, (1981). Google Scholar |
[10] |
R. Kupferman, M. Moshe and J. Solomon, Metric description of defects in amorphous materials,, Arch. Rat. Mech. Anal., 216 (2015), 1009. Google Scholar |
[11] |
J. Nye, Some geometrical relations in dislocated crystals,, Acta Met., 1 (1953), 153.
doi: 10.1016/0001-6160(53)90054-6. |
[12] |
A. Ozakin and A. Yavari, Affine development of closed curves in Weitzenböck manifolds and the burgers vector of dislocation mechanics,, Math. Mech. Solids, 19 (2014), 299.
doi: 10.1177/1081286512463720. |
[13] |
P. Petersen, Riemannian Geometry,, 2nd edition, (2006).
|
[14] |
H. Seung and D. Nelson, Defects in flexible membranes with crystalline order,, Phys. Rev. A, 38 (1988), 1005.
doi: 10.1103/PhysRevA.38.1005. |
[15] |
V. Volterra, Sur l'équilibre des corps élastiques multiplement connexes,, Ann. Sci. Ecole Norm. Sup. Paris 1907, 24 (1907), 401. Google Scholar |
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C.-C. Wang, On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations,, Arch. Rat. Mech. Anal., 27 (1967), 33.
doi: 10.1007/BF00276434. |
show all references
References:
[1] |
I. Agricola and C. Thier, The geodesics of metric connections with vectorial torsion,, Ann. Global Anal. Geom., 26 (2004), 321.
doi: 10.1023/B:AGAG.0000047509.63818.4f. |
[2] |
B. Bilby, R. Bullough and E. Smith, Continuous distributions of dislocations: A new application of the methods of Non-Riemannian geometry,, Proc. Roy. Soc. A, 231 (1955), 263.
doi: 10.1098/rspa.1955.0171. |
[3] |
B. Bilby and E. Smith, Continuous distributions of dislocations. III,, Proc. Roy. Soc. Edin. A, 236 (1956), 481.
doi: 10.1098/rspa.1956.0150. |
[4] |
M. Do Carmo, Riemannian Geometry,, Birkhäuser, (1992).
|
[5] |
D. J. H. Garling, Inequalities: A Journey into Linear Analysis,, Cambridge University Press, (2007).
doi: 10.1017/CBO9780511755217. |
[6] |
J. Guven, J. Hanna, O. Kahraman and M. Müller, Dipoles in thin sheets,, Eur. Phys. J. E, 36 (2013).
doi: 10.1140/epje/i2013-13106-0. |
[7] |
J. Heinonen, Lectures on Lipschitz Analysis,, Jyväskylän Yliopistopaino, (2005).
|
[8] |
K. Kondo, Geometry of elastic deformation and incompatibility,, in Memoirs of the Unifying Study of the Basic Problems in Engineering Science by Means of Geometry (ed. K. Kondo), 1 (1955), 5. Google Scholar |
[9] |
E. Kroner, The Physics of Defects,, in Les Houches Summer School Proceedings (eds. R. Balian, (1981). Google Scholar |
[10] |
R. Kupferman, M. Moshe and J. Solomon, Metric description of defects in amorphous materials,, Arch. Rat. Mech. Anal., 216 (2015), 1009. Google Scholar |
[11] |
J. Nye, Some geometrical relations in dislocated crystals,, Acta Met., 1 (1953), 153.
doi: 10.1016/0001-6160(53)90054-6. |
[12] |
A. Ozakin and A. Yavari, Affine development of closed curves in Weitzenböck manifolds and the burgers vector of dislocation mechanics,, Math. Mech. Solids, 19 (2014), 299.
doi: 10.1177/1081286512463720. |
[13] |
P. Petersen, Riemannian Geometry,, 2nd edition, (2006).
|
[14] |
H. Seung and D. Nelson, Defects in flexible membranes with crystalline order,, Phys. Rev. A, 38 (1988), 1005.
doi: 10.1103/PhysRevA.38.1005. |
[15] |
V. Volterra, Sur l'équilibre des corps élastiques multiplement connexes,, Ann. Sci. Ecole Norm. Sup. Paris 1907, 24 (1907), 401. Google Scholar |
[16] |
C.-C. Wang, On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations,, Arch. Rat. Mech. Anal., 27 (1967), 33.
doi: 10.1007/BF00276434. |
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