[1] J. G. Oldroyd, J. Non-Newt. Fluid Mech. 14, 9 (1984).
[2] P.-G. de Gennes, Physica 118A, 44 (1983). G. Ryskin,
Phys. Rev. A 32, 1239 (1985).
[3] H. Rehage and H. Hoffman, Mol. Phys. 74, 933 (1991).
[4] J.-F. Berret, D. C. Roux, and G. Porte, J. Phys. (France)
4, 1261 (1994).
[5] V. Schmitt, F. Lequeux, A. Pousse, and D. Roux, Langmuir
10, 955 (1994).
[6] C. Grand, J. Arrault, and M. E. Cates, J. Phys. II
(France) 7, 1071 (1997).
[7] P. T. Callaghan, private communication.
[8] M. M. Denn, Ann. Rev. Fluid Mech., 22, 13 (1990).
[9] P. T. Callaghan, M. E. Cates, C. J. Rofe, and J. B. A.
F. Smeulders, J. Phys. II (France) 6, 375 (1996).
[10] M. Doi and S. F. Edwards, The Theory of Polymer Dynamics
(Clarendon, Oxford, 1989).
[11] M. E. Cates, J. Phys. Chem. 94, 371 (1990).
[12] N. A. Spenley and M. E. Cates, Macromolecules 27, 3850
(1994).
[13] F. Greco and R. C. Ball, J. Non-Newt. Fluid Mech. 69,
195 (1997).
[14] D. S. Malkus, J. S. Nohel, and B. J. Plohr, J. Comp.
Phys. 87 (1990) 464; SIAM J. Appl. Math. 51 (1991)
899.
[15] Y. Y. Renardy, Th. Comp. Fl. Mech. 7, 463 (1995).
[16] From our point of view, 2D flow solver results which show
a selected stress for a local model [17] should be examined
further to see whether the algorithm implicitly introduced
non-locality (numerical diffusion).
[17] N. A. Spenley, X. F. Yuan, and M. E. Cates, J. Phys. II
(France) 6, 551 (1996).
[18] P. D Olmsted, O. Radulescu, and C.-Y. D. Lu, in preparation
(1999).
[19] G. Porte, J. F. Berret and J. L. Harden, J. Phys. II
(France) 7, 459 (1997).
[20] M. E. Cates, T. McLeish, G. Marrucci, Europhys. Lett.
21, 451, (1993).
[21] V. Schmitt, C. M. Marques, and F. Lequeux, Phys. Rev.
E52, 4009 (1995).
[22] J. R. A. Pearson, J. Rheol. 38, 309 (1994).
[23] P. D. Olmsted and P. M. Goldbart, Phys. Rev. A41, 4578
(1990); ibid, A46, 4966 (1992).
[24] P. D. Olmsted and C.-Y. D. Lu, Phys. Rev. E 56, R55
(1997).
[25] R. G. Larson, Constitutive Equations for Polymer Melts
and Solutions, (Butterworth, Boston,1988).
[26] A. W. El-Kareh and L. G. Leal, J. Non-Newt. Fl. Mech.
33, 257 (1989).
[27] Note that although the velocity is not a constant, it cannot
enter the equation of motion alone, due to Galilean
invariance.
[28] R. H. Abraham and C. D. Shaw, Dynamics – The Geometry
of Behavior, 2nd. ed., (Addison-Wesley, NY, 1992).
[29] It is possible to have a functional whose bulk contribution
is indifferent to the interface location, in which case
the interface contribution plays the decisive role.
[30] We assume A and B are the only singular points on the
saddle connection, so that s(A,B) does not change along
the connection.
[31] X.-F. Yuan, Europhys. Lett. 46, 542, (1999).