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2
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0039051533
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American Mathematical Society, Providence, Rhode Island
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M. Delbrück, in Mathematical Problems in the Biological Sciences: Proceedings of the Symposium in Applied Mathematics (American Mathematical Society, Providence, Rhode Island, 1962), Vol. 14, pp. 55-68.
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Delbrück, M.1
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9
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0343043228
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note
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Excluded volume can be neglected under the condition z = (d/l)√N ≪ 1 (Ref. [27], P. 91), where d is the segment diameter. Under this condition volume exclusion is completely insignificant, while the very fact that segments cannot pass through one another is preserved, and so is the topology.
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11
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0039023668
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D. W. Sumners and S. G. Whittington, J. Phys. A 21, 1689 (1988); N. Pippenger, Discrete Appl. Math. 25, 273 (1989).
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Pippenger, N.1
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12
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0343914829
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note
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2, integration runs along the entire polymer length Nl, and l is called the effective Kuhn segment.
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18
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0343043224
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private communication
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B. Duplantier (private communication).
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Duplantier, B.1
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19
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0343914828
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note
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We adopt here the terminology in which phantom stands for the chain whose segments can freely pass through one another, irrespective of excluded volume.
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23
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0000772181
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E. Orlandini, M. C. Tesi, E. J. Janse van Rensburg, and S. G. Whittington, J. Phys. A 31, 5953 (1988); E. J. Janse van Rensburg and S. G. Whittington, J. Phys. A 24, 3935 (1991).
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Orlandini, E.1
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Janse Van Rensburg, E.J.3
Whittington, S.G.4
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24
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0039643686
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E. Orlandini, M. C. Tesi, E. J. Janse van Rensburg, and S. G. Whittington, J. Phys. A 31, 5953 (1988); E. J. Janse van Rensburg and S. G. Whittington, J. Phys. A 24, 3935 (1991).
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Janse Van Rensburg, E.J.1
Whittington, S.G.2
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25
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0343043222
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note
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The concept of an unknotted polymer confined within a knotted tube is subtle. It can be explained in the following way: First, let us quench our polymer inside the tube with respect to the tube walls. Then, let us pretend that the tube is phantom and bring it to the trivial knot nonoverlapping state. If our polymer is in a trivial knot state after this procedure, we say that it was unknotted within the tube.
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27
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0043247465
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edited by S. Suzuki World Scientific, Singapore
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T. Deguchi and K. Tsurusaki, in Lectures at Knots96, edited by S. Suzuki (World Scientific, Singapore, 1997), p. 95.
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Deguchi, T.1
Tsurusaki, K.2
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28
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0034183593
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Katritch, V.1
Olson, W.K.2
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Dubochet, J.4
Stasiak, A.5
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30
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0024021097
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K. V. Klenin, A. V. Vologodskii, V. V. Anshelevich, A. M. Dykhne, and M. D. Frank-Kamenetskii, J. Biomol. Struct. Dyn. 5, 1173-1185 (1988).
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Klenin, K.V.1
Vologodskii, A.V.2
Anshelevich, V.V.3
Dykhne, A.M.4
Frank-Kamenetskii, M.D.5
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32
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0022909525
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Paris
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M. E. Cates and J. M. Deutsch, J. Phys. (Paris) 47, 2121 (1986); M. G. Brereton and T. A. Vilgis, J. Phys. A 28, 1149 (1995).
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M. E. Cates and J. M. Deutsch, J. Phys. (Paris) 47, 2121 (1986); M. G. Brereton and T. A. Vilgis, J. Phys. A 28, 1149 (1995).
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M. Muller, J. P. Wittmer, and M. E. Cates, Phys. Rev. E 53, 5063 (1996); 61, 4078 (2000).
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Muller, M.1
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M. Muller, J. P. Wittmer, and M. E. Cates, Phys. Rev. E 53, 5063 (1996); 61, 4078 (2000).
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