Abstract:
An effective method is proposed for investigating the statistical
characteristics of random walks associated with their topological
state with respect to a regular lattice of obstacles. Such problems
arise in the modeling of the behavior of macroscopic molecules in
concentrated systems consisting of strongly entangled polymer chains.
The method can be used, in particular, to calculate the change in the
elasticity free energy when there is isotropic swelling of polymer networks.
Citation:
E. A. Zheligovskaya, F. F. Ternovskii, A. R. Khokhlov, “Random walks on a lattice of obstacles”, TMF, 75:3 (1988), 451–464; Theoret. and Math. Phys., 75:3 (1988), 644–654
\Bibitem{ZheTerKho88}
\by E.~A.~Zheligovskaya, F.~F.~Ternovskii, A.~R.~Khokhlov
\paper Random walks on a~lattice of obstacles
\jour TMF
\yr 1988
\vol 75
\issue 3
\pages 451--464
\mathnet{http://mi.mathnet.ru/tmf4957}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=959728}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 75
\issue 3
\pages 644--654
\crossref{https://doi.org/10.1007/BF01036266}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1988U173000013}
Linking options:
https://www.mathnet.ru/eng/tmf4957
https://www.mathnet.ru/eng/tmf/v75/i3/p451
This publication is cited in the following 7 articles:
Alexei E. Likhtman, Mohamad S. Talib, Bart Vorselaars, Jorge Ramirez, “Determination of Tube Theory Parameters Using a Simple Grid Model as an Example”, Macromolecules, 46:3 (2013), 1187
Sachin Shanbhag, Seung Joon Park, Qiang Zhou, Ronald G. Larson, “Implications of microscopic simulations of polymer melts for mean-field tube theories”, Molecular Physics, 105:2-3 (2007), 249
Sachin Shanbhag, Ronald G. Larson, “Chain Retraction Potential in a Fixed Entanglement Network”, Phys. Rev. Lett., 94:7 (2005)
Ashish Batra, Claude Cohen, Lynden Archer, “Stress Relaxation of End-Linked Polydimethylsiloxane Elastomers with Long Pendent Chains”, Macromolecules, 38:16 (2005), 7174
S. Shanbhag, R. G. Larson, “A Slip-Link Model of Branch-Point Motion in Entangled Polymers”, Macromolecules, 37:21 (2004), 8160
P. M. Lavrov, V. I. Mudruk, “Statistics of a polymer chain in the presence of random topological constraints”, Theoret. and Math. Phys., 86:3 (1991), 235–241
S. Ya. Zhitomirskaya, V. A. Mandel'shtam, “Aharonov-Bohm problem on a square lattice”, Theoret. and Math. Phys., 86:3 (1991), 241–251
Citation in format AMSBIB
Contact us: