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On the Generalised Stretch Function
Author(s) -
Kharlamov Alexander A.,
Filip Petr
Publication year - 2012
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.201100102
Subject(s) - mathematics , interval (graph theory) , algebraic number , term (time) , mathematical analysis , unit (ring theory) , zero (linguistics) , function (biology) , power (physics) , power function , statistical physics , physics , thermodynamics , combinatorics , quantum mechanics , evolutionary biology , biology , linguistics , philosophy , mathematics education
The tube theory represents a powerful tool for the description of polymer behaviour. In this theory, the term in the form of an integral over a full solid angle of a magnitude of deformed unit vector represents the stretch function. This term relates the lengths of the random walk of a molecule in deformed and undeformed states. For the case of the Doi‐Edwards model, the integrand is raised to a power of one, however, for other models the power differs from one. The aim of this contribution is to derive an analytical algebraic approximation of a general form of this integral with the integrand raised to an arbitrary power within the physically justified interval between zero and two.