Knot quasi

The Quasi-Knot Concept for Polymers with Topological Constraints... 

The quasi-knot concept seems to be most obvious in the case when the knot can be considered as a local one, i.e. when it has its own internal scale much smaller than the chain scale as a whole. However, for chains in the coil state the computer experiments do not indicate the existence of such an internal knot scale (for the globular state the detailed experiments are absent). 

Nevertheless, A.N. Semenov in his works [56-59] have used the concept of local quasi-knot for Gaussian coil state, because the end-to-end distance in this state ( N1/2) is still less than the chain length ( N). Within the framework of this approach, the authors of Refs. [56, 57] have shown that the topological constraints do not influence the dynamics of the whole polymer coil suspended in dilute 0-solutions but lead to the essential slowing-down of the internal coil excitation modes. In accordance with Refs. [56-59], the maximum relaxation time of a coil is limited by the diffusion of the local knots along the chain, i.e. the... 

Non-uniformity also brings the question of where within each span each new knot should be inserted. Forcing it always to be at the centre is a totally arbitrary choice. A second question is close behind, whether to insert in every span anyway. Quasi-crystal theory, which inserts knots only one at a time, but where they are most needed, does not lead to obvious efficiency, but could provide some theoretical insight. 

A. Amman, L. Cederbaum and W. Gaus (eds). Fractals, Quasi-crystals, Chaos, Knots and Algebraic Quantum Mechanics, Kluwer Academic, Dordrecht, 1988. 

A.Grosberg, S.Nechaev Averaged Kauffman invariant and quasi-knot concept for linear polymers , Europhys. Lett. 20 613 (1992). 

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