Dynamics of Entangled Course-Grained Chains

When one is interested in slow modes of motion of the system, each macromolecule of the system can be schematically described in a coarse-grained way as consisting of N + 1 linearly-coupled Brownian particles, and we shall be able to look at the system as a suspension of n(N + 1) interacting Brownian particles. An anticipated result for dynamic equation of the chains in equilibrium situation can be presented as a system of stochastic non-Markovian equations 

1 Curtiss and Bird (1981a and 1981b) have posed and considered such a problem. 

One can think that this situation, described by equations (3.1), can be visualised as a picture of interacting (and connected in chains) Brownian particles suspended in anisotropic viscoelastic segment liquid . Introduction of macroscopic concepts is unavoidable consequence of transition from microscopic to mesoscopic approach, or better to say, from the microscopic model of interacting Kuhn-Kramers chains to mesoscopic model of interacting chains of Brownian particles. 

Up to now no specific results for memory function and effective potential in equations (3.1) are available,2 so that, to simplify the system (3.1), one has to make some suggestions, two of which are intensively exploited. 

Course-Grained Interacting Chains in Non-Relaxing Medium 

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