Topological restrictions

The presented scheme offers several extensions. For example, the model gives a clear route for an additional inclusion of entanglement constraints and packing effects [15]. Again, this can be realized with the successful mean field models based on the conformational tube picture [7,9] where the chains do not have free access to the total space between the cross-links but are trapped in a cage due to the additional topological restrictions, as visualized in the cartoon. 

This section presents results of the space-time analysis of the above-mentioned motional processes as obtained by the neutron spin echo technique. First, the entropically determined relaxation processes, as described by the Rouse model, will be discussed. We will then examine how topological restrictions are noticed if the chain length is increased. Subsequently, we address the dynamics of highly entangled systems and, finally, we consider the origin of the entanglements. 

But the topological nature has not been confirmed more directly to date. It is expected that the topological restriction increases with an increase in molecular weight (M) and the number density of entanglement (ve). Therefore, the studies of the M or ve dependence of crystallization behavior should be important in confirming directly the important role of topological nature in polymer crystallization. 

Parlati, F., McNew, J. A., Fukuda, R., Miller, R., Sollner, T. H. and Rothman, J. E. Topological restriction of SNARE-dependent membrane fusion. Nature 407 194-198, 2000. 

It turns out that this analysis applies only to systems with a bounded phase space. It is possible that topological restrictions on the accessible phase space - and not only the form of the particular Hamiltonian -play a crucial role in determining when the weak form of the QCT actually applies. For example, this might explain why the open-system quantum delta-kicked rotor is a counter-example to naive expectations regarding the QCT (S. Habib et.al., 2002). 

The assumptions of the calculation are rather arbitrary, of course. The result perhaps only illustrates that the observed order of magnitude of ne is not grossly inconsistent with the idea of topological restrictions by loops. The calculation gives no hint as to why the Fox-Alien parameter S2/d should control the value of ne or Me however. 

Keywords T-junctions of carbon nanotubes, defects, topological restrictions, molecular simulations, quantum-chemical calculations. 

Cover illustration Left panel Stochastic description of the kinetics of a population of particles, Fig 9.15. Middle panel Dissolution in topologically restricted media, Fig. 6.8B (reprinted with permission from Springer). Right panel A pseudophase space for a chaotic model of cortisol kinetics, Fig.11.11. 

Entanglement appears to be caused by a collective topological restriction of many neighbouring chains (see Section 9.1). 

Connectin also causes aggregation of actin filaments in a manner similar to myosin at low ionic strengths (Kimura and Maruyama, 1983a Kimura et ai, 1984b). Bundles of actin filaments wee formed in the presence of connectin. The bundles appeared to resemble those formed by a-actinin. However, unlike the case with a-actinin, bundle formation by connectin was not affected by tropomyosin bound to actin filaments (H. Yoshidomi, unpublished results). Furthermore, the 400-kDa fragment of connectin did not act on actin filaments at all. It is likely that connectin filaments enhance bundle formation of actin filaments by topological restrictions. 

Bodsky, J. L., and McCracken, A. A. (1997). ER-associated and proteasome-mediated protein degradation How two topologically restricted events came together. Trends Cell Biol. 7, 151-156. 

Cohen and co-workers considered rigid units of secondary structure and combinatorially generated all possible three-dimensional arrangements between them. " Chain connectivity, topological restrictions, and steric constraints were applied to eliminate incorrect or impossible structures. The number of resultant structures was reduced to a manageable set (on the order of 10-100), and the correct structure was always present within the set of solutions. There was no way to differentiate the correct answer from the other possibilities, however. Indeed, Novotny and coworkers showed that it is difficult to correctly... 

In the case of moderately crosslinked and topologically restricted networks, we obtain results which may be used to explain the low (non-affine) values of molecular deformation observed experimentally (Fig. 14). Values of a close to 1 indicate that the elastic properties of networks prepared by the end-linking reaction are very... 

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