Dynamics of networks

Takserman-Krozer.R., Ziabicki.A. General dynamic theory of macromolecular networks. IL Dynamics of network deformation. J. Polymer Sci. Part A-2 8, 321-332... 

Before presenting descriptions of specific ANNs (in the next section), we discuss in general terms the various architectures and dynamics of networks. The architecture of an ANN refers to the physical organization and arrangement of the PEs in the network and also how the PEs are connected. These considerations are important because they help bring order to the many different types of ANN that exist hy placing them into categories. 

After the above historical retrospective devoted to linear Rouse chains, we follow the extension of this approach to polymer systems that have more complex topologies. We focus first on the dynamics of networks cross-Unked from... 

Watts DJ (1999) Small worlds The dynamics of networks between order and randomness. Princeton University Press, Princeton, NJ... 

Structure and dynamics of networks formed in concentrated soiutions of nonionic surfactants... 

Since the discovery of cured phenolic formaldehyde resins and vulcanized rubbers, interest has grown in such areas as the mechanisms of network formation, the chemical structures of crosslinked systems, and the dynamics of networks. Although the vast majority of polymers used industrially are crosslinked to a greater or lesser degree, the ability to characterize these systems is highly limited. Traditional tech-... 

Under compression or shear most polymers show qualitatively similar behaviour. However, under the application of tensile stress, two different defonnation processes after the yield point are known. Ductile polymers elongate in an irreversible process similar to flow, while brittle systems whiten due the fonnation of microvoids. These voids rapidly grow and lead to sample failure [50, 51]- The reason for these conspicuously different defonnation mechanisms are thought to be related to the local dynamics of the polymer chains and to the entanglement network density. 

The local dynamics of tire systems considered tluis far has been eitlier steady or oscillatory. However, we may consider reaction-diffusion media where tire local reaction rates give rise to chaotic temporal behaviour of tire sort discussed earlier. Diffusional coupling of such local chaotic elements can lead to new types of spatio-temporal periodic and chaotic states. It is possible to find phase-synchronized states in such systems where tire amplitude varies chaotically from site to site in tire medium whilst a suitably defined phase is synclironized tliroughout tire medium 51. Such phase synclironization may play a role in layered neural networks and perceptive processes in mammals. Somewhat suriDrisingly, even when tire local dynamics is chaotic, tire system may support spiral waves... 

From a practical standpoint, the fiber or polymer must interact or process freely with the dynamics of web formation, and the resulting fiber network must be in register with the interlocking arrangement or media, in order for the fabric stmcture to transmit the maximum potential inherent in the properties of individual fibers. Ultimately, if a nonwoven fabric is to be totally effective and its properties fuUy utilized, it must be appropriately configured to meet its end use apptication or appropriately placed in the end use item in such a way that the performance of the product reflects the position and characteristics of individual fibers. 

In addition to the above techniques, inverse gas chromatography, swelling experiments, tensile tests, mechanical analyses, and small-angle neutron scattering have been used to determine the cross-link density of cured networks (240—245). Si soHd-state nmr and chemical degradation methods have been used to characterize cured networks stmcturaHy (246). H- and H-nmr and spin echo experiments have been used to study the dynamics of cured sihcone networks (247—250). 

More generally, changing flow alters the relative proportion of input, storage, transfer, and transformation processes for organic matter and nutrients. Hence, the relative extent and the dynamics of the temporary channels within a catchment may control the capacity of a river network to produce, transform, and store nutrients and organic matter. 

Wollheim WM, Peterson BJ, Thomas SM, Hopkinson CH, Vorosmarty CJ (2008) Dynamics of N removal over aimual time periods in a suburban river network. J Geophys Res 113 G03038. doi 10.1029/2007JG000660... 

Moreover, as a consequence of their transient character, a hierarchy of clusters in dynamic equilibrium that may differ in shape and size can be hypothesized [253], Mass, momentum, and charge transport within a cluster of reversed micelles is expected to be strongly enhanced as compared to that among isolated reversed micelles. It has been shown that the dynamics of a network of interacting reversed micelles is successfully described by a model developed by Cates [35,69,254],... 

While metabolic engineers traditionally sought the rate-limiting enzyme to unlock flow through a pathway, now they understand that there may be many points of control and feedback with the metabolic network, and seek to empirically determine the dynamics of the interactions between rate controllers and other factors. For example, the sizes of metabolic precursor pools and the catabolism or sequestration of products affect accumulation as well as flux through the pathway. 

Ewen, B, Richter, Da Neutron Spin Echo Investigations on the Segmental Dynamics of Polymers in Melts, Networks and Solutions. VoL 134, pp, 1-130. 

A fascinating future area of study will be experimental and computational evaluation of the dynamics of protein networks. For example, how do protein complexes and interaction networks change in response to environmental signals or developmental states How do the networks of... 

The discrete merge method is a special case of dynamic programming applied to branch list processing. It is applicable to a wide class of network... 

The paper is organized in the following way In Section 2, the principles of quasi-elastic neutron scattering are introduced, and the method of NSE is shortly outlined. Section 3 deals with the polymer dynamics in dense environments, addressing in particular the influence and origin of entanglements. In Section 4, polymer networks are treated. Section 5 reports on the dynamics of linear homo- and block copolymers, of cyclic and star-shaped polymers in dilute and semi-dilute solutions, respectively. Finally, Section 6 summarizes the conclusions and gives an outlook. 

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