Dynamics local

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... 

Another principal difficulty is that the precise effect of local dynamics on the NOE intensity cannot be determined from the data. The dynamic correction factor [85] describes the ratio of the effects of distance and angular fluctuations. Theoretical studies based on NOE intensities extracted from molecular dynamics trajectories [86,87] are helpful to understand the detailed relationship between NMR parameters and local dynamics and may lead to structure-dependent corrections. In an implicit way, an estimate of the dynamic correction factor has been used in an ensemble relaxation matrix refinement by including order parameters for proton-proton vectors derived from molecular dynamics calculations [72]. One remaining challenge is to incorporate data describing the local dynamics of the molecule directly into the refinement, in such a way that an order parameter calculated from the calculated ensemble is similar to the measured order parameter. 

Figure 1,8, for example, plots the probability that a cell has value 1 at time t4-l - labeled Pt+i - versus the probability that a cell had value 1 at time t -labeled Pt - for a particular four dimensional cellular automaton rule. The rule itself is unimportant, as there are many rules that display essentially the same kind of behavior. The point is that while the behavior of this rule is locally featureless - its space-time diagram would look like noise on a television screen - the global density of cells with value 1 jumps around in quasi-periodic fashion. We emphasize that this quasi-periodicity is a global property of the system, and that no evidence for this kind of behavior is apparent in the local dynamics. 

We see from both equations 8.32 and 8.33 that the most unstable mode is the mode and that ai t) = 1 - 1/a is stable for 1 < a < 3 and ai t) = 0 is stable for 0 < a < 1. In other words, the diffusive coupling does not introduce any instability into the homogeneous system. The only instabilities present are those already present in the uncoupled local dynamics. A similar conclusion would be reached if we were to carry out the same analysis for period p solutions. The conclusion is that if the uncoupled sites are stable, so are the homogeneous states of the CML. Now what about inhomogeneous states ... 

In this section we introduce a mobile CA model of land combat called EINSTein, developed at the Center for Naviil Analyses for the US Marine Corps. We include a discussion of this model here becau.se it is an interesting blend of CA-like local dynamics and agent-based modeling techniques. 

Moreover, behaviors frequently arise that appear to involve some form of intelligent division of red and blue forces to deal with local firestorms and skirmishes, particularly those forces whose personalities have been evolved (via a genetic algorithm sec below) to perform a specific mission, It is important to point out that such behaviors are not hard-wired but rather an emergent property of a decentralized and nonlinear local dynamics, A small sampling of behaviors is shown below. 

What is most surprising about many of the runs using GA-derived personalities is that the red force appears to task different agents with different missions, despite the fact that each red agent is endowed with exactly the same personality Thus, a higher-level tactic - such as use the two forward positioned agents to weaken the enemy s center - emerges out of the collective interactions of the same low-level decision rules i.e., an apparently centralized order induced by decentralized local dynamics. 

Svozil also suggests a third possibility, whereby a discretized field theory is strictly local in a higher dimensional space d > 4 but appears to be nonlocal in d = 4. While the physical reasons for a such a dimensional reduction remain unclear, such a dimensional shadowing clearly circumvents the no-go theorem by postulating a local dynamics in a higher dimension (see figure 12.9). 

Envisioning space-time as a four-dimensional CA lattice, wherein sites take on one of a finite number of values and interact via a local dynamics, Minsky explored various elementary properties of this universe particle (or packet ) size and speed, time contraction, symmetry, and how the notion of field might be made palatable within such a framework. 

J. Murdock, Normal Forms and Unfoldings for Local Dynamical Systems, Springer, New York, 2002. 

It is proposed that the B-state of Cu2 (bound in the gas phase) (57) is sufficiently strongly destabilized in the matrix to the extent that it is unstable with respect to dissociation to Cu(2D3/2) + Cu(2S1/2) fragments following photoexcitation of CU2 from the ground state, process (1) in above scheme. The extent to which the dissociation actually occurs depends on the local dynamics following photoexcitation and the details of the Cu2 rare gas potentials for the specific trapping site involved. 

Local Dynamics in Polypeptides Studied by Solid State 2H NMR Side Chain Dynamics of Poly(Y-benzyl L-glutamate) and Racemic Poly(Y-benzyl glutamate)... 

The first account is on Phase Incremented Pulses in NMR with Applications by S. Zhang, this is followed by Advances in NMR Studies of Liquid Crystals by R. Y. Dong, H. C. Bertram and H. J. Anderson report on Applications of NMR in Meat Science , NMR Characterization of Mechanical Waves is covered by G. Madelin, N. Baril, J. D. de Certaines, J.-M. Francone and E. Thiaudiere, the next account is on Aspects of Coherence Transfer in High Molecular Weight Proteins by P. Permi, the final chapter is on Local Dynamics in Polypeptides studied by Solid State 2H NMR by T. Hiraoki, S. Kitazawa and A. Tsutsumi. 

Hadjichristidis,. Chem. Phys., 119, 6883 (2003). Chain and Local Dynamics of Poly-isoprene as Probed by Experiments and Computer Simulations. 

Chem. Phys., 107, 4751 (1997). Local Dynamics in a Long-Chain Alkane Melt from Molecular Dynamics Simulations and Neutron Scattering Experiments. 

In close analogy to flux-balance analysis, we thus extend the constraint-based description of metabolic networks to incorporate (local) dynamic properties. Recall the expansion of the mass-balance equation into a Taylor series, already given in Eq. (68)... 

Fig. 12.1 Illustration of the temperature sensitivity of 15N relaxation parameters, Rlf R2t and NOE, as indicated. Shown are the relative deviations in these relaxation parameters from their values at 25 °C as a function of temperature in the range of + 3 °C. The expected variations in / ] and R2 due to temperature deviations of as little as +1 °C are already greater than the typical level of experimental precision ( % ) of these measurements (indicated by the dashed horizontal lines). For simplicity, only temperature variation of the overall tumbling time of the molecule (due to temperature dependence of the viscosity of water) is taken into account the effect of temperature variations on local dynamics is not considered here.

Recent progress in protein dynamics studies by NMR was greatly facilitated by the invention of the model-free formalism [28, 32]. In this approach, the local dynamics of a protein are characterized by an order parameter, S, measuring the amplitude of local motion on a scale from 0 to 1, and the correlation time of the motion, T oc. The model-free expression for the correlation function of local motion reads... 

In the extended model-free approach [29], the local dynamics are deconvolved into a fast and a slow motion rfagt < ttsiow, S2 = S2lowS ast) ... 

In the absence of a correlation between the local dynamics and the overall rotational diffusion of the protein, as assumed in the model-free approach, the total correlation function that determines the 15N spin-relaxation properties (Eqs. (1-5)) can be deconvolved (Tfast, Tslow < Tc) ... 

It is worth mentioning that the analytical approaches outlined here and currently used to treat relaxation data assume that the overall and local dynamics are not coupled. While this is a reasonable assumption for small, compact proteins, it might not be true for sys-... 

Intramolecular excimers have been used for probing bulk polymers, micelles, vesicles and biological membranes (Bokobza and Monnerie, 1986 Bokobza, 1990 Georgescauld et al., 1980 Vauhkonen et al., 1990, Viriot et al., 1983 Zachariasse et al., 1983). In particular, this method provides useful information on the local dynamics of polymer chains in the bulk (see Box 8.2). 

In conclusion, the method of intramolecular excimer formation is rapid and convenient, but the above discussion has shown that great care is needed for a reliable interpretation of the experimental results. In some cases it has been demonstrated that the results in terms of equivalent microviscosity are consistent with those obtained by the fluorescence polarization method (described in Section 8.5), but this is not a general rule. Nevertheless, the relative changes in fluidity and local dynamics upon an external perturbation are less dependent on the probe, and useful applications to the study of temperature or pressure effects have been reported. 

Thin Polymeric Films with Fluorescence Probes. Makromol. Chem. 192, 1981-1991. Balter, A. (1997) Probing Bioviscosity via Fluorescence, J. Fluorescence 7, S99—105. Bokobza L. (1990) Investigation of Local Dynamics of Polymer Chains in the Bulk by... 

The incorporation of non-Gaussian effects in the Rouse theory can only be accomplished in an approximate way. For instance, the optimized Rouse-Zimm local dynamics approach has been applied by Guenza et al. [55] for linear and star chains. They were able to obtain correlation times and results related to dynamic light scattering experiments as the dynamic structure factor and its first cumulant [88]. A similar approach has also been applied by Ganazzoli et al. [87] for viscosity calculations. They obtained the generalized ZK results for ratio g already discussed. 

It can also be verified that this formulation is entirely equivalent to the optimized Rouse-Zimm local dynamics approach [55]. 

Both routes have their limitations. The basic theory of complex structures, which are encountered with macromolecules, often does not allow analytic solutions. Incisive, though reasonable, approximations have to be introduced. On the other hand, rigorous simulations can be made by means of molecular dynamics, but this technique has the limitation that only rather small and fast moving objects can be treated within a reasonable time, even with the fastest computers presently available. This minute scale gives valuable information on the local structure and local dynamics, but no reliable predictions of the macro-molecular properties can be made by this technique. All other simulations have to start with some basic assumptions. These in turn are backed by results obtained from basic theories. Hence both approaches are complementary and are needed when constructing a reliable framework for macromolecules that reflects the desired relation to the materials properties. 

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