Global dynamics

Although CA are most often assumed to live 011 infinitely large lattices, we can equally well consider lattices that are finite in extent (which is done in practice regardless, since all CA simulations are ultimately restricted by a finite computer memory). If a lattice has N sites, there are clearly a finite number,, of possible global configurations. The global dynamical evolution can then be represented by a finite state transition graph Gc, much like the one considered in the description of an abstract automaton in section 2.1.4. 

Fig. 5.5 Local action of the topological operator with which any number of distinct structures supporting exactly the same global dynamics can be constructed. The various quantities are defined in equation (5.27). Solid lines represent 2-cycles.

Category 4 Category 4 includes a remarkable set of rules whose action appears to lead to a sustained global dynamics during which the value of Deftec remains almost constant. That is, particular combinations of E and fl effectively induce a... 

Dachs J, Eisenreich SJ, Baker JE, Ko FC, Jeremiason JD (1999) Coupling of phytoplankton uptake and airwater exchange of persistent organic pollutants. Environ Sci Technol 33 3653-3660 Dachs J, Lohmann R, Ockenden WA, Mejanelle L, Eisenreich S, Jones KC (2002) Oceanic bio-geochemical controls on global dynamics of persistent organic pollutants. Environ Sci Technol 36 4229 1237... 

In terms of nonlinear dynamical systems, the second waveguide of the junction can be considered as a system that is initially more or less far from its stable point. The global dynamics of the system is directly related to the spatial transfomation of the total field behind the plane of junction. In structure A, the initial linear mode transforms into a nonlinear mode of the waveguide with the same width and refractive index. In the structure B, the initial filed distribution corresponds to a nonlinear mode of the first waveguide it differs from nonlinear mode of the second waveguide, however. The dynamics in both cases is complicated and involves nonlinear modes as well as radiation. Global dynamics of a non-integrable system usually requires numerical simulations. For the junctions, the Cauchy problem also cannot be solved analytically. 

We find below a set of stationary nonlinear modes for the step-index nonlinear waveguide, investigate their stability and global dynamics. The latter is simulated numerically by the FD-BPM as a solution to the Cauchy problem for waveguide junctions under consideration. 

The above simulations were performed at stationary conditions. However, it is important to examine time-dependent situations to characterize global dynamics far from stationary attractors. 

P. Gueret and J. P. Vigier, Remarks on a possible dynamical and geometrical unification of external and internal groups of motions of elementary particles and their application to SO(6,1) global dynamical symmetry, Nuovo Cimento A 67(1), 238 (1970). 

Our goal is to develop a global dynamic model of pyrolysis rotary kilns. This global model can be viewed as three parts with coupling terms ... 

Dielectric spectroscopy was also used by the same group in order to study the local and global dynamics of the PI arm of the same miktoarm star samples [89]. Measurements were confined to the ordered state, where the dynamics of the PI chain tethered on PS cylinders were observed in different environments since in the SIB case the faster moving PB chains are tethered in the same point as the PI arm. The distribution of segmental relaxation times were broader for SI2 than SIB. The effect was less pronounced at higher temperatures. The PI normal mode time was found to be slower in SIB, when compared to SI2 although both arms had the same molecular weight. Additionally, the normal mode relaxation time distributions of the PI chains tethered to PS cylinders in the miktoarm samples were narrower than in P(S-h-I) systems of lamellar structure. 

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