Spatial domain structures

It turns out that, in the CML, the local temporal period-doubling yields spatial domain structures consisting of phase coherent sites. By domains, we mean physical regions of the lattice in which the sites are correlated both spatially and temporally. This correlation may consist either of an exact translation symmetry in which the values of all sites are equal or possibly some combined period-2 space and time symmetry. These coherent domains are separated by domain walls, or kinks, that are produced at sites whose initial amplitudes are close to unstable fixed points of = a, for some period-rr. Generally speaking, as the period of the local map... 

Very recently Tokita and Tanaka have performed a macroscopic measurement of the friction coefficient and have found its dramatic decrease with slight opacity near the critical point [86]. We conjecture that such a large anomaly was caused by stationary domain structures with large spatial scales and not by the thermal fluctuations decaying diffusively. 

The existence of the (quasi) steady-state in the model of particle accumulation (particle creation corresponds to the reaction reversibility) makes its analogy with dense gases or liquids quite convincing. However, it is also useful to treat the possibility of the pattern formation in the A + B —> 0 reaction without particle source. Indeed, the formation of the domain structure here in the diffusion-controlled regime was also clearly demonstrated [17]. Similar patterns of the spatial distributions were observed for the irreversible reactions between immobile particles - Fig. 1.20 [25] and Fig. 1.21 [26] when the long range (tunnelling) recombination takes place (recombination rate a(r) exponentially depends on the relative distance r and could... 

This progress is mainly due to the determination of the amino-acid sequences for all members of this group and the X-ray crystal structure of ascorbate oxidase. The three-dimensional structure of ascorbate oxidase showed the nature and spatial arrangement of the copper centers and the three-domain structure. However, modern spectroscopic techniques (e.g., low-temperature MCD and ENDOR) made invaluable contributions as well. 

One limitation, however, is that only a limited number of spots can be measured simultaneously. A compromise between the temporal analysis of FCS and fluorescence fluctuation analysis in the spatial domain [39] can be obtained by exploiting the time structure of sample/laser scanning confocal microscope images [40,41]. Thereby, spatial correlation analysis of the emitted fluorescence is combined with temporal characterization of the fluorescence emission from the serial data stream of subsequently scanned pixels. This... 

In general, chiral nematic polymer liquid crystals (LCP) cannot form monodomains in which the rodlike polymers have a spatially uniform orientation within the sample. Typically, because of the high density of orientational defects, the LCPs are textured, with a distribution of polymer orientation. Microscopically, the polymer chains have a preferred orientation with a relatively narrow distribution around the average orientation. Macroscopically, the variation in space of the orientation results in a domain structure. Defects and orientational variations give rise to the polydomain texture and the overall LCP sample may be randomly ordered (Fig. 3). 

Condensed matter phases and structures are commonly reached via symmetry breaking transitions. In such systems, when the continuous symmetry is broken, temporary domain-t5q)e patterns are formed. The domain structures eventually coarsen, and disappear in the long-time limit, leaving a uniform broken-symmetry state. This state possesses so-called long-range order (LRO), in which the spatially dependent order parameter correlation function does not decay to zero in the limit of large distances. 

Protein domains, the next level up in the hierarchy of protein constitution, are important enough to warrant a separate discussion. Domains can be defined based on function, structure, or sequence characterization in many cases the different approaches are compatible. We naturally adopt a structure-based definition a protein domain is a spatially distinct structure (or structural component) that could conceivably fold and function in isolation [63]. Some proteins consist of a single domain, while others are composed of multiple domains each folded separately from a subsection of the underlying amino acid chain. To this point, our notion of the genotype to phenotype relationship has been protein sequence protein structure. Given the discrete spatial nature of domains, protein SM sequence -> domain would be an equally valid definition. In fact, the notion of a protein fold (as in, "this fold is highly designable") translates naturally to the protein domain concept. 

Proteins often display substantial similarity in sequence and 3D stmcture, since many are derived from a basic complement of autonomously folding units (domains). This allows us to group proteins into a hierarchy of families, superfamilies and folds. Domains within protein structures are defined as spatially distinct structures that could conceivably fold and function in isolation. The concept of fold thus allows grouping of related structures for descriptive purposes and simplifies problems related to (he encoding of structure in primary sequences. 

Figure 7.15. Radiation and nonradiation (near-field) fields arising in the magnetic film with the domain structure. Only near-field spatial harmonics radiated from the surface layer of several hundredths of a micrometer can reach the probe.

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