Spatially modulated structures domains

The physical origin of these phenomena could be explained by faster response times of the modulated structures, as compared with uniform ones. When the equilibrium director distribution is approached, i.e., a relaxation process is over, the transient structures disappear. The emergence and subsequent evolution of the spatial periodicity of the transient structures were considered theoretically in [26] for different domain orientations with respect to the initial homogeneous and twisted director structure. 

References [59] investigate the static and dynamic behavior of the electrohydrodynamic instability in fireely suspended layers of nematic liquid crystals. The existence of a domain mode was shown, which consists of adjacent elongated domains with a spatial period proportional to the thickness of the layer. This mode occurs only if the thickness of the layer exceeds a critical value 7 /x), and can be understood in terms of the same anisotropic mechanism as the Carr-Helfrich-type, as in the case of the Kapustin-WiUiams modulated structure. 

Nanostructured materials are characterized by ordered structural domains,at the level of nanometers (7). These materials display the properties of condensed matter without a long range order. In general, four types of such materials based on the integral modulation dimensionalities of zero (nanoconfined particles), one (linear tunnel or channel structures two (multilayers) and three (nanophases) are possible (2). The simplest nanostructured materials are the nanoconfined systems of zero modulation dimensionality which consist of a host matrix with a nm-size spatial cavity that can act as an enclosure for dopant molecular particles. The nanostructured materials obtained by encapsulation of biological macromolecules in sol-gel derived porous Si02 structures that contain a trapped bioparticle represent a particularly novel and recent example in this category (5-4). 

Abstract Pattern formation is a widespread phenomenon observed in different physical, chemical and biological systems on varions spatial scales, including the nanometer scale. In this chapter discussed are the universal features of pattern formation pattern selection, modulational instabilities, structure and dynamics of domain walls, fronts and defects, as well as non-potential effects and wavy patterns. Principal mathematical models used for the description of patterns (Swift-Hohenberg equation, Newell-Whitehead-Segel equation, Cross-Newell equation, complex Ginzburg-Landau equation) are introduced and some asymptotic methods of their analysis are presented. 

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