Defects, topological

Figure C3.6.10 Defect-mediated turbulence in tire complex Ginzburg-Landau equation, (a) The phase, arg( ), as grey shades, (b) The amplitude [A], witli a similar color coding. In tire left panel topological defects can be identified as points around which one finds all shades of grey. Note tire apparently random spatial pattern of amplitudes.

J. Dzubiella, M. Schmidt, H. Lowen. Microstructure of topological defects in nematic droplets (submitted). 

Halperin, B.I. Statistical Mechanics of topological defects, edited by R. Balian, N. Kleman, and J.-P. Poirer (North Holland, Amsterdam, 1981. 

Abstract. We review the recent development of quantum dynamics for nonequilibrium phase transitions. To describe the detailed dynamical processes of nonequilibrium phase transitions, the Liouville-von Neumann method is applied to quenched second order phase transitions. Domain growth and topological defect formation is discussed in the second order phase transitions. Thermofield dynamics is extended to nonequilibrium phase transitions. Finally, we discuss the physical implications of nonequilibrium processes such as decoherence of order parameter and thermalization. 

Keywords Nonequilibrium phase transitions, Liouville-von Neumann approach, domain growth, topological defect formation. 

Now we study the effects of the dynamical processes of nonequilibrium phase transitions on domain growth and topological defects. The quench models describe such nonequilibrium processes, which can be... 

Topological defects describe the presence of rings other than hexagons, i.e. pentagons (n5) and heptagons (n7), which result in kinks and elbows in the usu-... 

In general, differences in chemical bonding and electron configuration between carbon atoms and dopants mandate the deviation from the geometric and electronic equilibrium structure of the aromatic layers in CNTs. As a consequence, topological defects such as Stone-Wales defects are formed with increased probability [37]. 

Defects in carbon nanostructures can be classified into (a) structural defects, (b) topological defects, (c) high curvature and (d) non-sp2 carbon defects. Even slight changes within the carbon nanostructure can modify the chemical and physical properties. Some defects in carbon systems results in high chemical reactivity, mainly due to the accumulation of electrons in the vicinity of the dopant. These defects can be used as anchoring sites in order to make the carbon nanostructures more compatible with ceramic or polymer matrices, thus enhancing interactions between carbon structures (filler) and the host matrices. 

J. C. Meyer, C. Kisielowski, R. Erni, M. D. Rosseii, M. F. Crommie, A. Zetti, Direct imaging of lattice atoms and topological defects in graphene membranes, Nano Lett., vol. 8, pp. 3582-3586, 2008. 

Defects in MWCNTs are always present. We can briefly differentiate between topological defects which lead to rehybridization (C5 and C7 rings instead of C6 lead to rehybridization between sp2 and sp3) and incomplete bonding defects (vacancies, dislocation) (Fig. 16.2). Functionalization or doping with heteroelements may add further modifications with respect to the ideal ordered structure, but are also the sites which allow for anchoring supported metals or metal oxides, or to functionalize the CNTs with organic groups. 

Fig. 16.2 TEM image of a CNT with indications of topological defects and vacancies. Reproduced with permission from Wiley VCH (2011) [7].

At the late stage of lamella orientation, classical topological defects (dislocations and disclinations) dominate [40, 41] (Fig. 8h and Fig. 9), and their movement and annihilation can be followed in Fig. 8h-i and Fig. 9. The latter presents an example of the apparent topological defect interactions and their transformations. Displayed are two dislocations of PMMA, which have an attractive interaction due to their opposite core sign. Therefore, in the next annealing step the dislocation is shifted... 

Fig. 22 Simulated images (upper panel) and SFM phase images (300 x 300 nm) (lower panel) presenting classical topological defect configurations in lying cylinders (a, e) cyl-dislocation (b, f) m-dislocation (c, g) +1/2 cyl-disclination and (d, h) +1/2 m-disclination. SB films were annealed under 70% of the saturated vapor pressure of chloroform. Reprinted from [36], with permission. Copyright 2008 American Chemical Society...

Contrarily to the flatness and horizon problem which have a very similar origin, the unwanted relic problem comes from a very different cause. During the expansion, the Universe becomes colder because of the redshift that radiation experiences. It can happen that during this cooling phase, some phase transition occur, during which some stable objects called topological defects are created. 

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