منابع مشابه
Hexagonal circle patterns and integrable systems. Patterns with constant angles
The theory of circle packings and, more generally, of circle patterns enjoys in recent years a fast development and a growing interest of specialists in complex analysis and discrete mathematics. This interest was initiated by Thurston’s rediscovery of the Koebe-Andreev theorem [K] about circle packing realizations of cell complexes of a prescribed combinatorics and by his idea about approximat...
متن کاملPropagation of hexagonal patterns near onset
ARJEN DOELMAN, BJÖRN SANDSTEDE , ARND SCHEEL 3 and GUIDO SCHNEIDER 4 1 Korteweg–de Vries Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands 2 Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, USA 3 Department of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, MN ...
متن کاملHexagonal convection patterns in atomistically simulated fluids.
Molecular dynamics simulation has been used to model pattern formation in three-dimensional Rayleigh-Bénard convection at the discrete-particle level. Two examples are considered, one in which an almost perfect array of hexagonally shaped convection rolls appears, the other a much narrower system that forms a set of linear rolls; both pattern types are familiar from experiment. The nature of th...
متن کاملPenta-hepta defect motion in hexagonal patterns.
The structure and dynamics of penta-hepta defects (PHD’s) in hexagonal patterns are studied in the framework of coupled amplitude equations for the underlying plane waves. An analytical solution for the phase field of moving PHD is found in the far field, which generalizes the static solution due to Pismen and Nepomnyashchy. The mobility tensor of the PHD is calculated using a combined analytic...
متن کاملThe Eckhaus instability in hexagonal patterns
The Eckhaus instability of hexagonal patterns is studied within the model of three coupled envelope equations for the underlying roll systems. The regions of instability in the parameter space are found analytically from both the phase approximation and a full system of amplitude equations. Beyond the stability limits of hexagons two different modes go unstable. Both provide symmetry breaking o...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 2009
ISSN: 1347-4081,0033-068X
DOI: 10.1143/ptp.121.29