A diagrammatic derivation of (convective) pattern equations

2011 ◽  
Vol 240 (2) ◽  
pp. 150-165 ◽  
Author(s):  
Y.-P. Ma ◽  
E.A. Spiegel
Keyword(s):  
2017 ◽  
Vol 35 (2) ◽  
pp. 98s-102s ◽  
Author(s):  
Van Anh Nguyen ◽  
Shinichi Tashiro ◽  
Bui Van Hanh ◽  
Manabu Tanaka

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1309-1316 ◽  
Author(s):  
Roland Zander ◽  
Michael Dittmann ◽  
Gerhard M. Schneider

AbstractThe demixing of a horizontal fluid layer of far-critical composition in the presence of a vertical temperature gradient can cause the formation of dissipative structures and thereby lead to a regular distribution of the precipitate. The occurrence of these convective structures is explained with the model of a Rayleigh-Benard instability (RBI) which is driven by parallel gradients of temperature and concentration. The distribution of the precipitate is a synergetic effect of the macroscopic convective pattern and the local action of the Marangoni flow at the surfaces of the drops. If boundary conditions prohibit an RBI, the distribution of the precipitate also becomes inhomogeneous in course of time; however, in this case no regular pattern is observable and the inhomogeneities develop mainly due to the Marangoni convection near the surfaces of the larger drops that have settled at the boundary of the sample volume


1987 ◽  
Vol 4 (2) ◽  
pp. 253-253 ◽  
Author(s):  
A Pocheau ◽  
V Croquette ◽  
P. Le Gal ◽  
C Poitou

1976 ◽  
Vol 13 (2) ◽  
pp. 331-340 ◽  
Author(s):  
E. R. Kanasewich

A series of azimuthal–equidistant map projections, centered on each of the plates of lithosphere, is used to demonstrate the high degree of ordering and symmetry in the major plates. The Pacific and African plates are approximately circular with a radius of 60°. The entire pattern is dominated by these two major plates, exactly antipodal to one another in the form of a dipole. Between the two 'circular' plates is a ring of elliptical plates with irregular boundaries but a organized geometric interrelationship. The average major and minor axes of the 'elliptical' plates, measured at the center of the earth, are 62° ± 6 °and 30° ± 5°, and the major axes are oriented at angles of 56° ± 3 °to lines joining the center of the African plate. The centers of the 'elliptical' plates are arranged within 6° ± 3 °of a great circle path through the North pole. This organized distribution of the major plates is most likely the result of convection currents involving the entire mantle, from the lithosphere to the core. To a first approximation, the convective pattern may be modelled by a superposition of third order spherical harmonics, P03, P13, and P23 in a pattern that regressed from a first spherical harmonic, −P01.


1992 ◽  
Vol 55 (3-4) ◽  
pp. 287-308 ◽  
Author(s):  
F. Daviaud ◽  
J. Lega ◽  
P. Bergé ◽  
P. Coullet ◽  
M. Dubois

1987 ◽  
Vol 56 (2) ◽  
pp. 502-505 ◽  
Author(s):  
Hideki Yamazaki ◽  
Shoichi Kai ◽  
Kazuyoshi Hirakawa

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