Deformed foam structure and transitions in a tube |
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Authors: | D Reinelt P Boltenhagen N Rivier |
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Institution: | (1) Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA, US;(2) Laboratoire de Dynamique des Fluides Complexes, UMR 7506, 3 rue de l'Université, F-67084, Strasbourg Cedex, France, FR |
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Abstract: | The “staircase” (2,1,1) foam structure in an ordered foam under expansion in a cylindrical tube and the structural transition
to the “bamboo” (1,1,0) structure are studied experimentally, analytically, and numerically using the Surface Evolver minimization
program. An analytical expression of the oblique interface in the (2,1,1) structure, a minimal surface, but curved by stretching
of the foam, is given as a classic example of singular perturbation (boundary layer) theory. The structural transition from
staircase structure to bamboo structure takes place at a considerable dilation. The transition is not due to an edge length
tending to zero continuously with dilation, but results from the equilibrium (2,1,1) solution losing its stability due to
a saddle node bifurcation.
Received 3 August 2000 |
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Keywords: | PACS 61 72 -y Defects and impurities in crystals microstructure – 63 70 +h Statistical mechanics of lattice vibrations and displacive phase transitions – 02 30 Mv Approximations and expansions |
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