A Double Bubble Assembly as a New Phase of a Ternary Inhibitory System
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| 024 | 7 | 0 | |a 10.1007/s00205-014-0798-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-014-0798-x | ||
| 245 | 0 | 2 | |a A Double Bubble Assembly as a New Phase of a Ternary Inhibitory System |h [Elektronische Daten] |c [Xiaofeng Ren, Juncheng Wei] |
| 520 | 3 | |a A ternary inhibitory system is a three component system characterized by two properties: growth and inhibition. A deviation from homogeneity has a strong positive feedback on its further increase. In the meantime a longer ranging confinement mechanism prevents unlimited spreading. Together they lead to a locally self-enhancing and self-organizing process. The model considered here is a planar nonlocal geometric problem derived from the triblock copolymer theory. An assembly of perturbed double bubbles is mathematically constructed as a stable stationary point of the free energy functional. Triple junction, a phenomenon in which the three components meet at a single point, is a key issue addressed in the construction. Coarsening, an undesirable scenario of excessive growth, is prevented by a lower bound on the long range interaction term in the free energy. The proof involves several ideas: perturbation of double bubbles in a restricted class; use of internal variables to remove nonlinear constraints, local minimization in a restricted class formulated as a nonlinear problem on a Hilbert space; and reduction to finite dimensional minimization. This existence theorem predicts a new morphological phase of a double bubble assembly. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 700 | 1 | |a Ren |D Xiaofeng |u Department of Mathematics, The George Washington University, 20052, Washington, DC, USA |4 aut | |
| 700 | 1 | |a Wei |D Juncheng |u Department of Mathematics, University of British Columbia, V6T 1Z2, Vancouver, BC, Canada |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 215/3(2015-03-01), 967-1034 |x 0003-9527 |q 215:3<967 |1 2015 |2 215 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-014-0798-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-014-0798-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ren |D Xiaofeng |u Department of Mathematics, The George Washington University, 20052, Washington, DC, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Wei |D Juncheng |u Department of Mathematics, University of British Columbia, V6T 1Z2, Vancouver, BC, Canada |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 215/3(2015-03-01), 967-1034 |x 0003-9527 |q 215:3<967 |1 2015 |2 215 |o 205 | ||