Pattern formation by phase-field relaxation of bending energy with fixed surface area and volume

Timothy Banham, Bo Li, and Yanxiang Zhao
Phys. Rev. E 90, 033308 – Published 17 September 2014

Abstract

We explore a wide variety of patterns of closed surfaces that minimize the elastic bending energy with fixed surface area and volume. To avoid complicated discretization and numerical instabilities for sharp surfaces, we reformulate the underlying constrained minimization problem by constructing phase-field functionals of bending energy with penalty terms for the constraints and develop stable numerical methods to relax these functionals. We report our extensive computational results with different initial surfaces. These results are discussed in terms of the reduced volume and are compared with the known results obtained using the sharp-interface approach. Finally, we discuss the implications of our numerical findings.

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  • Received 6 December 2013
  • Revised 28 July 2014

DOI:https://doi.org/10.1103/PhysRevE.90.033308

©2014 American Physical Society

Authors & Affiliations

Timothy Banham*

  • West Virginia Wesleyan College, 59 College Ave, Buckhannon, West Virginia 26201, USA

Bo Li

  • Department of Mathematics and Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, MC 0112, La Jolla, California 92093-0112, USA

Yanxiang Zhao

  • Department of Mathematics, George Washington University, Washington, DC 20052, USA

  • *banham_t@wvwc.edu
  • bli@math.ucsd.edu
  • yxzhao@email.gwu.edu

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Vol. 90, Iss. 3 — September 2014

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