title: Pattern formation by phase-field relaxation of bending energy with fixed surface area and volume.
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.
authors.affiliation: West Virginia Wesleyan College, 59 College Ave, Buckhannon, West Virginia 26201, USA.
authors.forename: Timothy
authors.initials: T
authors.lastname: Banham
authors.affiliation: 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.
authors.forename: Bo
authors.initials: B
authors.lastname: Li
authors.affiliation: Department of Mathematics, George Washington University, Washington, DC 20052, USA.
authors.forename: Yanxiang
authors.initials: Y
authors.lastname: Zhao
mesh_terms: D055595:Mechanical Phenomena; D008958:Models, Molecular; D008968:Molecular Conformation; D013499:Surface Properties; D013816:Thermodynamics