US EPA

623226 

Journal Article 

Asymptotic analysis of phase field formulations of bending elasticity models 

Xiaoqiang, W 

2008 

39 

5 

1367-1401 

In this paper, we give the asymptotic analysis of sharp interface analysis of the phase field function in some phase field models for Willmore's problem and equilibrium lipid bilayer cell membrane problems. We derive the explicit expression of the asymptotic expansion of the phase field functions minimizing the Willmore energy. Based on the structure of the phase field functions obtained via the asymptotic analysis, we can then demonstrate the consistency of phase field models and the sharp interface models. Also some error estimates of energy and Euler number formulae are further analyzed. Some numerical experiments are performed to verify our assumptions and results. The results of this paper lead to a better understanding of the structure of the phase field functions in the phase field models for Willmore's problem and the equilibrium configurations of the lipid vesicle membranes. [ABSTRACT FROM AUTHOR] Copyright of SIAM Journal on Mathematical Analysis is the property of Society for Industrial and Applied Mathematics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts) 

ELASTICITY; FORCE & energy; LIPID membranes; ASYMPTOTIC expansions; SPECTRUM analysis; SIMULATION methods; APPROXIMATION theory; approximation; asymptotic expansion; elastic bending energy; numerical simulation; phase field; spectral method; Willmore's problem