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March 2007 Diffuse Interface Energies Capturing the Euler Number: Relaxation and Renomalization
Qiang Du, Chun Liu, Rolf Ryham, Xiaoqiang Wang
Commun. Math. Sci. 5(1): 233-242 (March 2007).


We introduce a set of new interfacial energies for approximating the Euler number of level surfaces in the phase field (diffuse-interface) representation. These new formulae have simpler forms than those studied earlier in Q. Du, C. Liu and X. Wang, Retrieving topological information for phase field models, and do not contain higher order derivatives of the phase field function. Theoretical justifications are provided via formal asymptotic analysis, and practical validations are performed through numerical experiments. Relaxation and renormalization schemes are also developed to improve the robustness of the new energy functionals.


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Qiang Du. Chun Liu. Rolf Ryham. Xiaoqiang Wang. "Diffuse Interface Energies Capturing the Euler Number: Relaxation and Renomalization." Commun. Math. Sci. 5 (1) 233 - 242, March 2007.


Published: March 2007
First available in Project Euclid: 5 April 2007

zbMATH: 1136.74007
MathSciNet: MR2310641

Primary: 57M50 , 74A50 , 74S99 , 92C05

Keywords: bending energy , diffuse interface , Euler number , implicitly defined surfaces , interfacial energy , phase field , Surface tension , topological index , vesicle membrane

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 1 • March 2007
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