1. PHASE FIELD MODELS AND SIMULATIONS OF VESICLE BIO-MEMBRANES Open Access Author: Wang, Xiaoqiang Title: PHASE FIELD MODELS AND SIMULATIONS OF VESICLE BIO-MEMBRANES Graduate Program: Mathematics Keywords: Vesicle membraneelastic bending energyenergetic variational approachdiffusive interface approximationphase field modelnumerical methodsthree dimensional simulationNavier-Stokes equation File: Download bubble.pdf Committee Members: Qiang Du, Committee Chair/Co-ChairChun Liu, Committee MemberLudmil Tomov Zikatanov, Committee MemberHongyuan Zha, Committee Member