 
Qiang's research Gallery 5
Elastic vesicle membrane, cell deformation 

The usual vesicle membranes are formed by bilayers of lipid molecules. These lipid membranes exist everywhere in life and compartmentalize living matter into cells and subcellular structures and present themselves as highly structured interfaces which are essential for many biological functions  The equilibrium shapes of bilayer vesicle membranes have been successfully modeled via the minimization of certain shape energy such as the elastic bending energy. Recently, we have developed effective phase field bending elasticity models and simulation tools for such problems. 
Twinbubble  discocytes  

stomatocytes  torus  
Herseykiss  dupincyclide 
Some references:
Some slides,
Slide 1
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Slide 2
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Slide 3
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Slide 4
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Slide 5
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Slide 6
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A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
by Q. Du, C. Liu and X. Wang,
J. Computational
Physics, 198, pp450468, 2004
A phase field formulation of the Willmore problem
,
by Q. Du, C. Liu, R. Ryham and X. Wang,
Nonlinearity, 18, pp.12491267, 2005.
Retrieving Topological Information for Phase Field Models
by Q. Du, C. Liu, and X. Wang,
SIAM J. Appl. Math,
65, pp. 19131932, 2005
Modeling the spontaneous curvature effects in static cell membrane deformations by a phase field formulation
by Q. Du, C. Liu, R. Ryham and X. Wang,
Comm Pure Appl Anal, 4, pp.537548, 2005
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
by Q. Du, C. Liu, and X. Wang,
J.
Computational Phys., 212, pp.757777, 2005
Modeling Vesicle Deformations in Flow Fields via Energetic Variational Approaches
by Q. Du, C. Liu, R. Ryham and X. Wang, submitted for publication, 2005
Analysis of a Mixed Finite Element Method for a Phase Field Bending Elasticity Model of Vesicle Membrane Deformation
by Q. Du and L. Zhu,
J. Computational Math., 24, pp.265280, 2006.
Convergence of numerical approximations to a phase field bending elasticity model of membrane deformations
by Q. Du and X. Wang,
Inter. J. Numer. Anal and Modeling, 4, pp.441459, 2007.
Analysis of a Phase Field NavierStokes
VesicleFluid Interaction Model,
by Q. Du, M. Li and C. Liu,
Disc.
Cont. Dyn. Sys. B, 8, No3, pp.539556, 2007
Modelling and Simulations of Multicomponent Lipid
Membranes and Open Membranes via Diffusive Interface
Approaches,
by X. Wang and Q. Du,
J.
Mathematical Biology, 56, no3, pp.347371, 2008
Adaptive Finite Element
Method for a Phase Field Bending Elasticity Model
of Vesicle Membrane Deformations,
by Q. Du and J. Zhang,
SIAM J. Sci. Comp.,
30, no3, pp.16341657, 2008
Adhesion of vesicles to curved substrates,
by S. Das and Q. Du,
Phys.
Rev. E, 77, 011907(17), 2008
A phase field model for vesiclesubstrate adhesion,
by J. Zhang, S. Das and Q. Du,
J. Computational Phys.
, 228, pp.78377849, 2009
Adhesion of
Multicomponent Vesicle Membranes
,
by Y. Zhao, S. Das and Q. Du,
Phys. Rev. E, 81, 041919, 2010
(Selected for the May 1, 2010 issue of Virtual Journal of Biological Physics Research).
A
Diffuse Interface Model of Multicomponent Vesicle Adhesion
and Fusion
,
by Y. Zhao and Q. Du,
Physical Rev E, 84, pp.011903, 2011.
Phase
field calculus, curvaturedependent energies, and vesicle
membranes
, by Q. Du,
Philosophical Magazine, 91, pp.165181, 2011
Slides at IMA summer school 2013
Lectures part I
Lectures part II
Lectures part III
Contact Qiang Du 20030408