Commun. Comput. Phys.,
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Volume 3.

Numerical Simulation of Fluid Membranes in Two-Dimensional Space

Peng Song 1*, Dan Hu 1, Pingwen Zhang 1

1 LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China.

Received 17 May 2007; Accepted (in revised version) 9 October 2007
Available online 11 December 2007


The membrane's dynamics is very important for cells. A membrane in 2-dimensional space can be seen as an incompressible closed curve in a plane or a cylindrical surface in 3-dimensional space. In this paper, we design a second-order accurate numerical algorithm to simulate the shape transformation of the membrane. In the algorithm, we use the tangent angles to present the curve and avoid the difficulties from the constraint of curve's incompressible condition. A lot of interesting phenomena are obtained. Some of them are very like the life processes of cells, such as exocytosis and endocytosis. Furthermore, we can see the relation between two dynamic models clearly. At last, considering the influence of the inner incompressible fluids partially, we add a constraint: the area circled by the membrane maintain invariable. The numerical results show the dynamic motions of a curve remaining its local arc length and inner area constant.

AMS subject classifications: 65M06, 65M12, 92C17

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Key words: Director model of the membrane, reduced model, osmotic pressure, spontaneous curvature, constraint of the area.

*Corresponding author.
Email: (P. Song), (D. Hu), (P. W. Zhang)

The Global Science Journal