Volume 3, Issue 4
Numerical Simulation of Fluid Membranes in Two-Dimensional Space

Peng Song, Dan Hu & Pingwen Zhang

DOI:

Commun. Comput. Phys., 3 (2008), pp. 794-821.

Published online: 2008-03

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  • Abstract

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.

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@Article{CiCP-3-794, author = {}, title = {Numerical Simulation of Fluid Membranes in Two-Dimensional Space}, journal = {Communications in Computational Physics}, year = {2008}, volume = {3}, number = {4}, pages = {794--821}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7875.html} }
TY - JOUR T1 - Numerical Simulation of Fluid Membranes in Two-Dimensional Space JO - Communications in Computational Physics VL - 4 SP - 794 EP - 821 PY - 2008 DA - 2008/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7875.html KW - AB -

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.

Peng Song, Dan Hu & Pingwen Zhang. (2020). Numerical Simulation of Fluid Membranes in Two-Dimensional Space. Communications in Computational Physics. 3 (4). 794-821. doi:
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