Volume 1, Issue 2
A Front-Tracking Method for Motion by Mean Curvature with Surfactant
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Adv. Appl. Math. Mech., 1 (2009), pp. 288-300.

Published online: 2009-01

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• Abstract

In this paper, we present a finite difference method to track a network of curves whose motion is determined by mean curvature. To study the effect of inhomogeneous surface tension on the evolution of the network of curves, we include surfactant which can diffuse along the curves. The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve. Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network. Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network, including the von Neumann law for cell growth in two space dimensions.

• Keywords

Front-tracking method motion by mean curvature triple-junction surface tension surfactant

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@Article{AAMM-1-288, author = {}, title = {A Front-Tracking Method for Motion by Mean Curvature with Surfactant}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {2}, pages = {288--300}, abstract = {

In this paper, we present a finite difference method to track a network of curves whose motion is determined by mean curvature. To study the effect of inhomogeneous surface tension on the evolution of the network of curves, we include surfactant which can diffuse along the curves. The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve. Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network. Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network, including the von Neumann law for cell growth in two space dimensions.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/8370.html} }
TY - JOUR T1 - A Front-Tracking Method for Motion by Mean Curvature with Surfactant JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 288 EP - 300 PY - 2009 DA - 2009/01 SN - 1 DO - http://dor.org/ UR - https://global-sci.org/intro/aamm/8370.html KW - Front-tracking method KW - motion by mean curvature KW - triple-junction KW - surface tension KW - surfactant AB -

In this paper, we present a finite difference method to track a network of curves whose motion is determined by mean curvature. To study the effect of inhomogeneous surface tension on the evolution of the network of curves, we include surfactant which can diffuse along the curves. The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve. Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network. Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network, including the von Neumann law for cell growth in two space dimensions.

Ming-Chih Lai, Che-Wei Hsu & Huaxiong Huang. (1970). A Front-Tracking Method for Motion by Mean Curvature with Surfactant. Advances in Applied Mathematics and Mechanics. 1 (2). 288-300. doi:
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