Numerical simulation of the dynamics of fluid membranes
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Inclou dades d'ús des de 2022
Cita com:
hdl:2099.1/8380
Tipus de documentProjecte Final de Màster Oficial
Data2008-07
Condicions d'accésAccés obert
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continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
The goal of this project is to explore the mechanics of lipid fluid membranes as
found in biological and made-man systems through continuum models and numerical
simulations. Traditionally, the focus has been on the equilibrium configurations of
vesicles through minimization of the curvature energy subject to constraints. Here,
the goal is to describe the time-evolution of out-of-equilibrium vesicle configurations,
which are of relevance in biological systems. Towards this goal, an accurate description
of the dissipative mechanisms is crucial, in particular the viscous dissipation
induced by the 2D flow of lipids on the deforming surface that describes a vesicle [1].
The resulting equations can only be solved analytically in very simple settings. So the
problem is solved numerically using a B-Spline description of the membrane vesicle.
The dynamics are described using two types of viscosity: the L2 or Willmore viscosity
and the inner flow viscosity. By comparing the evolution in time of the two systems, it
is stated that the dynamics are clearly different. It is found that one describes better
the physics of the system.
Col·leccions
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00.pdf | Memoria | 7,244Mb | Visualitza/Obre |