4,329 research outputs found
Shape instabilities in vesicles: a phase-field model
A phase field model for dealing with shape instabilities in fluid membrane
vesicles is presented. This model takes into account the Canham-Helfrich
bending energy with spontaneous curvature. A dynamic equation for the
phase-field is also derived. With this model it is possible to see the vesicle
shape deformation dynamically, when some external agent instabilizes the
membrane, for instance, inducing an inhomogeneous spontaneous curvature. The
numerical scheme used is detailed and some stationary shapes are shown together
with a shape diagram for vesicles of spherical topology and no spontaneous
curvature, in agreement with known results
Toroidal membrane vesicles in spherical confinement
We investigate the morphology of a toroidal fluid membrane vesicle confined
inside a spherical container. The equilibrium shapes are assembled in a
geometrical phase diagram as a function of scaled area and reduced volume of
the membrane. For small area the vesicle can adopt its free form. When
increasing the area, the membrane cannot avoid contact and touches the
confining sphere along a circular contact line, which extends to a zone of
contact for higher area. The elastic energies of the equilibrium shapes are
compared to those of their confined counterparts of spherical topology to
predict under which conditions a topology change is favored energetically.Comment: 16 pages, 7 figure
Front Propagation in the Pearling Instability of Tubular Vesicles
Recently Bar-Ziv and Moses discovered a dynamical shape transformation
induced in cylindrical lipid bilayer vesicles by the action of laser tweezers.
We develop a hydrodynamic theory of fluid bilayers in interaction with the
surrounding water and argue that the effect of the laser is to induce a sudden
tension in the membrane. We refine our previous analysis to account for the
fact that the shape transformation is not uniform but propagates outward from
the laser trap. Applying the marginal stability criterion to this situation
gives us an improved prediction for the selected initial wavelength and a new
prediction for the propagation velocity, both in rough agreement with the
experimental values. For example, a tubule of initial radius 0.7\micron\ has a
predicted initial sinusoidal perturbation in its diameter with wavelength
5.5\micron, as observed. The perturbation propagates as a front with the
qualitatively correct front velocity a bit less than 100\micron/sec. In
particular we show why this velocity is initially constant, as observed, and so
much smaller than the natural scale set by the tension. We also predict that
the front velocity should increase linearly with laser power. Finally we
introduce an approximate hydrodynamic model applicable to the fully nonlinear
regime. This model exhibits propagating fronts as well as fully-developed
``pearled" vesicles similar to those seen in the experiments.Comment: 42 pages, 6 eps figures included with text in uuencoded file, ps file
available from ftp://dept.physics.upenn.edu/pub/Nelson/pearl_propagation.ps
submitted to Journal de Physiqu
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