3 research outputs found
A scalar auxiliary variable unfitted FEM for the surface Cahn-Hilliard equation
The paper studies a scalar auxiliary variable (SAV) method to solve the
Cahn-Hilliard equation with degenerate mobility posed on a smooth closed
surface {\Gamma}. The SAV formulation is combined with adaptive time stepping
and a geometrically unfitted trace finite element method (TraceFEM), which
embeds {\Gamma} in R3. The stability is proven to hold in an appropriate sense
for both first- and second-order in time variants of the method. The
performance of our SAV method is illustrated through a series of numerical
experiments, which include systematic comparison with a stabilized
semi-explicit method.Comment: 23 pages, 12 figure
A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow
The paper considers a thermodynamically consistent phase-field model of a
two-phase flow of incompressible viscous fluids. The model allows for a
non-linear dependence of fluid density on the phase-field order parameter.
Driven by applications in biomembrane studies, the model is written for
tangential flows of fluids constrained to a surface and consists of (surface)
Navier-Stokes-Cahn-Hilliard type equations. We apply an unfitted finite element
method to discretize the system and introduce a fully discrete time-stepping
scheme with the following properties: (i) the scheme decouples the fluid and
phase-field equation solvers at each time step, (ii) the resulting two
algebraic systems are linear, and (iii) the numerical solution satisfies the
same stability bound as the solution of the original system under some
restrictions on the discretization parameters. Numerical examples are provided
to demonstrate the stability, accuracy, and overall efficiency of the approach.
Our computational study of several two-phase surface flows reveals some
interesting dependencies of flow statistics on the geometry.Comment: 22 pages, 5 figures, 1 tabl
On fusogenicity of positively charged phased-separated lipid vesicles: experiments and computational simulations
This paper studies the fusogenicity of cationic liposomes in relation to
their surface distribution of cationic lipids and utilizes membrane phase
separation to control this surface distribution. It is found that concentrating
the cationic lipids into small surface patches on liposomes, through
phase-separation, can enhance liposome's fusogenicity. Further concentrating
these lipids into smaller patches on the surface of liposomes led to an
increased level of fusogenicity. These experimental findings are supported by
numerical simulations using a mathematical model for phase-separated charged
liposomes. Findings of this study may be used for design and development of
highly fusogenic liposomes with minimal level of toxicity