VesicleForms.jl

Shapes of axisymmetric Vesicles can be computed by solving the corresponding shape equations using DifferentialEquations.jl.

Installation

• Download the latests stable release of julia from https://www.julialang.org
• Start the julia executable to enter the REPL
• Add this package via:

using Pkg
Pkg.add("https://gitlab.gwdg.de/PhD/VesiclesForms.jl/")

Usage

Solving the shape equations for a known solution can be done via ODEsolve:

using Plots, VesicleForms
vesicle = VesicleForms.prolate0_7 # the package comes with a bunch of vesicle prototypes
tspan = (0.0,1.0) # The arc-length is scaled to be in [0,1]
sol = ODEsolve(vesicle, tspan) # return a ODESolution
plot(sol)

For finding new solutions the shooting method can be used via ODEshoot_root! powered by NLsolve.jl:

vesicle = copy(VesicleForms.prolate0_7) # copy, since `ODEshoot_root!` is mutating
vesicle.v = 0.695
tspan = (0.0,1.0)
ODEshoot_root!(vesicle, (0.0,1.0), ftol = 1e-12)
plot(vesicle)

Further examples can be found in the scripts folder.

Visualization

This package provides a Vesicle type with defined plot recipes for convenient visualization via Plots.jl:

using Plots, VesicleForms
vesicle = VesicleForms.sphere()
plot(vesicle) # displays the contour of the vesicle by default