VesicleForms.jl

Basic data structure to hold all parameters that uniquely define a vesicle.

• spont_curvature::Real

• area::Real

• volume::Real

• parameters::Array{F,1} where F<:Real

  these parameters are: osmotic pressure, surface tension, s-pole curvature, n-pole curvature, arc length

• red_volume::Real

• bend_rigidity::Real

Finds the best parameters of the vesicle using root-finding.

ODEshoot_root!(vesicle, tspan)
ODEshoot_root!(vesicle, tspan, residual; solver, kwargs...)

Positional arguments

• vesicle : input vesicle (gets mutated)
• tspan : the interval of the arclength to integrate over, typically (0.0, 1.0)
• residual: function that calculates the residual for the root-finding algorithm (root_residualAV)

Keyword arguments

• solver : Currently supported solvers are :nlsolve and :minpack (:nlsolve)
• additional keywords are passed to the solver routine

ODEshoot_root!(, vesicle, tspan)
ODEshoot_root!(, vesicle, tspan, residual; res_options, kwargs...)

Alter the parameters using root-finding with NLsolve.nlsolve. Returns the object returned by NLsolve.nlsolve.

ODEsolve(vesicle, tspan; plotkws, kwargs...)

Integrate the shape equations from tspan[1] to tspan[end] for the parameters of vesicle.

Changes the value of the variable of a vesicle given as field in steps of dv until target is reached.

change(vesicle, target, tspan)
change(vesicle, target, tspan, field)
change(vesicle, target, tspan, field, dv; silent, stop, store, residual, factor, kwargs...)

Positional arguments

• vesicle: the vesicle to start with
• target : the target value to reach
• tspan : the interval of the arclength to integrate over, typically (0.0, 1.0)
• field : valid symbol of a property of the vesicle to change (like :v (default) or :m̄)
• dv : stepsize (default: 1/100 of the distance to target)

Keyword arguments

• silent : whether to print the progress to stdout (false)
• stop : callback that can be applied to stop before reaching the target (nothing)
• store : container to store intermediate results that will be push!ed to it (nothing)
• residual : function to compute the residual for the non-linear solver (root_residualAV)
• factor : initial factor for controlling the size of the trust-region
• additional keyword arguments are passed to ODEshoot_root

Returns the final Vesicle.

Don't move this function!

matchShot(vesicle, tspan)
matchShot(vesicle, tspan, save; dt, alg)

Construct a shape by integrating the shapeEquations in the intervalls [ tspan[1], tspan[end÷2] ] and [ tspan[end], tspan[end÷2] ] with the parameters given by collect( vesicle ). Return ( u, t, prob ).

relax_to_v(vesicle, target_v, tspan)
relax_to_v(vesicle, target_v, tspan, dv; silent, residual, factor, kwargs...)

Adapt stepwise the reduced volume and adjust parameters via ODEshoot_root! until target_v is reached. Return the final Vesicle.

root_residualAV!(res, parameters, vesicle, tspan; res_options, kwargs...)

Integrate the shapeEquations using solve_shapeEquations save the difference to endConditionsAV in res.

solveProb(problem; alg, tols, dt, kwargs...)

Integrate a given problem without callbacks.

Solve the shape equations with fixed parameters.

solve_shapeEquations(vesicle, tspan; dt, rcut, kwargs...)

Positional arguments

• vesicle : vesicle to start with
• tspan : the interval of the arclength to integrate over, typically (0.0, 1.0)

Keyword arguments

• dt : stepsize for the integration (1e-3)
• rcut : value of the radial coordinate until which taylor expansions are used instead of integrating the shapeEquations (1e-2)
• additional keywords are passed to integrate_shapeEquations

Returns (sol::ODESolution, Δu), where sol is the augmented solution object returned from DifferentialEquations.jl and Δu is the difference of the endpoint of the integration and the taylor expansion around the true endpoint evaluated at the actual endpoint.