A finite element scheme for the evolution of orientational order in fluid membranes

Bartels, Sören; Dolzmann, Georg; Nochetto, Ricardo H.

doi:10.1051/m2an/2009040

Cited by 13 publications

(15 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Continuum finite element studies using a surface-director Hamiltonian similar to Eq. 1 have simulated three-dimensional vesicles (52,53), but these studies considered neither changes in topology nor separate monolayers of a bilayer.…”

Section: Assumptions Of This Studymentioning

confidence: 99%

Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion

Ryham

Klotz

Yao

et al. 2016

Biophysical Journal

View full text Add to dashboard Cite

We use continuum mechanics to calculate an entire least energy pathway of membrane fusion, from stalk formation, to pore creation, and through fusion pore enlargement. The model assumes that each structure in the pathway is axially symmetric. The static continuum stalk structure agrees quantitatively with experimental stalk architecture. Calculations show that in a stalk, the distal monolayer is stretched and the stored stretching energy is significantly less than the tilt energy of an unstretched distal monolayer. The string method is used to determine the energy of the transition barriers that separate intermediate states and the dynamics of two bilayers as they pass through them. Hemifusion requires a small amount of energy independently of lipid composition, while direct transition from a stalk to a fusion pore without a hemifusion intermediate is highly improbable. Hemifusion diaphragm expansion is spontaneous for distal monolayers containing at least two lipid components, given sufficiently negative diaphragm spontaneous curvature. Conversely, diaphragms formed from single-component distal monolayers do not expand without the continual injection of energy. We identify a diaphragm radius, below which central pore expansion is spontaneous. For larger diaphragms, prior studies have shown that pore expansion is not axisymmetric, and here our calculations supply an upper bound for the energy of the barrier against pore formation. The major energy-requiring deformations in the steps of fusion are: widening of a hydrophobic fissure in bilayers for stalk formation, splay within the expanding hemifusion diaphragm, and fissure widening initiating pore formation in a hemifusion diaphragm.

show abstract

Section: Assumptions Of This Studymentioning

confidence: 99%

Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion

Ryham

Klotz

Yao

et al. 2016

Biophysical Journal

View full text Add to dashboard Cite

show abstract

“…We finally mention the coupling of membrane bending with orientational order of bilipds via director fields [10]. These models lead to PDE in Ω similar to (1.1).…”

Section: Introductionmentioning

confidence: 97%

Preconditioning a class of fourth order problems by operator splitting

2010

Self Cite

View full text Add to dashboard Cite

Abstract. We develop preconditioners for systems arising from finite element discretizations of parabolic problems which are fourth order in space. We consider boundary conditions which yield a natural splitting of the discretized fourth order operator into two (discrete) linear second order elliptic operators, and exploit this property in designing the preconditioners. The underlying idea is that efficient methods and software to solve second order problems with optimal computational effort are widely available. We propose symmetric and non-symmetric preconditioners, along with theory and numerical experiments. They both document crucial properties of the preconditioners as well as their practical performance. It is important to note that we neither need H s -regularity, s > 1, of the continuous problem nor quasi-uniform grids.

show abstract

“…The purpose of the regularization is purely mathematical. Our method builds on [8,9] and consists of a special discrete energy that does not use any regularization, hence we can compute minimizers that exhibit line and plane defects.…”

Section: Introductionmentioning

confidence: 99%

Numerics for Liquid Crystals with Variable Degree of Orientation

Nochetto

Walker

Zhang³

2015

MRS Proc.

Self Cite

View full text Add to dashboard Cite

We consider the simplest one-constant model, put forward by J. Eriksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field n and its degree of orientation s, where the pair (n, s) minimizes a sum of Frank-like energies and a double well potential. In particular, the Euler-Lagrange equations for the minimizer contain a degenerate elliptic equation for n, which allows for line and plane defects to have finite energy. Using a special discretization of the liquid crystal energy, and a strictly monotone energy decreasing gradient flow scheme, we present a simulation of a plane-defect in three dimensions to illustrate our method.

show abstract

A finite element scheme for the evolution of orientational order in fluid membranes

Cited by 13 publications

References 39 publications

Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion

Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion

Preconditioning a class of fourth order problems by operator splitting

Numerics for Liquid Crystals with Variable Degree of Orientation

Contact Info

Product

Resources

About