10,691 research outputs found
Bending models of lipid bilayer membranes: spontaneous curvature and area-difference elasticity
We preset a computational study of bending models for the curvature
elasticity of lipid bilayer membranes that are relevant for simulations of
vesicles and red blood cells. We compute bending energy and forces on
triangulated meshes and evaluate and extend four well established schemes for
their approximation: Kantor and Nelson 1987, Phys. Rev. A 36, 4020, J\"ulicher
1996, J. Phys. II France 6, 1797, Gompper and Kroll 1996, J. Phys. I France 6,
1305, and Meyer et. al. 2003 in Visualization and Mathematics III, Springer,
p35, termed A, B, C, D. We present a comparative study of these four schemes on
the minimal bending model and propose extensions for schemes B, C and D. These
extensions incorporate the reference state and non-local energy to account for
the spontaneous curvature, bilayer coupling, and area-difference elasticity
models. Our results indicate that the proposed extensions enhance the models to
account for shape transformation including budding/vesiculation as well as for
non-axisymmetric shapes. We find that the extended scheme B is superior to the
rest in terms of accuracy, and robustness as well as simplicity of
implementation. We demonstrate the capabilities of this scheme on several
benchmark problems including the budding-vesiculating process and the
reproduction of the phase diagram of vesicles
Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics
As two-dimensional fluid shells, lipid bilayer membranes resist bending and
stretching but are unable to sustain shear stresses. This property gives
membranes the ability to adopt dramatic shape changes. In this paper, a finite
element model is developed to study static equilibrium mechanics of membranes.
In particular, a viscous regularization method is proposed to stabilize
tangential mesh deformations and improve the convergence rate of nonlinear
solvers. The Augmented Lagrangian method is used to enforce global constraints
on area and volume during membrane deformations. As a validation of the method,
equilibrium shapes for a shape-phase diagram of lipid bilayer vesicle are
calculated. These numerical techniques are also shown to be useful for
simulations of three-dimensional large-deformation problems: the formation of
tethers (long tube-like exetensions); and Ginzburg-Landau phase separation of a
two-lipid-component vesicle. To deal with the large mesh distortions of the
two-phase model, modification of vicous regularization is explored to achieve
r-adaptive mesh optimization
Global Energy Matching Method for Atomistic-to-Continuum Modeling of Self-Assembling Biopolymer Aggregates
This paper studies mathematical models of biopolymer supramolecular aggregates that are formed by the self-assembly of single monomers. We develop a new multiscale numerical approach to model the structural properties of such aggregates. This theoretical approach establishes micro-macro relations between the geometrical and mechanical properties of the monomers and supramolecular aggregates. Most atomistic-to-continuum methods are constrained by a crystalline order or a periodic setting and therefore cannot be directly applied to modeling of soft matter. By contrast, the energy matching method developed in this paper does not require crystalline order and, therefore, can be applied to general microstructures with strongly variable spatial correlations. In this paper we use this method to compute the shape and the bending stiffness of their supramolecular aggregates from known chiral and amphiphilic properties of the short chain peptide monomers. Numerical implementation of our approach demonstrates consistency with results obtained by molecular dynamics simulations
Dynamic analysis of flexible mechanical systems using LATDYN
A 3-D, finite element based simulation tool for flexible multibody systems is presented. Hinge degrees-of-freedom is built into equations of motion to reduce geometric constraints. The approach avoids the difficulty in selecting deformation modes for flexible components by using assumed mode method. The tool is applied to simulate a practical space structure deployment problem. Results of examples demonstrate the capability of the code and approach
- ā¦