17,337 research outputs found
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
Dislocation subgrain structures and modeling the plastic hardening of metallic single crystals
A single crystal plasticity theory for insertion into finite element simulation is formulated using sequential laminates to model subgrain dislocation structures. It is known that local models do not adequately account for latent hardening, as latent hardening is not only a material property, but a nonlocal property (e.g. grain size and shape). The addition of the nonlocal energy from the formation of subgrain structure dislocation walls and the boundary layer misfits provide both latent and self-hardening of a crystal slip. Latent hardening occurs as the formation of new dislocation walls limits motion of new mobile dislocations, thus hardening future slip systems. Self-hardening is accomplished by an evolution of the subgrain structure length scale. The substructure length scale is computed by minimizing the nonlocal energy. The minimization of the nonlocal energy is a competition between the dislocation wall energy and the boundary layer energies. The nonlocal terms are also directly minimized within the subgrain model as they affect deformation response. The geometrical relationship between the dislocation walls and slip planes affecting the dislocation mean free path is taken into account, giving a first-order approximation to shape effects. A coplanar slip model is developed due to requirements while modeling the subgrain structure. This subgrain structure plasticity model is noteworthy as all material parameters are experimentally determined rather than fit. The model also has an inherit path dependence due to the formation of the subgrain structures. Validation is accomplished by comparison with single crystal tension test results
From the double-stranded helix to the chiral nematic phase of B-DNA: a molecular model
B-DNA solutions of suitable concentration form left-handed chiral nematic
phases (cholesterics). Such phases have also been observed in solutions of
other stiff or semiflexible chiral polymers; magnitude and handedness of the
cholesteric pitch are uniquely related to the molecular features. In this work
we present a theoretical method and a numerical procedure which, starting from
the structure of polyelectrolytes, lead to the prediction of the cholesteric
pitch. Molecular expressions for the free energy of the system are obtained on
the basis of steric and electrostatic interactions between polymers; the former
are described in terms of excluded volume, while a mean field approximation is
used for the latter. Calculations have been performed for 130 bp fragments of
B-DNA. The theoretical predictions provide an explanation for the experimental
behavior, by showing the counteracting role played by shape and charge
chirality of the molecule.Comment: 42 pages, 6 figure
Equilibrium properties of charged microgels: a Poisson-Boltzmann-Flory approach
The equilibrium properties of ionic microgels are investigated using a
combination of the Poisson-Boltzmann and Flory theories. Swelling behavior,
density profiles, and effective charges are all calculated in a self-consistent
way. Special attention is given to the effects of salinity on these quantities.
It is found that the equilibrium microgel size is strongly influenced by the
amount of added salt. Increasing the salt concentration leads to a considerable
reduction of the microgel volume, which therefore releases its internal
material -- solvent molecules and dissociated ions -- into the solution.
Finally, the question of charge renormalization of ionic microgels in the
context of the cell model is briefly addressed
Correlations and charge distributions of medium heavy nuclei
The effects of long- and short-range correlations on the charge distributions
of some medium and heavy nuclei are investigated. The long-range correlations
are treated within the Random Phase Approximation framework and the short-range
correlations with a model inspired to the Correlation Basis Function theory.
The two type of correlations produce effects of the same order of magnitude. A
comparison with the empirical charge distribution difference between 206Pb and
205Tl shows the need of including both correlations to obtain a good
description of the data.Comment: 20 pages, Latex, accepted for publication in Jour. Phys.
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