scholarly journals Controlled deformation of vesicles by flexible structured media

2016 ◽  
Vol 2 (8) ◽  
pp. e1600978 ◽  
Author(s):  
Rui Zhang ◽  
Ye Zhou ◽  
José A. Martínez-González ◽  
Juan P. Hernández-Ortiz ◽  
Nicholas L. Abbott ◽  
...  

Liquid crystalline (LC) materials, such as actin or tubulin networks, are known to be capable of deforming the shape of cells. Here, elements of that behavior are reproduced in a synthetic system, namely, a giant vesicle suspended in a LC, which we view as a first step toward the preparation of active, anisotropic hybrid systems that mimic some of the functionality encountered in biological systems. To that end, we rely on a coupled particle-continuum representation of deformable networks in a nematic LC represented at the level of a Landau–de Gennes free energy functional. Our results indicate that, depending on its elastic properties, the LC is indeed able to deform the vesicle until it reaches an equilibrium, anisotropic shape. The magnitude of the deformation is determined by a balance of elastic and surface forces. For perpendicular anchoring at the vesicle, a Saturn ring defect forms along the equatorial plane, and the vesicle adopts a pancake-like, oblate shape. For degenerate planar anchoring at the vesicle, two boojum defects are formed at the poles of the vesicle, which adopts an elongated, spheroidal shape. During the deformation, the volume of the topological defects in the LC shrinks considerably as the curvature of the vesicle increases. These predictions are confirmed by our experimental observations of spindle-like shapes in experiments with giant unilamellar vesicles with planar anchoring. We find that the tension of the vesicle suppresses vesicle deformation, whereas anchoring strength and large elastic constants promote shape anisotropy.

Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.


Nonlinearity ◽  
2009 ◽  
Vol 22 (12) ◽  
pp. 2919-2952 ◽  
Author(s):  
E A Carlen ◽  
M C Carvalho ◽  
R Esposito ◽  
J L Lebowitz ◽  
R Marra

2006 ◽  
Vol 16 (2) ◽  
pp. 233-264 ◽  
Author(s):  
E. A. Carlen ◽  
M. C. Carvalho ◽  
R. Esposito ◽  
J. L. Lebowitz ◽  
R. Marra

Author(s):  
François Alouges ◽  
Giovanni Di Fratta

The objective of this paper is to perform, by means of Γ - convergence and two-scale convergence , a rigorous derivation of the homogenized Gibbs–Landau free energy functional associated with a composite periodic ferromagnetic material, i.e. a ferromagnetic material in which the heterogeneities are periodically distributed inside the media. We thus describe the Γ -limit of the Gibbs–Landau free energy functional, as the period over which the heterogeneities are distributed inside the ferromagnetic body shrinks to zero.


2016 ◽  
Vol 18 (3) ◽  
pp. 1771-1785 ◽  
Author(s):  
Kazuo Takatsuka ◽  
Kentaro Matsumoto

We present a basic theory to study real-time chemical dynamics embedded in a statistically treated large environment. It is shown that dynamically treated molecules should run on the free-energy functional surface, if and only if the spatial gradients of temperature functional are all zero.


Author(s):  
Razvan-Dumitru Ceuca

We consider a Landau-de Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not cubic symmetry and then we compute the free effective energy of the composite material. In the cubic symmetry case, we impose different types of surface anchoring energy densities, such as quartic, Rapini-Papoular or more general versions, and, in this case, we show that we can tune any coefficient from the corresponding bulk potential, especially the phase transition temperature. In the case with loss of cubic symmetry, we prove similar results in which the effective free energy functional has now an additional term, which describes a change in the preferred alignment of the liquid crystal particles inside the domain. Moreover, we compute the rate of convergence for how fast the surface energies converge to the homogenised one and also for how fast the minimisers of the free energies tend to the minimiser of the homogenised free energy.


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