arXiv subjects

O. V. Manyuhina

Publications and source records attributed to O. V. Manyuhina.

15 recordsLinked to original sources

arXiv2015

Viral nematics in confined geometries

Motivated by recent experiments on the rod-like virus bacteriophage fd, confined to circular and annular domains, we present a theoretical study of structural transitions in these geometries. Using the continuum theory of nematic liquid crystals, we examine the competition between bulk elasticity and surface anchoring, mediated by the formation of topological defects. We show analytically that bulk defects are unstable with respect to defects sitting at the boundary. Moreover, in case of an annulus, whose topology does not require the presence of topological defects, under weak anchoring conditions we find that nematic textures with boundary defects are stable compared to the defect free configurations. Thus our simple approach, with no fitting parameters, suggests a possible symmetry breaking mechanism responsible for the formation of one-, two- and three-fold textures under annular confinement.

cond-mat.soft↗

arXiv2015

Thick smectic shells

The known ground state of ultrathin smectic films confined to the surface of a sphere is described by four +1/2 defects assembled on a great circle and a director which follows geodesic lines. Using a simple perturbative approach we show that for thick smectic films on a sphere with planar anchoring this solution breaks down, distorting the smectic layers. The instability happens when the bend elastic constant exceeds the anchoring strength times the radius of the inner sphere. Above this threshold, the formation of a periodic chevron-like structure, observed experimentally as well, relieves geometric frustration. We quantify the effect of thickness and curvature of smectic shells and provide insight into the wavelength of the observed texture.

cond-mat.soft↗

arXiv2015

Forming a cube from a sphere with tetratic order

Composed of square particles, the tetratic phase is characterised by a four-fold symmetry with quasi-long-range orientational order but no translational order. We construct the elastic free energy for tetratics and find a closed form solution for 1/4-disclinations in planar geometry. Applying the same covariant formalism to a sphere we show analytically that within the one elastic constant approximation eight +1/4-disclinations favor positions defining the vertices of a cube. The interplay between defect-defect interactions and bending energy results in a flattening of the sphere towards superspheroids with the symmetry of a cube.

cond-mat.soft↗

arXiv2014

Elastic instabilities in a layered cerebral cortex: A revised axonal tension model for cortex folding

We model the elasticity of the cerebral cortex as a layered material with bending energy along the layers and elastic energy between them in both planar and polar geometries. The cortex is also subjected to axons pulling from the underlying white matter. Above a critical threshold force, a "flat" cortex configuration becomes unstable and periodic unduluations emerge, i.e. a buckling instability occurs. These undulations may indeed initiate folds in the cortex. We identify analytically the critical force and the critical wavelength of the undulations. Both quantities are physiologically relevant values. Our model is a revised version of the axonal tension model for cortex folding, with our version taking into account the layered structure of the cortex. Moreover, our model draws a connection with another competing model for cortex folding, namely the differential growth-induced buckling model. For the polar geometry, we study the relationship between brain size and the critical force and wavelength to understand why small mice brains exhibit no folds, while larger human brains do, for example. Finally, an estimate of the bending rigidity constant for the cortex can be made based on the critical wavelength.

cond-mat.soft↗

arXiv2014

Protein crowding on biomembranes: analysis of contour instabilities

Collective behavior of proteins on biomembranes is usually studied within the spontaneous curvature model. Here we consider an alternative phenomenological approach, which accounts consistently for partial ordering of proteins as well as the anchoring forces exerted on a membrane by layer of proteins. We show analytically that such anisotropic interactions can drive membrane bending, resulting in non-trivial equilibrium morphologies. The predicted instabilities can advance our conceptual understanding of physical mechanisms behind collective phenomena in biological systems, in particular those with inherent anisotropy.

cond-mat.soft↗

arXiv2013

Doubly-periodic instability pattern in a smectic A liquid crystal

We report the observation of a doubly-periodic surface defect-pattern in the liquid crystal 8CB, formed during the nematic--smectic A phase transition. The pattern results from the antagonistic alignment of the 8CB molecules, which is homeotropic at the surface and planar in the bulk of the sample cell. Within the continuum Landau-deGennes theory of smectic liquid crystals, we find that the long period (~10 μm) of the pattern is given by the balance between the surface anchoring and the elastic energy of curvature wall defects. The short period (~1 μm) we attribute to a saddle-splay distortion, leading to a non-zero Gaussian curvature and causing the curvature walls to break up.

cond-mat.soft↗

arXiv2012

Thin nematic films: anchoring effects and stripe instability revisited

We study theoretically the formation of long-wavelength instability patterns observed at spreading of nematic droplets on liquid substrates. The role of surface-like elastic terms such as saddle-splay and anchoring in nematic films of submicron thickness is (re)examined by extending our previous work [Manyuhina et al EPL, 92, 16005 (2010)] to hybrid aligned nematics. We identify the upper threshold for the formation of stripes and compare our results with experimental observations. We find that the wavelength and the amplitude of the in-plane director undulations can be related to the small but finite azimuthal anchoring. Within a simplified model we analyse the possibility of non-planar base state below the Barbero-Barberi critical thickness.

cond-mat.soft↗

arXiv2012

Saddle-splay elasticity and field induced soliton in nematics

The symmetry breaking Freedericksz transitions, when a uniformly aligned nematic state is replaced by a homogeneously or periodically distorted state, have been extensively studied before. Here we analyse the influence of the saddle-splay elasticity on the non-linear ground state of nematic liquid crystal in presence of magnetic field above the Freedericksz threshold. We identify the bifurcation point when the kink-soliton is linearly unstable with respect to the perturbations of the wave vector in the direction perpendicular to the initial plane of soliton. This instability occurs only if the ratio of saddle-splay elastic constant to elastic modulus of nematics in one-constant approximation is above the critical value |K_{24}/K|>0.707.

cond-mat.soft↗

arXiv2011

Cell motility: a viscous fingering analysis of active gels

The symmetry breaking of the actin network from radial to longitudinal symmetry has been identified as the major mechanism for keratocytes (fish cells) motility on solid substrate. For strong friction coefficient, the two dimensional actin flow which includes the polymerisation at the edge and depolymerisation in the bulk can be modelled as a Darcy flow, the cell shape and dynamics being then modelled by standard complex analysis methods. We use the theory of active gels to describe the orientational order of the filaments which varies from the border to the bulk. We show analytically that the reorganisation of the cortex is enough to explain the motility of the cell and find the velocity as a function of the orientation order parameter in the bulk.

cond-mat.soft↗

arXiv2010

Instability patterns in ultrathin nematic films: comparison between theory and experiment

Motivated by recent experimental observations [U. Delabre et al, Langmuir 24, 3998, 2008] we reconsider an instability of ultrathin nematic films, spread on liquid substrates. Within a continuum elastic theory of liquid crystals, in the harmonic approximation, we find an analytical expressions for the critical thickness as well as for the critical wavenumber, characterizing the onset of instability towards the stripe phase. Comparing theoretical predictions with experimental observations, we establish the utility of surface-like term such as an azimuthal anchoring.

cond-mat.soft↗

arXiv2010

Non-spherical shapes of capsules within a fourth-order curvature model

We minimize a discrete version of the fourth-order curvature based Landau free energy by extending Brakke's Surface Evolver. This model predicts spherical as well as non-spherical shapes with dimples, bumps and ridges to be the energy minimizers. Our results suggest that the buckling and faceting transitions, usually associated with crystalline matter, can also be an intrinsic property of non-crystalline membranes.

cond-mat.soft↗

arXiv2009

Topological defects and shape of aromatic self-assembled vesicles

We show that the stacking of flat aromatic molecules on a curved surface results in topological defects. We consider, as an example, spherical vesicles, self-assembled from molecules with 5- and 6-thiophene cores. We predict that the symmetry of the molecules influences the number of topological defects and the resulting equilibrium shape.

cond-mat.soft↗

arXiv2009

Topological instabilities of spherical vesicles

Within the framework of the Helfrich elastic theory of membranes and of differential geometry we study the possible instabilities of spherical vesicles towards double bubbles. We find that not only temperature, but also magnetic fields can induce topological transformations between spherical vesicles and double bubbles and provide a phase diagram for the equilibrium shapes.

cond-mat.soft↗

arXiv2007

Slow dynamics in a model of the cellulose network

We present numerical simulations of a model of cellulose consisting of long stiff rods, representing cellulose microfibrils, connected by stretchable crosslinks, representing xyloglucan molecules, hydrogen bonded to the microfibrils. Within a broad range of temperature the competing interactions in the resulting network give rise to a slow glassy dynamics. In particular, the structural relaxation described by orientational correlation functions shows a logarithmic time dependence. The glassy dynamics is found to be due to the frustration introduced by the network of xyloglucan molecules. Weakening of interactions between rod and xyloglucan molecules results in a more marked reorientation of cellulose microfibrils, suggesting a possible mechanism to modify the dynamics of the plant cell wall.

cond-mat.dis-nn↗

arXiv2007

Anharmonic magnetic deformation of self-assembled molecular nanocapsules

High magnetic fields were used to deform spherical nanocapsules, self-assembled from bola-amphiphilic sexithiophene molecules. At low fields the deformation -- measured through linear birefringence -- scales quadratically with the capsule radius and with the magnetic field strength. These data confirm a long standing theoretical prediction (W. Helfrich, Phys. Lett. {\bf 43A}, 409 (1973)), and permits the determination of the bending rigidity of the capsules as (2.6$\pm$0.8)$\times 10^{-21}$ J. At high fields, an enhanced rigidity is found which cannot be explained within the Helfrich model. We propose a complete form of the free energy functional that accounts for this behaviour, and allows discussion of the formation and stability of nanocapsules in solution.

cond-mat.soft↗