Instability and Periodic Deformation in Bilayer Membranes Induced by Freezing

The instability and periodic deformation of bilayer membranes during freezing processes are studied as a function of the difference of the shape energy between the high and the low temperature membrane states. It is shown that there exists a threshold stability condition, bellow which a planar configuration will be deformed. Among the deformed shapes, the periodic curved square textures are shown being one kind of the solutions of the associated shape equation. In consistency with recent expe rimental observations, the optimal ratio of period and amplitude for such a texture is found to be approximately equal to (2)^{1/2}\pi.Comment: 8 pages in Latex form, 1 Postscript figure. To be appear in Mod. Phys. Lett. B. 199

Lateral migration of a 2D vesicle in unbounded Poiseuille flow

The migration of a suspended vesicle in an unbounded Poiseuille flow is investigated numerically in the low Reynolds number limit. We consider the situation without viscosity contrast between the interior of the vesicle and the exterior. Using the boundary integral method we solve the corresponding hydrodynamic flow equations and track explicitly the vesicle dynamics in two dimensions. We find that the interplay between the nonlinear character of the Poiseuille flow and the vesicle deformation causes a cross-streamline migration of vesicles towards the center of the Poiseuille flow. This is in a marked contrast with a result [L.G. Leal, Ann. Rev. Fluid Mech. 12, 435(1980)]according to which the droplet moves away from the center (provided there is no viscosity contrast between the internal and the external fluids). The migration velocity is found to increase with the local capillary number (defined by the time scale of the vesicle relaxation towards its equilibrium shape times the local shear rate), but reaches a plateau above a certain value of the capillary number. This plateau value increases with the curvature of the parabolic flow profile. We present scaling laws for the migration velocity.Comment: 11 pages with 4 figure

Lipid membranes with an edge

Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature of its geometry; that describing the edge is proportional to its length. In this note we determine the boundary conditions satisfied by the equilibria of the membrane on this edge, exploiting variational principles. The derivation is free of any assumptions on the symmetry of the membrane geometry. With respect to earlier work for axially symmetric configurations, we discover the existence of an additional boundary condition which is identically satisfied in that limit. By considering the balance of the forces operating at the edge, we provide a physical interpretation for the boundary conditions. We end with a discussion of the effect of the addition of a Gaussian rigidity term for the membrane.Comment: 8 page

Helfrich-Canham bending energy as a constrained non-linear sigma model

The Helfrich-Canham bending energy is identified with a non-linear sigma model for a unit vector. The identification, however, is dependent on one additional constraint: that the unit vector be constrained to lie orthogonal to the surface. The presence of this constraint adds a source to the divergence of the stress tensor for this vector so that it is not conserved. The stress tensor which is conserved is identified and its conservation shown to reproduce the correct shape equation.Comment: 5 page

Circadian Organization in Hemimetabolous Insects

The circadian system of hemimetabolous insects is reviewed in respect to the locus of the circadian clock and multioscillatory organization. Because of relatively easy access to the nervous system, the neuronal organization of the clock system in hemimetabolous insects has been studied, yielding identification of the compound eye as the major photoreceptor for entrainment and the optic lobe for the circadian clock locus. The clock site within the optic lobe is inconsistent among reported species; in cockroaches the lobula was previously thought to be a most likely clock locus but accessory medulla is recently stressed to be a clock center, while more distal part of the optic lobe including the lamina and the outer medulla area for the cricket. Identification of the clock cells needs further critical studies. Although each optic lobe clock seems functionally identical, in respect to photic entrainment and generation of the rhythm, the bilaterally paired clocks form a functional unit. They interact to produce a stable time structure within individual insects by exchanging photic and temporal information through neural pathways, in which serotonin and pigment-dispersing factor (PDF) are involved as chemical messengers. The mutual interaction also plays an important role in seasonal adaptation of the rhythm

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.Comment: 6 pages, 4 figures (LaTeX macros EPJ), accepted for publication in EPJ

Statistical mechanics of semiflexible ribbon polymers

The statistical mechanics of a ribbon polymer made up of two semiflexible chains is studied using both analytical techniques and simulation. The system is found to have a crossover transition at some finite temperature, from a type of short range order to a fundamentally different sort of short range order. In the high temperature regime, the 2-point correlation functions of the object are identical to worm-like chains, while in the low temperature regime they are different due to a twist structure. The crossover happens when the persistence length of individual strands becomes comparable to the thickness of the ribbon. In the low temperature regime, the ribbon is observed to have a novel ``kink-rod'' structure with a mutual exclusion of twist and bend in contrast to smooth worm-like chain behaviour. This is due to its anisotropic rigidity and corresponds to an {\it infinitely} strong twist-bend coupling. The double-stranded polymer is also studied in a confined geometry. It is shown that when the polymer is restricted in a particular direction to a size less than the bare persistence length of the individual strands, it develops zigzag conformations which are indicated by an oscillatory tangent-tangent correlation function in the direction of confinement. Increasing the separation of the confining plates leads to a crossover to the free behaviour, which takes place at separations close to the bare persistence length. These results are expected to be relevant for experiments which involve complexation of two or more stiff or semiflexible polymers.Comment: 20 pages, 11 figures. PRE (in press

Coiling Instability of Multilamellar Membrane Tubes with Anchored Polymers

We study experimentally a coiling instability of cylindrical multilamellar stacks of phospholipid membranes, induced by polymers with hydrophobic anchors grafted along their hydrophilic backbone. Our system is unique in that coils form in the absence of both twist and adhesion. We interpret our experimental results in terms of a model in which local membrane curvature and polymer concentration are coupled. The model predicts the occurrence of maximally tight coils above a threshold polymer occupancy. A proper comparison between the model and experiment involved imaging of projections from simulated coiled tubes with maximal curvature and complicated torsions.Comment: 11 pages + 7 GIF figures + 10 JPEG figure

Membrane geometry with auxiliary variables and quadratic constraints

Consider a surface described by a Hamiltonian which depends only on the metric and extrinsic curvature induced on the surface. The metric and the curvature, along with the basis vectors which connect them to the embedding functions defining the surface, are introduced as auxiliary variables by adding appropriate constraints, all of them quadratic. The response of the Hamiltonian to a deformation in each of the variables is examined and the relationship between the multipliers implementing the constraints and the conserved stress tensor of the theory established.Comment: 8 page

Phase ordering and shape deformation of two-phase membranes

Within a coupled-field Ginzburg-Landau model we study analytically phase separation and accompanying shape deformation on a two-phase elastic membrane in simple geometries such as cylinders, spheres and tori. Using an exact periodic domain wall solution we solve for the shape and phase ordering field, and estimate the degree of deformation of the membrane. The results are pertinent to a preferential phase separation in regions of differing curvature on a variety of vesicles.Comment: 4 pages, submitted to PR