Nonlinear electro-hydrodynamics of liquid crystals

We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is expressed as a sum of external electric field and the fields originating from feedback of liquid crystal order parameter, and a field, created by charged impurities. The system tends to decrease the total electric field, because it lowers the energy density. This basically nonlinear problem is not a pure academic interest. In the realm of liquid crystals and their applications, utilized nowadays modern experimental techniques have progressed to the point where even small deviations from the linear behavior can be observed and measured with a high accuracy. Hydrodynamics is the macroscopic description of condensed matter systems in the low frequency, long wavelength limit. Nonlinear hydrodynamic equations are well established to describe simple fluids. Similar approaches (with degrees of freedom related to the broken orientational or translational symmetry included) have been used also for liquid crystals. However to study behavior of strongly perturbed well above the thresholds of various electro-hydrodynamic instabilities of liquid crystals the nonlinear equations should include soft electromagnetic degrees of freedom as well. The self-consistent derivation of the complete set of the nonlinear electro-hydrodynamic equations for liquid crystals became an actual task. The aim of our work is to present these equations, which is a mandatory step to handle any nonlinear phenomenon in liquid crystals.Comment: 12 pages, no figure

Circulating Marangoni flows within droplets in smectic films

We present theoretical study and numerical simulation of Marangoni convection within ellipsoidal isotropic droplets embedded in free standing smectic films (FSSF). The thermocapillary flows are analyzed for both isotropic droplets spontaneously formed in FSSF overheated above the bulk smectic-isotropic transition, and oil lenses deposited on the surface of the smectic film. The realistic model, for which the upper drop interface is free from the smectic layers, while at the lower drop surface the smectic layering still persists is considered in detail. For isotropic droplets and oil lenses this leads effectively to a sticking of fluid motion at the border with a smectic shell. The above mentioned asymmetric configuration is realized experimentally when the temperature of the upper side of the film is higher than at the lower one. The full set of stationary solutions for Stokes stream functions describing the Marangoni convection flows within the ellipsoidal drops were derived analytically. The temperature distribution in the ellipsoidal drop and the surrounding air was determined in the frames of the perturbation theory. As a result the analytical solutions for the stationary thermocapillary convection were derived for different droplet ellipticity ratios and the heat conductivity of the liquid crystal and air. In parallel, the numerical hydrodynamic calculations of the thermocapillary motion in the drops were performed. Both the analytical and numerical simulations predict the axially-symmetric circulatory convection motion determined by the Marangoni effect at the droplet free surface. Due to a curvature of the drop interface a temperature gradient along its free surface always persists. Thus, the thermocapillary convection within the ellipsoidal droplets in overheated FSSF is possible for the arbitrarily small Marangoni numbers

Marangoni instability in oblate droplets suspended on a circular frame

We study theoretically internal flows in a small oblate droplet suspended on the circular frame. Marangoni convection arises due to a vertical temperature gradient across the drop and is driven by the surface tension variations at the free drop interface. Using the analytical basis for the solutions of Stokes equation in coordinates of oblate spheroid we have derived the linearly independent stationary solutions for Marangoni convection in terms of Stokes stream functions. The numerical simulations of the thermocapillary motion in the drops are used to study the onset of the stationary regime. Both analytical and numerical calculations predict the axially-symmetric circulatory convection motion in the drop, the dynamics of which is determined by the magnitude of the temperature gradient across the drop. The analytical solutions for the critical temperature distribution and velocity fields are obtained for the large temperature gradients across the oblate drop. These solutions reveal the lateral separation of the critical and stationary motions within the drops. The critical vortices are localized near the central part of a drop, while the intensive stationary flow is located closer to its butt end. A crossover to the limit of the plane film is studied within the formalism of the stream functions by reducing the droplet ellipticity ratio to zero value. The initial stationary regime for the strongly oblate drops becomes unstable relative to the many-vortex perturbations in analogy with the plane fluid films with free boundaries

Long-range interactions between membrane inclusions: Electric field induced giant amplification of the pairwise potential

The aim of this work is to revisit the phenomenological theory of the interaction between membrane inclusions, mediated by the membrane fluctuations. We consider the case where the inclusions are separated by distances larger than their characteristic size. Within our macroscopic approach a physical nature of such inclusions is not essential, however we have always in mind two prototypes of such inclusions: proteins and RNA macromolecules. Because the interaction is driven by the membrane fluctuations, and the coupling between inclusions and the membrane, it is possible to change the interaction potential by external actions affecting these factors. As an example of such external action we consider an electric field. Under external electric field (both dc or ac), we propose a new coupling mechanism between inclusions possessing dipole moments (as it is the case for most protein macromolecules) and the membrane. We found, quite unexpected and presumably for the first time, that the new coupling mechanism yields to giant enhancement of the pairwise potential of the inclusions. This result opens up a way to handle purposefully the interaction energy, and as well to test of the theory set forth in our article.Comment: 12 page

Genome sequence of the deep-sea γ-proteobacterium Idiomarina loihiensis reveals amino acid fermentation as a source of carbon and energy

We report the complete genome sequence of the deep-sea γ-proteobacterium, Idiomarina loihiensis, isolated recently from a hydrothermal vent at 1,300-m depth on the Lōihi submarine volcano, Hawaii. The I. loihiensis genome comprises a single chromosome of 2,839,318 base pairs, encoding 2,640 proteins, four rRNA operons, and 56 tRNA genes. A comparison of I. loihiensis to the genomes of other γ-proteobacteria reveals abundance of amino acid transport and degradation enzymes, but a loss of sugar transport systems and certain enzymes of sugar metabolism. This finding suggests that I. loihiensis relies primarily on amino acid catabolism, rather than on sugar fermentation, for carbon and energy. Enzymes for biosynthesis of purines, pyrimidines, the majority of amino acids, and coenzymes are encoded in the genome, but biosynthetic pathways for Leu, Ile, Val, Thr, and Met are incomplete. Auxotrophy for Val and Thr was confirmed by in vivo experiments. The I. loihiensis genome contains a cluster of 32 genes encoding enzymes for exopolysaccharide and capsular polysaccharide synthesis. It also encodes diverse peptidases, a variety of peptide and amino acid uptake systems, and versatile signal transduction machinery. We propose that the source of amino acids for I. loihiensis growth are the proteinaceous particles present in the deep sea hydrothermal vent waters. I. loihiensis would colonize these particles by using the secreted exopolysaccharide, digest these proteins, and metabolize the resulting peptides and amino acids. In summary, the I. loihiensis genome reveals an integrated mechanism of metabolic adaptation to the constantly changing deep-sea hydrothermal ecosystem