Free Energies of Isolated 5- and 7-fold Disclinations in Hexatic Membranes

We examine the shapes and energies of 5- and 7-fold disclinations in low-temperature hexatic membranes. These defects buckle at different values of the ratio of the bending rigidity, $\kappa$, to the hexatic stiffness constant, $K_A$, suggesting {\em two} distinct Kosterlitz-Thouless defect proliferation temperatures. Seven-fold disclinations are studied in detail numerically for arbitrary $\kappa/K_A$. We argue that thermal fluctuations always drive $\kappa/K_A$ into an ``unbuckled'' regime at long wavelengths, so that disclinations should, in fact, proliferate at the {\em same} critical temperature. We show analytically that both types of defects have power law shapes with continuously variable exponents in the ``unbuckled'' regime. Thermal fluctuations then lock in specific power laws at long wavelengths, which we calculate for 5- and 7-fold defects at low temperatures.Comment: LaTeX format. 17 pages. To appear in Phys. Rev.

Longitudinal Current Dissipation in Bose-glass Superconductors

A scaling theory of vortex motion in Bose glass superconductors with currents parallel to the common direction of the magnetic field and columnar defects is presented. Above the Bose-glass transition the longitudinal DC resistivity $\rho_{||}(T)\sim (T-T_{BG})^{\nu' z'}$ vanishes much faster than the corresponding transverse resistivity $\rho_{\perp}(T)\sim (T-T_{BG})^{\nu' (z'-2)}$, thus {\it reversing} the usual anisotropy of electrical transport in the normal state of layered superconductors. In the presence of a current $\bf J$ at an angle $\theta_J$ with the common field and columnar defect axis, the electric field angle $\theta_E$ approaches $\pi/2$ as $T\rightarrow T_{BG}^+$. Scaling also predicts the behavior of penetration depths for the AC currents as $T\rightarrow T_{BG}^-$, and implies a {\it jump discontinuity} at $T_{BG}$ in the superfluid density describing transport parallel to the columns.Comment: 5 pages, revte

Patterned Geometries and Hydrodynamics at the Vortex Bose Glass Transition

Patterned irradiation of cuprate superconductors with columnar defects allows a new generation of experiments which can probe the properties of vortex liquids by confining them to controlled geometries. Here we show that an analysis of such experiments that combines an inhomogeneous Bose glass scaling theory with the hydrodynamic description of viscous flow of vortex liquids can be used to infer the critical behavior near the Bose glass transition. The shear viscosity is predicted to diverge as $|T-T_{BG}|^{-z}$ at the Bose glass transition, with $z\simeq 6$ the dynamical critical exponent.Comment: 5 pages, 4 figure

Spicules and the effect of rigid rods on enclosing membrane tubes

Membrane tubes (spicules) arise in cells, or artificial membranes, in the nonlinear deformation regime due to, e.g. the growth of microtubules, actin filaments or sickle hemoglobin fibers towards a membrane. We calculate the axial force exerted by the cylindrical membrane tube, and its average radius, by taking into account steric interactions between the fluctuating membrane and the enclosed rod. The force required to confine a fluctuating membrane near the surface of the enclosed rod diverges as the separation approaches zero. This results in a smooth crossover of the axial force between a square root and a linear dependence on the membrane tension as the tension increases and the tube radius shrinks. This crossover can occur at the most physiologically relevant membrane tensions. Our work may be important in (i) interpreting experiments in which axial force is related to the tube radius or membrane tension (ii) dynamical theories for biopolymer growth in narrow tubes where these fluctuation effects control the tube radius.Comment: 10 pages, 1 figur

Plasticity in current-driven vortex lattices

We present a theoretical analysis of recent experiments on current-driven vortex dynamics in the Corbino disk geometry. This geometry introduces controlled spatial gradients in the driving force and allows the study of the onset of plasticity and tearing in clean vortex lattices. We describe plastic slip in terms of the stress-driven unbinding of dislocation pairs, which in turn contribute to the relaxation of the shear, yielding a nonlinear response. The steady state density of free dislocations induced by the applied stress is calculated as a function of the applied current and temperature. A criterion for the onset of plasticity at a radial location $r$ in the disk yields a temperature-dependent critical current that is in qualitative agreement with experiments.Comment: 11 pages, 4 figure

Disclination Asymmetry in Two-Dimensional Nematic Liquid Crystals with Unequal Frank Constants

The behavior of a thin film of nematic liquid crystal with unequal Frank constants is discussed. Distinct Frank constants are found to imply unequal core energies for $+1/2$ and $-1/2$ disclinations. Even so, a topological constraint is shown to ensure that the bulk densities of the two types of disclinations are the same. For a system with free boundary conditions, such as a liquid membrane, unequal core energies simply renormalize the Gaussian rigidity and line tension.Comment: RevTex forma

Saddle-splay modulus of a particle-laden fluid interface

The scaled-particle theory equation of state for the two-dimensional hard-disk fluid on a curved surface is proposed and used to determine the saddle-splay modulus of a particle-laden fluid interface. The resulting contribution to saddle-splay modulus, which is caused by thermal motion of the adsorbed particles, is comparable in magnitude with the saddle-splay modulus of a simple fluid interface.Comment: 10 pages, 2 figure

Collapsing transition of spherical tethered surfaces with many holes

We investigate a tethered (i.e. fixed connectivity) surface model on spherical surfaces with many holes by using the canonical Monte Carlo simulations. Our result in this paper reveals that the model has only a collapsing transition at finite bending rigidity, where no surface fluctuation transition can be seen. The first-order collapsing transition separates the smooth phase from the collapsed phase. Both smooth and collapsed phases are characterized by Hausdorff dimension H\simeq 2, consequently, the surface becomes smooth in both phases. The difference between these two phases can be seen only in the size of surface. This is consistent with the fact that we can see no surface fluctuation transition at the collapsing transition point. These two types of transitions are well known to occur at the same transition point in the conventional surface models defined on the fixed connectivity surfaces without holes.Comment: 7 pages with 11 figure

A Magellanic Origin for the Warp of the Galaxy

We show that a Magellanic Cloud origin for the warp of the Milky Way can explain most quantitative features of the outer HI layer recently identified by Levine, Blitz & Heiles (2005). We construct a model similar to that of Weinberg (1998) that produces distortions in the dark matter halo, and we calculate the combined effect of these dark-halo distortions and the direct tidal forcing by the Magellanic Clouds on the disk warp in the linear regime. The interaction of the dark matter halo with the disk and resonances between the orbit of the Clouds and the disk account for the large amplitudes observed for the vertical m=0,1,2 harmonics. The observations lead to six constraints on warp forcing mechanisms and our model reasonably approximates all six. The disk is shown to be very dynamic, constantly changing its shape as the Clouds proceed along their orbit. We discuss the challenges to MOND placed by the observations.Comment: 4 pages, 3 figures, submitted to ApJ Letters. Additional graphics, 3d visualizations and movies available at http://www.astro.umass.edu/~weinberg/lm

Phase transitions of an intrinsic curvature model on dynamically triangulated spherical surfaces with point boundaries

An intrinsic curvature model is investigated using the canonical Monte Carlo simulations on dynamically triangulated spherical surfaces of size upto N=4842 with two fixed-vertices separated by the distance 2L. We found a first-order transition at finite curvature coefficient \alpha, and moreover that the order of the transition remains unchanged even when L is enlarged such that the surfaces become sufficiently oblong. This is in sharp contrast to the known results of the same model on tethered surfaces, where the transition weakens to a second-order one as L is increased. The phase transition of the model in this paper separates the smooth phase from the crumpled phase. The surfaces become string-like between two point-boundaries in the crumpled phase. On the contrary, we can see a spherical lump on the oblong surfaces in the smooth phase. The string tension was calculated and was found to have a jump at the transition point. The value of \sigma is independent of L in the smooth phase, while it increases with increasing L in the crumpled phase. This behavior of \sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu, where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpled phase. We should note that a possibility of a continuous transition is not completely eliminated.Comment: 15 pages with 10 figure