Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule

Folding of the triangular lattice in a discrete three-dimensional space is investigated by means of the transfer-matrix method. This model was introduced by Bowick and co-workers as a discretized version of the polymerized membrane in thermal equilibrium. The folding rule (constraint) is incompatible with the periodic-boundary condition, and the simulation has been made under the open-boundary condition. In this paper, we propose a modified constraint, which is compatible with the periodic-boundary condition; technically, the restoration of translational invariance leads to a substantial reduction of the transfer-matrix size. Treating the cluster sizes L \le 7, we analyze the singularities of the crumpling transitions for a wide range of the bending rigidity K. We observe a series of the crumpling transitions at K=0.206(2), -0.32(1), and -0.76(10). At each transition point, we estimate the latent heat as Q=0.356(30), 0.08(3), and 0.05(5), respectively

Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime

Folding of the triangular lattice in a discrete three-dimensional space is studied numerically. Such ``discrete folding'' was introduced by Bowick and co-workers as a simplified version of the polymerized membrane in thermal equilibrium. According to their cluster-variation method (CVM) analysis, there appear various types of phases as the bending rigidity K changes in the range -infty < K < infty. In this paper, we investigate the K<0 regime, for which the CVM analysis with the single-hexagon-cluster approximation predicts two types of (crumpling) transitions of both continuous and discontinuous characters. We diagonalized the transfer matrix for the strip widths up to L=26 with the aid of the density-matrix renormalization group. Thereby, we found that discontinuous transitions occur successively at K=-0.76(1) and -0.32(1). Actually, these transitions are accompanied with distinct hysteresis effects. On the contrary, the latent-heat releases are suppressed considerably as Q=0.03(2) and 0.04(2) for respective transitions. These results indicate that the singularity of crumpling transition can turn into a weak-first-order type by appreciating the fluctuations beyond a meanfield level

Optical fiber coupling method and apparatus

Systems are described for coupling a pair of optical fibers to pass light between them, which enables a coupler to be easily made, and with simple equipment, while closely controlling the characteristics of the coupler. One method includes mounting a pair of optical fibers on a block having a large hole therein, so the fibers extend across the hole while lying adjacent and parallel to one another. The fibers are immersed in an etchant to reduce the thickness of cladding around the fiber core. The fibers are joined together by applying a liquid polymer so the polymer-air interface moves along the length of the fibers to bring the fibers together in a zipper-like manner, and to progressively lay a thin coating of the polymer on the fibers

Multistep greedy algorithm identifies community structure in real-world and computer-generated networks

We have recently introduced a multistep extension of the greedy algorithm for modularity optimization. The extension is based on the idea that merging l pairs of communities (l>1) at each iteration prevents premature condensation into few large communities. Here, an empirical formula is presented for the choice of the step width l that generates partitions with (close to) optimal modularity for 17 real-world and 1100 computer-generated networks. Furthermore, an in-depth analysis of the communities of two real-world networks (the metabolic network of the bacterium E. coli and the graph of coappearing words in the titles of papers coauthored by Martin Karplus) provides evidence that the partition obtained by the multistep greedy algorithm is superior to the one generated by the original greedy algorithm not only with respect to modularity but also according to objective criteria. In other words, the multistep extension of the greedy algorithm reduces the danger of getting trapped in local optima of modularity and generates more reasonable partitions.Comment: 17 pages, 2 figure

A comparison of experimental and theoretical results for rotordynamic coefficients of four annular gas seals

The test facility and initial test program developed to experimentally measure the fluid forces induced by annular gas seals is described. A comparison of theoretically predicted and experimentally obtained data for smooth and honeycomb seals is provided. And a comparison of experimental data from the tests of three smooth-rotor/smooth-stator seals is provided. The leakage of the working fluid through the seal, the pressure gradient along the seal length, entrance pressure-loss data, and rotordynamic coefficients provide a basis for comparison. A short discussion on seal theory is included, and various rotordynamic coefficient identification schemes are described

Reduced Persistence Length and Fluctuation-Induced Interactions of Directed Semiflexible Polymers on Fluctuating surfaces

We consider directed semiflexible polymers embedded in a fluctuating surface which is governed by either surface tension or bending rigidity. The attractive interactions induced by the fluctuations of the surface reduce the rigidity of the polymers. In particular, it is shown that for arbitrarily stiff parallel polymers, there is a characteristic separation below which they prefer to bend rather than stay linear. The out-of plane fluctuations of the polymer, screen out the long-range fluctuation-induced forces, resulting in only a short-ranged effective attraction.Comment: REVTEX, one postscript figur

Extracting Spooky-activation-at-a-distance from Considerations of Entanglement

Following an early claim by Nelson & McEvoy \cite{Nelson:McEvoy:2007} suggesting that word associations can display `spooky action at a distance behaviour', a serious investigation of the potentially quantum nature of such associations is currently underway. This paper presents a simple quantum model of a word association system. It is shown that a quantum model of word entanglement can recover aspects of both the Spreading Activation equation and the Spooky-activation-at-a-distance equation, both of which are used to model the activation level of words in human memory.Comment: 13 pages, 2 figures; To appear in Proceedings of the Third Quantum Interaction Symposium, Lecture Notes in Artificial Intelligence, vol 5494, Springer, 200

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

Non-Hermitian Luttinger Liquids and Vortex Physics

As a model of two thermally excited flux liquids connected by a weak link, we study the effect of a single line defect on vortex filaments oriented parallel to the surface of a thin planar superconductor. When the applied field is tilted relative to the line defect, the physics is described by a nonhermitian Luttinger liquid of interacting quantum bosons in one spatial dimension with a point defect. We analyze this problem using a combination of analytic and numerical density matrix renormalization group methods, uncovering a delicate interplay between enhancement of pinning due to Luttinger liquid effects and depinning due to the tilted magnetic field. Interactions dramatically improve the ability of a single columnar pin to suppress vortex tilt when the Luttinger liquid parameter g is less than or equal to one.Comment: 4 pages, 5 eps figures, minor changes made, one reference adde

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