Nonequilibrium relaxation analysis of a quasi-one-dimensional frustrated XY model for charge-density waves in ring-shaped crystals

We propose a model for charge density waves in ring shaped crystals, which depicts frustration between intra- and inter-chain couplings coming from cylindrical bending. It is then mapped to a three dimensional uniformly frustrated XY model with one dimensional anisotropy in connectivity. The nonequilibrium relaxation dynamics is investigated by Monte Carlo simulations to find a phase transition which is quite different from that of usual whisker crystal. We also find that the low temperature state is a three dimensional phase vortex lattice with a two dimensional phase coherence in a cylindrical shell and the system shows power law relaxation in the ordered phase.Comment: 6 pages, 6 epsfiles, revised versio

Monte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees

We perform Monte-Carlo simulations to study the Bernoulli ($p$) bond percolation on the enhanced binary tree which belongs to the class of nonamenable graphs with one end. Our numerical results show that the system has two different percolation thresholds $p_{c1}$ and $p_{c2}$. All the points in the intermediate phase $(p_{c1} < p < p_{c2})$ are critical and there exist infinitely many infinite clusters in the intermediate phase. In this phase the corresponding fractal exponent continuously increases with $p$ from zero to unity.Comment: 4 pages, 6 figure

Geometrically Frustrated Crystals: Elastic Theory and Dislocations

Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the generation of edge dislocations due to geometrical frustration caused by the bending is studied. The analogy to superconducting (or superfluid) vortex state is pointed out and the phase diagram of the ring-crystal, which depends on radius and thickness, is discussed.Comment: 4 pages, 3 figure

Local Anisotropy of Fluids using Minkowski Tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\leq \beta_\nu^{a,b}\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $\beta_\nu^{a,b}\approx 0.3$ for vapor phases to $\beta_\nu^{a,b}\to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $\beta_\nu^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs

Ordinary Percolation with Discontinuous Transitions

Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel percolation transition with explosive cluster growth can emerge at a nontrivial critical point. There, the usual order parameter, describing the probability of any node to be part of the largest cluster, jumps instantly to a finite value. Here, we provide a simple example of this transition in form of a small-world network consisting of a one-dimensional lattice combined with a hierarchy of long-range bonds that reveals many features of the transition in a mathematically rigorous manner.Comment: RevTex, 5 pages, 4 eps-figs, and Mathematica Notebook as Supplement included. Final version, with several corrections and improvements. For related work, see http://www.physics.emory.edu/faculty/boettcher

Models of plastic depinning of driven disordered systems

Two classes of models of driven disordered systems that exhibit history-dependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The second class allows for proliferation of topological defects due to the interplay of strong disorder and drive. In mean field theory both models exhibit a tricritical point as a function of disorder strength. At weak disorder depinning is continuous and the sliding state is unique. At strong disorder depinning is discontinuous and hysteretic.Comment: 3 figures, invited talk at StatPhys 2

Phase Transition of the Ising model on a Hyperbolic Lattice

The matrix product structure is considered on a regular lattice in the hyperbolic plane. The phase transition of the Ising model is observed on the hyperbolic $(5, 4)$ lattice by means of the corner-transfer-matrix renormalization group (CTMRG) method. Calculated correlation length is always finite even at the transition temperature, where mean-field like behavior is observed. The entanglement entropy is also always finite.Comment: 4 pages, 3 figure

Characterization of a modular enzyme of exo-1,5-α-l-arabinofuranosidase and arabinan binding module from Streptomyces avermitilis NBRC14893

A gene encoding an α-l-arabinofuranosidase, designated SaAraf43A, was cloned from Streptomyces avermitilis. The deduced amino acid sequence implies a modular structure consisting of an N-terminal glycoside hydrolase family 43 module and a C-terminal family 42 carbohydrate-binding module (CBM42). The recombinant enzyme showed optimal activity at pH 6.0 and 45°C and was stable over the pH range of 5.0–6.5 at 30°C. The enzyme hydrolyzed p-nitrophenol (PNP)-α-l-arabinofuranoside but did not hydrolyze PNP-α-l-arabinopyranoside, PNP-β-d-xylopyranoside, or PNP-β-d-galactopyranoside. Debranched 1,5-arabinan was hydrolyzed by the enzyme but arabinoxylan, arabinogalactan, gum arabic, and arabinan were not. Among the synthetic regioisomers of arabinofuranobiosides, only methyl 5-O-α-l-arabinofuranosyl-α-l-arabinofuranoside was hydrolyzed by the enzyme, while methyl 2-O-α-l-arabinofuranosyl-α-l-arabinofuranoside and methyl 3-O-α-l-arabinofuranosyl-α-l-arabinofuranoside were not. These data suggested that the enzyme only cleaves α-1,5-linked arabinofuranosyl linkages. The analysis of the hydrolysis product of arabinofuranopentaose suggested that the enzyme releases arabinose in exo-acting manner. These results indicate that the enzyme is definitely an exo-1,5-α-l-arabinofuranosidase. The C-terminal CBM42 did not show any affinity for arabinogalactan and debranched arabinan, although it bound arabinan and arabinoxylan, suggesting that the CBM42 bound to branched arabinofuranosyl residues. Removal of the module decreased the activity of the enzyme with regard to debranched arabinan. The CBM42 plays a role in enhancing the debranched arabinan hydrolytic action of the catalytic module in spite of its preference for binding arabinofuranosyl side chains