Conformal field theory correlations in the Abelian sandpile mode

We calculate all multipoint correlation functions of all local bond modifications in the two-dimensional Abelian sandpile model, both at the critical point, and in the model with dissipation. The set of local bond modifications includes, as the most physically interesting case, all weakly allowed cluster variables. The correlation functions show that all local bond modifications have scaling dimension two, and can be written as linear combinations of operators in the central charge -2 logarithmic conformal field theory, in agreement with a form conjectured earlier by Mahieu and Ruelle in Phys. Rev. E 64, 066130 (2001). We find closed form expressions for the coefficients of the operators, and describe methods that allow their rapid calculation. We determine the fields associated with adding or removing bonds, both in the bulk, and along open and closed boundaries; some bond defects have scaling dimension two, while others have scaling dimension four. We also determine the corrections to bulk probabilities for local bond modifications near open and closed boundaries.Comment: 13 pages, 5 figures; referee comments incorporated; Accepted by Phys. Rev.

Automatic Dimension Selection for a Non-negative Factorization Approach to Clustering Multiple Random Graphs

We consider a problem of grouping multiple graphs into several clusters using singular value thesholding and non-negative factorization. We derive a model selection information criterion to estimate the number of clusters. We demonstrate our approach using "Swimmer data set" as well as simulated data set, and compare its performance with two standard clustering algorithms.Comment: This paper has been withdrawn by the author due to a newer version with overlapping content

Higher Order and boundary Scaling Fields in the Abelian Sandpile Model

The Abelian Sandpile Model (ASM) is a paradigm of self-organized criticality (SOC) which is related to $c=-2$ conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the first corrections to such fields, in a field theoretical approach, when the lattice parameter is non-vanishing and consider them in the presence of a boundary.Comment: 7 pages, no figure

Monodomain to polydomain transition in ferroelectric PbTiO3 thin films with La0.67Sr0.3MnO3 electrodes

Finite size effects in ferroelectric thin films have been probed in a series of epitaxial perovskite c-axis oriented PbTiO3 films grown on thin La0.67Sr0.33MnO3 epitaxial electrodes. The film thickness ranges from 480 down to 28 A (7 unit cells). The evolution of the film tetragonality c/a, studied using high resolution x-ray diffraction measurements, shows first a decrease of c/a with decreasing film thickness followed by a recovery of c/a at small thicknesses. This recovery is accompanied by a change from a monodomain to a polydomain configuration of the polarization, as directly demonstrated by piezoresponse atomic force microscopy measurements

Synthesis and Characterization of the k^2-acac-O,O Complex Os_(IV)(acac)_2PhCl and Study of CH Activation with Benzene

We have synthesized and fully characterized the air-stable complex (κ^2-acac-O,O)2Os^(IV)(Ph)Cl (Cl-1-Ph; acac-O,O = acetylacetonate), which reacts with C_6D_6 to generate Cl-1-Ph-d_5 in high yield and catalyzes the H/D exchange reaction between benzene and toluene-d_8 upon heating to 140 °C. To our knowledge, this is the first example of stoichiometric and catalytic, homogeneous, intermolecular CH activation of arenes by a discrete Os complex. The reactions show extended induction periods. DFT studies of Cl-1-Ph and cis-(κ^2-acac-O,O)_2Os^(III)(C_6H_5)(C_6D_6) (cis-(C_6D_6)-2-Ph) found a mechanism involving CH activation by traces of Os(III) and Cl atom transfer between Cl-1-Ph and cis-(C_6D_6)-2-Ph. Experimental data showing that addition of reductants eliminates the induction periods suggest that CH activation occurs from an oxidation state lower than Os^(IV), consistent with the DFT predictions. Consistent with a Cl atom transfer mechanism, the triflate analogue of Cl-1-Ph, OTf-1-Ph, does not undergo a stoichiometric or catalytic reaction with C_6D_6

Boundary conditions and defect lines in the Abelian sandpile model

We add a defect line of dissipation, or crack, to the Abelian sandpile model. We find that the defect line renormalizes to separate the two-dimensional plane into two half planes with open boundary conditions. We also show that varying the amount of dissipation at a boundary of the Abelian sandpile model does not affect the universality class of the boundary condition. We demonstrate that a universal coefficient associated with height probabilities near the defect can be used to classify boundary conditions.Comment: 8 pages, 1 figure; suggestions from referees incorporated; to be published in Phys. Rev.

Fiber Optic Tactical Local Network (FOTLAN)

A 100 Mbit/s FDDI (fiber distributed data interface) network interface unit is described that supports real-time data, voice and video. Its high-speed interrupt-driven hardware architecture efficiently manages stream and packet data transfer to the FDDI network. Other enhancements include modular single-mode laser-diode fiber optic links to maximize node spacing, optic bypass switches for increased fault tolerance, and a hardware performance monitor to gather real-time network diagnostics