Elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.

Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

Deformations of the Tracy-Widom distribution

In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists of removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristic of extreme values of an uncorrelated sequence, is obtained.

Quantum Hall Effect near the Charge Neutrality Point in a Two-Dimensional Electron-Hole System

We study the transport properties of HgTe-based quantum wells containing simultaneously electrons and holes in a magnetic field B. At the charge neutrality point (CNP) with nearly equal electron and hole densities, the resistance is found to increase very strongly with B while the Hall resistivity turns to zero. This behavior results in a wide plateau in the Hall conductivity sigma(xy) approximate to 0 and in a minimum of diagonal conductivity sigma(xx) at nu = nu(p) - nu(n) = 0, where nu(n) and nu(p) are the electron and hole Landau level filling factors. We suggest that the transport at the CNP point is determined by electron-hole ""snake states'' propagating along the nu = 0 lines. Our observations are qualitatively similar to the quantum Hall effect in graphene as well as to the transport in a random magnetic field with a zero mean value.

Unraveling effects of disorder on the electronic structure of SiO(2) from first principles

We present a first-principles systematic study of the electronic structure of SiO(2) including the crystalline polymorphs alpha quartz and beta cristobalite, and different types of disorder leading to the amorphous phase. We start from calculations within density functional theory and proceed to more sophisticated quasiparticle calculations according to the GW scheme. Our results show that different origins of disorder have also different impact on atomic and electronic-density fluctuations, which affect the electronic structure and, in particular, the size of the mobility gap in each case.

Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

Communication structure of cortical networks

Large-scale cortical networks exhibit characteristic topological properties that shape communication between brain regions and global cortical dynamics. Analysis of complex networks allows the description of connectedness, distance, clustering, and centrality that reveal different aspects of how the network's nodes communicate. Here, we focus on a novel analysis of complex walks in a series of mammalian cortical networks that model potential dynamics of information flow between individual brain regions. We introduce two new measures called absorption and driftness. Absorption is the average length of random walks between any two nodes, and takes into account all paths that may diffuse activity throughout the network. Driftness is the ratio between absorption and the corresponding shortest path length. For a given node of the network, we also define four related measurements, namely in-and out-absorption as well as in-and out-driftness, as the averages of the corresponding measures from all nodes to that node, and from that node to all nodes, respectively. We find that the cat thalamo-cortical system incorporates features of two classic network topologies, Erdos-Renyi graphs with respect to in-absorption and in-driftness, and configuration models with respect to out-absorption and out-driftness. Moreover, taken together these four measures separate the network nodes based on broad functional roles (visual, auditory, somatomotor, and frontolimbic).

Directed Abelian algebras and their application to stochastic models

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma(tau)=3/2). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma(tau)=1.780 +/- 0.005.

Fluoride-modified electrical properties of lead borate glasses and electrochemically induced crystallization in the glassy state

Lead fluoroborate glasses were prepared by the melt-quenching technique and characterized in terms of (micro)structural and electrical properties. The study was conducted on as prepared as well as temperature- and/or electric field-treated glass samples. The results show that, in the as-prepared glassy-state materials, electrical conductivity improved with increasing the PbF(2) glass content. This result involves both an increase of the fluoride charge carrier density and, especially, a decrease of the activation energy from a glass structure expansion improving charge carrier mobility. Moreover, for the electric field-treated glass samples, surface crystallization was observed even below the glass transition temperature. As previously proposed in literature, and shown here, the occurrence of this phenomenon arose from an electrochemically induced redox reaction at the electrodes, followed by crystallite nucleation. Once nucleated, growth of beta-PbF(2) crystallites, with the indication of incorporating reduced lead ions (Pb(+)), was both (micro)structurally and electrically detectable and analyzed. The overall crystallization-associated features observed here adapt well with the floppy-rigid model that has been proposed to further complete the original continuous-random-network model by Zachariasen for closely addressing not only glasses' structure but also crystallization mechanism. Finally, the crystallization-modified kinetic picture of the glasses' electrical properties, through application of polarization/depolarization measurements originally combined with impedance spectroscopy, was extensively explored. (c) 2008 American Institute of Physics.

Structural models for yttrium aluminium borate laser glasses: NMR and EPR studies of the system (Y(2)O(3))(0.2)-(Al(2)O(3))(x)-(B(2)O(3))(0.8-x)

The structure of laser glasses in the system (Y(2)O(3))(0.2){(Al(2)O(3))(x))(B(2)O(3))(0.8-x)} (0.15 <= x <= 0.40) has been investigated by means of (11)B, (27)Al, and (89)Y solid state NMR as well as electron spin echo envelope modulation (ESEEM) of Yb-doped samples. The latter technique has been applied for the first time to an aluminoborate glass system. (11)B magic-angle spinning (MAS)-NMR spectra reveal that, while the majority of the boron atoms are three-coordinated over the entire composition region, the fraction of three-coordinated boron atoms increases significantly with increasing x. Charge balance considerations as well as (11)B NMR lineshape analyses suggest that the dominant borate species are predominantly singly charged metaborate (BO(2/2)O(-)), doubly charged pyroborate (BO(1/2)(O(-))(2)), and (at x = 0.40) triply charged orthoborate groups. As x increases along this series, the average anionic charge per trigonal borate group increases from 1.38 to 2.91. (27)Al MAS-NMR spectra show that the alumina species are present in the coordination states four, five and six, and the fraction of four-coordinated Al increases markedly with increasing x. All of the Al coordination states are in intimate contact with both the three-and the four-coordinate boron species and vice versa, as indicated by (11)B/(27)Al rotational echo double resonance (REDOR) data. These results are consistent with the formation of a homogeneous, non-segregated glass structure. (89)Y solid state NMR spectra show a significant chemical shift trend, reflecting that the second coordination sphere becomes increasingly ""aluminate-like'' with increasing x. This conclusion is supported by electron spin echo envelope modulation (ESEEM) data of Yb-doped glasses, which indicate that both borate and aluminate species participate in the medium range structure of the rare-earth ions, consistent with a random spatial distribution of the glass components.

Sodium distribution in mixed alkali K-Na metaphosphate glasses

The local order and distribution of Na in the mixed alkali metaphosphate glasses K(x)Na(1-x)PO(3) were analyzed, with the aim to identify segregation or a random mixture of both cation species. X-Ray photoelectron spectroscopy and several nuclear magnetic resonance (NMR) techniques were applied, including (31)P and (23)Na high-resolution spectroscopy, (23)Na triple quantum-MAS NMR, rotational echo double resonance between (31)P and (23)Na, and (23)Na NMR spin echo decay. The structural picture emerging from these results reveals the similarity in the local Na environments in the glasses but also subtle structural adjustments with increasing degree of K replacement. While both cations are intimately mixed at the atomic scale, the (23)Na spin echo decay data suggest a detectable like-cation preference in the spatial distribution of the ions. These structural properties are consistent with those determined in Li-Rb metaphosphates, indicating that the origin of the mixed alkali effect observed in the conductivity of Na-K metaphosphate glasses may also be explained by structurally blocked ion diffusion.

Covariant Gauge on the Lattice: A New Implementation

We derive a new implementation of linear covariant gauges on the lattice, based on a minimizing functional that can be interpreted as the Hamiltonian of a spin-glass model in a random external magnetic field. We show that our method solves most problems encountered in earlier implementations, mostly related to the no-go condition formulated by Giusti [Nucl. Phys. B498, 331 (1997)]. We carry out tests in the SU(2) case in four space-time dimensions. We also present preliminary results for the transverse gluon propagator at different values of the gauge parameter xi.