Effect of Hexagonal Boron Nitride on Energy Band Gap of Graphene Antidot Structures

The zero band gap (Eg) graphene becomes narrow Eg semiconductor when graphene is patterned with periodic array of hexagonal shaped antidots, the resultant is the hexagonal Graphene Antidot Lattice (hGAL). Based on the number of atomic chains between antidots, hGALs can be even and odd. The even hGALs (ehGAL) are narrow Eg semiconductors and odd hGALs (ohGAL) are semi-metals. The Eg opening up by hGALs is not sufficient to operate a realistic switching transistor. Also hGAL transistors realized on Si/SiO2 substrate are suffering with low carrier mobility and ON-OFF current ratio. In order to achieve a sizable Eg with good mobility, AB Bernal stacked hGALs on hexagonal Boron Nitride (hBN), ABA Bernal stacked hBN / hGAL / hBN sandwiched structures and AB misaligned hGAL /hBN structures are reported here for the first time. Using the first principles method the electronic structure calculations are performed. A sizable Eg of about 1.04 eV (940+100 meV) is opened when smallest neck width medium radius ehGAL supported on hBN and about 1.1 eV (940 + 200 meV) is opened when the same is sandwiched between hBN layers. A band gap on the order of 71 meV is opened for Bernal stacked ohGAL / hBN and nearly 142 meV opened for hBN / ohGAL /hBN structures for smallest radius and width of nine atomic chains between antidots. Unlike a misaligned graphene on hBN, the misaligned ohGAL/hBN structure shows increased Eg. This study could open up new ways of band gap engineering for graphene based nanostructures. Keywords: Graphene, graphene antidots, hexagonal boron nitride, band structure, band gap engineeringComment: 14 pages, 5 figures, Innovative Systems Design and Engineering,Vol 3, No 12 (2012

Age spreads in clusters and associations: the lithium test

We report the evidence that several low-mass stars (<~0.4 Msun) of the Orion and Upper Scorpius clusters have lithium abundances well below the interstellar value. Due to time-dependent depletion, our result implies stellar ages greater than ~5 Myr, suggesting that star formation has been proceeding for a long time in these systems.Comment: to appear in IMF@50: The Initial Mass Function 50 years later, eds. E. Corbelli et al. (Kluwer Acad. Press), 2004, in pres

On the Chiral WZNW Phase Space, Exchange r-Matrices and Poisson-Lie Groupoids

This is a review of recent work on the chiral extensions of the WZNW phase space describing both the extensions based on fields with generic monodromy as well as those using Bloch waves with diagonal monodromy. The symplectic form on the extended phase space is inverted in both cases and the chiral WZNW fields are found to satisfy quadratic Poisson bracket relations characterized by monodromy dependent exchange r-matrices. Explicit expressions for the exchange r-matrices in terms of the arbitrary monodromy dependent 2-form appearing in the chiral WZNW symplectic form are given. The exchange r-matrices in the general case are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are constructed that encode this equation analogously as PL groups encode the classical YB equation. For an arbitrary simple Lie group $G$, exchange r-matrices are exhibited that are in one-to-one correspondence with the possible PL structures on $G$ and admit them as PL symmetries.Comment: Based on a lecture by L.F. at the Seminaire de Mathematiques Superieures, Montreal, 1999; LaTeX, 21 page

Diffraction in the semiclassical description of mesoscopic devices

In pseudo integrable systems diffractive scattering caused by wedges and impurities can be described within the framework of Geometric Theory of Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory of Diffraction (POTD). We derive formulas expressing the reflection and transition matrix elements for one and many diffractive points and apply it for impurity and wedge diffraction. Diffraction can cause backscattering in situations, where usual semiclassical backscattering is absent causing an erodation of ideal conductance steps. The length of diffractive periodic orbits and diffractive loops can be detected in the power spectrum of the reflection matrix elements. The tail of the power spectrum shows $\sim 1/l^{1/2}$ decay due to impurity scattering and $\sim 1/l^{3/2}$ decay due to wedge scattering. We think this is a universal sign of the presence of diffractive scattering in pseudo integrable waveguides.Comment: 18 pages, Latex , ep

Quantum corrections of Abelian Duality Transformations

A modification of the Abelian Duality transformations is proposed guaranteeing that a (not necessarily conformally invariant) $\sigma$-model be quantum equivalent (at least up to two loops in perturbation theory) to its dual. This requires a somewhat non standard perturbative treatment of the {\sl dual} $\sigma$-model. Explicit formulae of the modified duality transformation are presented for a special class of block diagonal purely metric $\sigma$-models.Comment: Latex 11 pages; remarks on a free model and references adde

Scaling function in AdS/CFT from the O(6) sigma model

Asymptotic behavior of the anomalous dimensions of Wilson operators with high spin and twist is governed in planar N=4 SYM theory by the scaling function which coincides at strong coupling with the energy density of a two-dimensional bosonic O(6) sigma model. We calculate this function by combining the two-loop correction to the energy density for the O(n) model with two-loop correction to the mass gap determined by the all-loop Bethe ansatz in N=4 SYM theory. The result is in agreement with the prediction coming from the thermodynamical limit of the quantum string Bethe ansatz equations, but disagrees with the two-loop stringy corrections to the folded spinning string solution.Comment: 25 pages, 2 figure

Coadjoint orbits of the Virasoro algebra and the global Liouville equation

The classification of the coadjoint orbits of the Virasoro algebra is reviewed and is then applied to analyze the so-called global Liouville equation. The review is self-contained, elementary and is tailor-made for the application. It is well-known that the Liouville equation for a smooth, real field $\phi$ under periodic boundary condition is a reduction of the SL(2,R) WZNW model on the cylinder, where the WZNW field g in SL(2,R) is restricted to be Gauss decomposable. If one drops this restriction, the Hamiltonian reduction yields, for the field $Q=\kappa g_{22}$ where $\kappa\neq 0$ is a constant, what we call the global Liouville equation. Corresponding to the winding number of the SL(2,R) WZNW model there is a topological invariant in the reduced theory, given by the number of zeros of Q over a period. By the substitution $Q=\pm\exp(- \phi/2)$, the Liouville theory for a smooth $\phi$ is recovered in the trivial topological sector. The nontrivial topological sectors can be viewed as singular sectors of the Liouville theory that contain blowing-up solutions in terms of $\phi$. Since the global Liouville equation is conformally invariant, its solutions can be described by explicitly listing those solutions for which the stress-energy tensor belongs to a set of representatives of the Virasoro coadjoint orbits chosen by convention. This direct method permits to study the `coadjoint orbit content' of the topological sectors as well as the behaviour of the energy in the sectors. The analysis confirms that the trivial topological sector contains special orbits with hyperbolic monodromy and shows that the energy is bounded from below in this sector only.Comment: Plain TEX, 48 pages, final version to appear in IJMP

NGC 3603 - a Local Template for Massive Young Clusters

We present a study of the star cluster associated with the massive Galactic HII region NGC3603 based on near-IR broad-- and narrowband observations taken with ISAAC/VLT under excellent seeing conditions (<0.4''). We discuss color-color diagrams and address the impact of the high UV flux on the disk evolution of the low-mass stars.Comment: 3 pages, 3 figures. To appear in the Proceedings of IAU Symposium 207 "Extragalactic Star Clusters", eds. E. Grebel, D. Geisler and D. Minitt

An Introduction to Community Detection in Multi-layered Social Network

Social communities extraction and their dynamics are one of the most important problems in today's social network analysis. During last few years, many researchers have proposed their own methods for group discovery in social networks. However, almost none of them have noticed that modern social networks are much more complex than few years ago. Due to vast amount of different data about various user activities available in IT systems, it is possible to distinguish the new class of social networks called multi-layered social network. For that reason, the new approach to community detection in the multi-layered social network, which utilizes multi-layered edge clustering coefficient is proposed in the paper.Comment: M.D. Lytras et al. (Eds.): WSKS 2011, CCIS 278, pp. 185-190, 201

Local modularity measure for network clusterizations

Many complex networks have an underlying modular structure, i.e., structural subunits (communities or clusters) characterized by highly interconnected nodes. The modularity $Q$ has been introduced as a measure to assess the quality of clusterizations. $Q$ has a global view, while in many real-world networks clusters are linked mainly \emph{locally} among each other (\emph{local cluster-connectivity}). Here, we introduce a new measure, localized modularity $LQ$, which reflects local cluster structure. Optimization of $Q$ and $LQ$ on the clusterization of two biological networks shows that the localized modularity identifies more cohesive clusters, yielding a complementary view of higher granularity.Comment: 5 pages, 4 figures, RevTex4; Changed conten