Continuum theory of edge states of topological insulators: variational principle and boundary conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

Theory and Algorithms for Hop-Count-Based Localization with Random Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes in a region of Euclidean space. Following deployment, the nodes self-organize into a mesh topology with a key aspect being self-localization. Having obtained a mesh topology in a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this work, we analyze this approximation through two complementary analyses. We assume that the mesh topology is a random geometric graph on the nodes; and that some nodes are designated as anchors with known locations. First, we obtain high probability bounds on the Euclidean distances of all nodes that are h hops away from a fixed anchor node. In the second analysis, we provide a heuristic argument that leads to a direct approximation for the density function of the Euclidean distance between two nodes that are separated by a hop distance h. This approximation is shown, through simulation, to very closely match the true density function. Localization algorithms that draw upon the preceding analyses are then proposed and shown to perform better than some of the well-known algorithms present in the literature. Belief-propagation-based message-passing is then used to further enhance the performance of the proposed localization algorithms. To our knowledge, this is the first usage of message-passing for hop-count-based self-localization.

Energy-dependent orbital modulation of X-rays and constraints on emission of the jet in Cyg X-3

We study the orbital modulation of X-rays from Cyg X-3, using data from Swift, INTEGRAL and RXTE. Using the wealth of data presently available and an improved averaging method, we obtain energy-dependent folded and averaged light curves with unprecedented accuracy. We find that above similar to 5?keV the modulation depth decreases with increasing energy, which is consistent with the modulation being caused by both boundfree absorption and Compton scattering in the stellar wind of the donor, with minima corresponding to the highest optical depth, which occurs around the superior conjunction. We find a decrease of the depth below similar to 3?keV, which appears to be due to re-emission of the absorbed continuum by the wind in soft X-ray lines. Based on the shape of the folded light curves, any X-ray contribution from the jet in Cyg X-3, which emits ?-rays detected at energies >0.1?GeV in the soft spectral states, is found to be minor up to similar to 100?keV. This implies the presence of a rather sharp low-energy break in the jet MeV-range spectrum. We also calculate phase-resolved RXTE X-ray spectra and show that the difference between the spectra corresponding to phases around superior and inferior conjunctions can indeed be accounted for by the combined effect of boundfree absorption in an ionized medium and Compton scattering.

A new diketopyrrolopyrrole-based co-polymer for ambipolar field-effect transistors and solar cells

A new thieno3,2-b]thiophenediketopyrrolopyrrole-benzo1,2-b:4,5-b']dithio phene based narrow optical gap co-polymer (PTTDPP-BDT) has been synthesized and characterized for field-effect transistors and solar cells. In field-effect transistors the polymer exhibited ambipolar charge transport behaviour with maximum hole and electron mobilities of 10(-3) cm(2) V-1 s(-1) and 10(-5) cm(2)V(-1) s(-1), respectively. The respectable charge transporting properties of the polymer were consistent with X-ray diffraction measurements that showed close molecular packing in the solid state. The difference in hole and electron mobilities was explained by density functional theory calculations, which showed that the highest occupied molecular orbital was delocalized along the polymer backbone with the lowest unoccupied molecular orbital localized on the bis(thieno3,2-b]thiophene)diketopyrrolopyrrole units. Bulk heterojunction photovoltaic devices with the fullerene acceptor PC70BM were fabricated and delivered a maximum conversion efficiency of 3.3% under AM1.5G illumination. (C) 2012 Elsevier B.V. All rights reserved.

A finite population model of mlecular evolution: theory and computation

This article is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work has impacted antiviral treatment and vaccine design strategies. Yet, predictions of the quasispecies model are at best viewed as a guideline, primarily because it assumes an infinite population size, whereas realistic population sizes can be quite small. In this paper we consider a population genetics-based model aimed at understanding the evolution of such organisms with finite population sizes and present a rigorous study of the convergence and computational issues that arise therein. Our first result is structural and shows that, at any time during the evolution, as the population size tends to infinity, the distribution of genomes predicted by our model converges to that predicted by the quasispecies model. This justifies the continued use of the quasispecies model to derive guidelines for intervention. While the stationary state in the quasispecies model is readily obtained, due to the explosion of the state space in our model, exact computations are prohibitive. Our second set of results are computational in nature and address this issue. We derive conditions on the parameters of evolution under which our stochastic model mixes rapidly. Further, for a class of widely used fitness landscapes we give a fast deterministic algorithm which computes the stationary distribution of our model. These computational tools are expected to serve as a framework for the modeling of strategies for the deployment of mutagenic drugs.

Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

Ampcalculator (AMPC) is a Mathematica (c) based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one loop (upto O(p(4))) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling G(27). Another illustrative set of amplitudes at tree level we provide is in the context of tau-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. The Kaon-Compton amplitude has been checked and a minor error in the published results has been pointed out. This exercise is a tutorial-based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.

Intermolecular charge transfer and vibrational analysis of hydrogen bonding in acetazolamide

In the present work the structural and spectral characteristics of acetazolamide have been studied by methods of infrared, Raman spectroscopy and quantum chemistry. Electrostatic potential surface, optimized geometry, harmonic vibrational frequencies, infrared intensities and activities of Raman scattering were calculated by density functional theory (DFT) employing B3LYP with complete relaxation in the potential energy surface using 6-311++G(d,p) basis set. Based on these results, we have discussed the correlation between the vibrational modes and the structure of the dimers of acetazolamide. The calculated vibrational spectra of three dimers of acetazolamide have been compared with observed spectra, and the assignment of observed bands was carried out using potential energy distribution. The observed spectra agree well with the values computed from the OFT. A comparison of observed and calculated vibrational spectra clearly shows the effect of hydrogen bonding. The frequency shifts observed for the different dimers are in accord with the hydrogen bonding in acetazolamide. Natural bond orbital (NBO) analyses reflect the charge transfer interaction in the individual hydrogen bond units and the stability of different dimers of acetazolamide. (C) 2012 Elsevier B.V. All rights reserved.

Pattern clustering using cooperative game theory

In this paper, we approach the classical problem of clustering using solution concepts from cooperative game theory such as Nucleolus and Shapley value. We formulate the problem of clustering as a characteristic form game and develop a novel algorithm DRAC (Density-Restricted Agglomerative Clustering) for clustering. With extensive experimentation on standard data sets, we compare the performance of DRAC with that of well known algorithms. We show an interesting result that four prominent solution concepts, Nucleolus, Shapley value, Gately point and \tau-value coincide for the defined characteristic form game. This vindicates the choice of the characteristic function of the clustering game and also provides strong intuitive foundation for our approach.

Can the viscosity in astrophysical black hole accretion disks be close to its string theory bound?

String theory and gauge/gravity duality suggest the lower bound of shear viscosity (eta) to entropy density (s) for any matter to be mu h/4 pi k(B), when h and k(B) are reduced Planck and Boltzmann constants respectively and mu <= 1. Motivated by this, we explore eta/s in black hole accretion flows, in order to understand if such exotic flows could be a natural site for the lowest eta/s. Accretion flow plays an important role in black hole physics in identifying the existence of the underlying black hole. This is a rotating shear flow with insignificant molecular viscosity, which could however have a significant turbulent viscosity, generating transport, heat and hence entropy in the flow. However, in presence of strong magnetic field, magnetic stresses can help in transporting matter independent of viscosity, via celebrated Blandford-Payne mechanism. In such cases, energy and then entropy produces via Ohmic dissipation. In,addition, certain optically thin, hot, accretion flows, of temperature greater than or similar to 10(9) K, may be favourable for nuclear burning which could generate/absorb huge energy, much higher than that in a star. We find that eta/s in accretion flows appears to be close to the lower bound suggested by theory, if they are embedded by strong magnetic field or producing nuclear energy, when the source of energy is not viscous effects. A lower bound on eta/s also leads to an upper bound on the Reynolds number of the flow.

Analytical theory and stability analysis of an elongated nanoscale object under external torque

We consider the rotational motion of an elongated nanoscale object in a fluid under an external torque. The experimentally observed dynamics could be understood from analytical solutions of the Stokes equation, with explicit formulae derived for the dynamical states as a function of the object dimensions and the parameters defining the external torque. Under certain conditions, multiple analytical solutions to the Stokes equations exist, which have been investigated through numerical analysis of their stability against small perturbations and their sensitivity towards initial conditions. These experimental results and analytical formulae are general enough to be applicable to the rotational motion of any isolated elongated object at low Reynolds numbers, and could be useful in the design of non-spherical nanostructures for diverse applications pertaining to microfluidics and nanoscale propulsion technologies.

DETERMINATION OF THE STRONG COUPLING FROM HADRONIC TAU DECAYS USING RENORMALIZATION GROUP SUMMED PERTURBATION THEORY

Be the strong coupling constant alpha(s) from the tau hadronn width using a renormalization group summed (RGS) expansion of the QCD Adler lunction. The main theoretical uncertainty in the extraction of as is due to the manner in which renormalization group invariance is implemented, and the as yet uncalculated higher order terms in the QCD perturbative series. We show that new expansion exhibits good renormalization group improvement and the behavior of the series is similar to that of the standard RGS expansion. The value of the strong coupling in (MS) over bar scheme obtained with the RCS expansion is alpha(s) (M-tau(2)) = 0.338 +/- 0.010. The convergence properties of the new expansion can be improved by Bond transformation and analytic continuation in t he Bond plane. This is discussed elsewhere in these issues.

Expansions of tau hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling alpha(s) and other QCD parameters from the hadronic decays of the tau lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher-order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called ``reference model,'' including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.

Gap renormalization of molecular crystals from density-functional theory

Fundamental gap renormalization due to electronic polarization is a basic phenomenon in molecular crystals. Despite its ubiquity and importance, all conventional approaches within density-functional theory completely fail to capture it, even qualitatively. Here, we present a new screened range-separated hybrid functional, which, through judicious introduction of the scalar dielectric constant, quantitatively captures polarization-induced gap renormalization, as demonstrated on the prototypical organic molecular crystals of benzene, pentacene, and C-60. This functional is predictive, as it contains system-specific adjustable parameters that are determined from first principles, rather than from empirical considerations.

Novel procedure for the estimation of swelling pressures of compacted bentonites based on diffuse double layer theory

Bentonite clays are proven to be attractive as buffer and backfill material in high-level nuclear waste repositories around the world. A quick estimation of swelling pressures of the compacted bentonites for different clay-water-electrolyte interactions is essential in the design of buffer and backfill materials. The theoretical studies on the swelling behavior of bentonites are based on diffuse double layer (DDL) theory. To establish theoretical relationship between void ratio and swelling pressure (e versus P), evaluation of elliptic integral and inverse analysis are unavoidable. In this paper, a novel procedure is presented to establish theoretical relationship of e versus P based on the Gouy-Chapman method. The proposed procedure establishes a unique relationship between electric potentials of interacting and non-interacting diffuse clay-water-electrolyte systems. A procedure is, thus, proposed to deduce the relation between swelling pressures and void ratio from the established relation between electric potentials. This approach is simple and alleviates the need for elliptic integral evaluation and also the inverse analysis. Further, application of the proposed approach to estimate swelling pressures of four compacted bentonites, for example, MX 80, Febex, Montigel and Kunigel V1, at different dry densities, shows that the method is very simple and predicts solutions with very good accuracy. Moreover, the proposed procedure provides continuous distributions of e versus P and thus it is computationally efficient when compared with the existing techniques.