Heterogeneous nucleation of nanometre-sized Bi particles embedded in a Zn matrix

It is argued that the nanometric dispersion of Bi in a Zn matrix is an ideal model system for heterogeneous nucleation experiments. The classical theory of heterogeneous nucleation with a hemispherical cap model is applied to analyse the nucleation data. It is shown that, unlike the results of earlier experiments, the derived site density for catalytic nucleation and contact angle are realistic and strongly suggest the validity of the classical theory. The surface energy between the 0001 plane of Zn and the <10(1)over bar 2> plane of Bi, which constitute the epitaxial nucleation interface, is estimated to be 39 mJ m(-2).

Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction

Regenerating codes are a class of distributed storage codes that allow for efficient repair of failed nodes, as compared to traditional erasure codes. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that a failed node be repaired by connecting to any d nodes. The amount of data downloaded for repair is typically much smaller than the size of the source data. Previous constructions of exact-regenerating codes have been confined to the case n = d + 1. In this paper, we present optimal, explicit constructions of (a) Minimum Bandwidth Regenerating (MBR) codes for all values of [n, k, d] and (b) Minimum Storage Regenerating (MSR) codes for all [n, k, d >= 2k - 2], using a new product-matrix framework. The product-matrix framework is also shown to significantly simplify system operation. To the best of our knowledge, these are the first constructions of exact-regenerating codes that allow the number n of nodes in the network, to be chosen independent of the other parameters. The paper also contains a simpler description, in the product-matrix framework, of a previously constructed MSR code with [n = d + 1, k, d >= 2k - 1].

Study of symmetrical and related components through the theory of linear vector spaces

The paper proposes a study of symmetrical and related components, based on the theory of linear vector spaces. Using the concept of equivalence, the transformation matrixes of Clarke, Kimbark, Concordia, Boyajian and Koga are shown to be column equivalent to Fortescue's symmetrical-component transformation matrix. With a constraint on power, criteria are presented for the choice of bases for voltage and current vector spaces. In particular, it is shown that, for power invariance, either the same orthonormal (self-reciprocal) basis must be chosen for both voltage and current vector spaces, or the basis of one must be chosen to be reciprocal to that of the other. The original �¿, ��, 0 components of Clarke are modified to achieve power invariance. For machine analysis, it is shown that invariant transformations lead to reciprocal mutual inductances between the equivalent circuits. The relative merits of the various components are discussed.

Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory

In the present work, the effect of longitudinal magnetic field on wave dispersion characteristics of equivalent continuum structure (ECS) of single-walled carbon nanotubes (SWCNT) embedded in elastic medium is studied. The ECS is modelled as an Euler-Bernoulli beam. The chemical bonds between a SWCNT and the elastic medium are assumed to be formed. The elastic matrix is described by Pasternak foundation model, which accounts for both normal pressure and the transverse shear deformation. The governing equations of motion for the ECS of SWCNT under a longitudinal magnetic field are derived by considering the Lorentz magnetic force obtained from Maxwell's relations within the frame work of nonlocal elasticity theory. The wave propagation analysis is performed using spectral analysis. The results obtained show that the velocity of flexural waves in SWCNTs increases with the increase of longitudinal magnetic field exerted on it in the frequency range: 0-20 THz. The present analysis also shows that the flexural wave dispersion in the ECS of SWCNT obtained by local and nonlocal elasticity theories differ. It is found that the nonlocality reduces the wave velocity irrespective of the presence of the magnetic field and does not influences it in the higher frequency region. Further it is found that the presence of elastic matrix introduces the frequency band gap in flexural wave mode. The band gap in the flexural wave is found to independent of strength of the longitudinal magnetic field. (C) 2011 Elsevier Inc. All rights reserved.

Nonlocal continuum mechanics based ultrasonic flexural wave dispersion characteristics of a monolayer graphene embedded in polymer matrix

Wave propagation in graphene sheet embedded in elastic medium (polymer matrix) has been a topic of great interest in nanomechanics of graphene sheets, where the equivalent continuum models are widely used. In this manuscript, we examined this issue by incorporating the nonlocal theory into the classical plate model. The influence of the nonlocal scale effects has been investigated in detail. The results are qualitatively different from those obtained based on the local/classical plate theory and thus, are important for the development of monolayer graphene-based nanodevices. In the present work, the graphene sheet is modeled as an isotropic plate of one-atom thick. The chemical bonds are assumed to be formed between the graphene sheet and the elastic medium. The polymer matrix is described by a Pasternak foundation model, which accounts for both normal pressure and the transverse shear deformation of the surrounding elastic medium. When the shear effects are neglected, the model reduces to Winkler foundation model. The normal pressure or Winkler elastic foundation parameter is approximated as a series of closely spaced, mutually independent, vertical linear elastic springs where the foundation modulus is assumed equivalent to stiffness of the springs. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. An ultrasonic type of flexural wave propagation model is also derived and the results of the wave dispersion analysis are shown for both local and nonlocal elasticity calculations. From this analysis we show that the elastic matrix highly affects the flexural wave mode and it rapidly increases the frequency band gap of flexural mode. The flexural wavenumbers obtained from nonlocal elasticity calculations are higher than the local elasticity calculations. The corresponding wave group speeds are smaller in nonlocal calculation as compared to local elasticity calculation. The effect of y-directional wavenumber (eta(q)) on the spectrum and dispersion relations of the graphene embedded in polymer matrix is also observed. We also show that the cut-off frequencies of flexural wave mode depends not only on the y-direction wavenumber but also on nonlocal scaling parameter (e(0)a). The effect of eta(q) and e(0)a on the cut-off frequency variation is also captured for the cases of with and without elastic matrix effect. For a given nanostructure, nonlocal small scale coefficient can be obtained by matching the results from molecular dynamics (MD) simulations and the nonlocal elasticity calculations. At that value of the nonlocal scale coefficient, the waves will propagate in the nanostructure at that cut-off frequency. In the present paper, different values of e(0)a are used. One can get the exact e(0)a for a given graphene sheet by matching the MD simulation results of graphene with the results presented in this article. (c) 2012 Elsevier Ltd. All rights reserved.

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.

Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory

We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a trap potential. Since the theory is formulated self-consistently, the numerical implementation relies on a massively parallel evaluation of the self-energy and the Green's function at each lattice site, employing thousands of CPUs. While the computation of the self-energy is straightforward to parallelize, the evaluation of the Green's function requires the inversion of a large sparse 10(d) x 10(d) matrix, with d > 6. As a crucial ingredient, our solution heavily relies on the smallness of the hopping as compared to the interaction strength and yields a widely scalable realization of a rapidly converging iterative algorithm which evaluates all elements of the Green's function. Results are validated by comparing with the homogeneous case via the local-density approximation. These calculations also show that the local-density approximation is valid in nonequilibrium setups without mass transport.

Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1))

The intersection of the ten-dimensional fuzzy conifold Y-F(10) with S-F(5) x S-F(5) is the compact eight-dimensional fuzzy space X-F(8). We show that X-F(8) is (the analogue of) a principal U(1) x U(1) bundle over fuzzy SU(3) / U(1) x U(1)) ( M-F(6)). We construct M-F(6) using the Gell-Mann matrices by adapting Schwinger's construction. The space M-F(6) is of relevance in higher dimensional quantum Hall effect and matrix models of D-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of SU(3) eigenvectors. We construct the Dirac operator on M-F(6) from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.

A matrix model for QCD: QCD color is mixed

We use general arguments to show that colored QCD states when restricted to gauge invariant local observables are mixed. This result has important implications for confinement: a pure colorless state can never evolve into two colored states by unitary evolution. Furthermore, the mean energy in such a mixed colored state is infinite. Our arguments are confirmed in a matrix model for QCD that we have developed using the work of Narasimhan and Ramadas(3) and Singer.(2) This model, a (0 + 1)-dimensional quantum mechanical model for gluons free of divergences and capturing important topological aspects of QCD, is adapted to analytical and numerical work. It is also suitable to work on large N QCD. As applications, we show that the gluon spectrum is gapped and also estimate some low-lying levels for N = 2 and 3 (colors). Incidentally the considerations here are generic and apply to any non-Abelian gauge theory.

Markov chains, R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on R-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Mobius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.

A matrix model for QCD

Gribov's observation that global gauge fixing is impossible has led to suggestions that there may be a deep connection between gauge fixing and confinement. We find an unexpected relation between the topological nontriviality of the gauge bundle and colored states in SU(N) Yang-Mills theory, and show that such states are necessarily impure. We approximate QCD by a rectangular matrix model that captures the essential topological features of the gauge bundle, and demonstrate the impure nature of colored states explicitly. Our matrix model also allows the inclusion of the QCD theta-term, as well as to perform explicit computations of low-lying glueball masses. This mass spectrum is gapped. Since an impure state cannot evolve to a pure one by a unitary transformation, our result shows that the solution to the confinement problem in pure QCD is fundamentally quantum information-theoretic.

Unified Continuum Damage Model for Matrix Cracking in Composite Rotor Blades

This paper deals with modeling of the first damage mode, matrix micro-cracking, in helicopter rotor/wind turbine blades and how this effects the overall cross-sectional stiffness. The helicopter/wind turbine rotor system operates in a highly dynamic and unsteady environment leading to severe vibratory loads present in the system. Repeated exposure to this loading condition can induce damage in the composite rotor blades. These rotor/turbine blades are generally made of fiber-reinforced laminated composites and exhibit various competing modes of damage such as matrix micro-cracking, delamination, and fiber breakage. There is a need to study the behavior of the composite rotor system under various key damage modes in composite materials for developing Structural Health Monitoring (SHM) system. Each blade is modeled as a beam based on geometrically non-linear 3-D elasticity theory. Each blade thus splits into 2-D analyzes of cross-sections and non-linear 1-D analyzes along the beam reference curves. Two different tools are used here for complete 3-D analysis: VABS for 2-D cross-sectional analysis and GEBT for 1-D beam analysis. The physically-based failure models for matrix in compression and tension loading are used in the present work. Matrix cracking is detected using two failure criterion: Matrix Failure in Compression and Matrix Failure in Tension which are based on the recovered field. A strain variable is set which drives the damage variable for matrix cracking and this damage variable is used to estimate the reduced cross-sectional stiffness. The matrix micro-cracking is performed in two different approaches: (i) Element-wise, and (ii) Node-wise. The procedure presented in this paper is implemented in VABS as matrix micro-cracking modeling module. Three examples are presented to investigate the matrix failure model which illustrate the effect of matrix cracking on cross-sectional stiffness by varying the applied cyclic

Non-covalent C-Cl center dot center dot center dot pi interaction in acetylene-carbon tetrachloride adducts: Matrix isolation infrared and ab initio computational studies

Non-covalent halogen-bonding interactions between n cloud of acetylene (C2H2) and chlorine atom of carbon tetrachloride (CCl4) have been investigated using matrix isolation infrared spectroscopy and quantum chemical computations. The structure and the energies of the 1:1 C2H2-CCl4 adducts were computed at the B3LYP, MP2 and M05-2X levels of theory using 6-311++G(d,p) basis set. The computations indicated two minima for the 1:1 C2H2-CCl4 adducts; with the C-Cl center dot center dot center dot pi adduct being the global minimum, where pi cloud of C2H2 is the electron donor. The second minimum corresponded to a C-H...Cl adduct, in which C2H2 is the proton donor. The interaction energies for the adducts A and B were found to be nearly identical. Experimentally, both C-Cl center dot center dot center dot pi and C-H center dot center dot center dot Cl adducts were generated in Ar and N2 matrixes and characterized using infrared spectroscopy. This is the first report on halogen bonded adduct, stabilized through C-Cl center dot center dot center dot pi interaction being identified at low temperatures using matrix isolation infrared spectroscopy. Atoms in Molecules (AIM) and Natural Bond Orbital (NBO) analyses were performed to support the experimental results. The structures of 2:1 ((C2H2)(2)-CCl4) and 1:2 (C2H2-(CCl4)(2)) multimers and their identification in the low temperature matrixes were also discussed. (C) 2015 Elsevier B.V. All rights reserved.

Sidewall inclined slot in a rectangular waveguide: Theory and experiment

A novel analysis to compute the admittance characteristics of the slots cut in the narrow wall of a rectangular waveguide, which includes the corner diffraction effects and the finite waveguide wall thickness, is presented. A coupled magnetic field integral equation is formulated at the slot aperture which is solved by the Galerkin approach of the method of moments using entire domain sinusoidal basis functions. The externally scattered fields are computed using the finite difference method (FDM) coupled with the measured equation of invariance (MEI). The guide wall thickness forms a closed cavity and the fields inside it are evaluated using the standard FDM. The fields scattered inside the waveguide are formulated in the spectral domain for faster convergence compared to the traditional spatial domain expansions. The computed results have been compared with the experimental results and also with the measured data published in previous literature. Good agreement between the theoretical and experimental results is obtained to demonstrate the validity of the present analysis.

Einstein Relation in n-Channel Inversion Layers of Nonlinear Optical, Optoelectronic and Related Materials: Simplified Theory, Relative Comparison and Suggestion for an Experimental Determination

In this paper, we study the Einstein relation for the diffusivity to mobility ratio (DMR) in n-channel inversion layers of non-linear optical materials on the basis of a newly formulated electron dispersion relation by considering their special properties within the frame work of k.p formalism. The results for the n-channel inversion layers of III-V, ternary and quaternary materials form a special case of our generalized analysis. The DMR for n-channel inversion layers of II-VI, IV-VI and stressed materials has been investigated by formulating the respective 2D electron dispersion laws. It has been found, taking n-channel inversion layers of CdGeAs2, Cd(3)AS(2), InAs, InSb, Hg1-xCdxTe, In1-xGaxAsyP1-y lattice matched to InP, CdS, PbTe, PbSnTe, Pb1-xSnxSe and stressed InSb as examples, that the DMR increases with the increasing surface electric field with different numerical values and the nature of the variations are totally band structure dependent. The well-known expression of the DMR for wide gap materials has been obtained as a special case under certain limiting conditions and this compatibility is an indirect test for our generalized formalism. Besides, an experimental method of determining the 2D DMR for n-channel inversion layers having arbitrary dispersion laws has been suggested.