Edge states of a three-dimensional topological insulator

We use the bulk Hamiltonian for a three-dimensional topological insulator such as Bi-2 Se-3 to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based on a lattice discretization of the bulk Hamiltonian. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge is studied as a function of the edge potential. We show that a magnetic field in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states.

Laterally structured ripple and square phases with one and two dimensional thickness modulations in a model bilayer system

Molecular dynamics simulations of bilayers in a surfactant/co-surfactant/water system with explicit solvent molecules show formation of topologically distinct gel phases depending upon the bilayer composition. At low temperatures, the bilayers transform from the tilted gel phase, L beta', to the one dimensional (1D) rippled, P beta' phase as the surfactant concentration is increased. More interestingly, we observe a two dimensional (2D) square phase at higher surfactant concentration which, upon heating, transforms to the gel L beta' phase. The thickness modulations in the 1D rippled and square phases are asymmetric in two surfactant leaflets and the bilayer thickness varies by a factor of similar to 2 between maximum and minimum. The 1D ripple consists of a thinner interdigitated region of smaller extent alternating with a thicker non-interdigitated region. The 2D ripple phase is made up of two superimposed square lattices of maximum and minimum thicknesses with molecules of high tilt forming a square lattice translated from the lattice formed with the thickness minima. Using Voronoi diagrams we analyze the intricate interplay between the area-per-head-group, height modulations and chain tilt for the different ripple symmetries. Our simulations indicate that composition plays an important role in controlling the formation of low temperature gel phase symmetries and rippling accommodates the increased area-per-head-group of the surfactant molecules.

In-cylinder investigations and analysis of a SI gas engine fuelled with H-2 and CO rich syngas fuel: Sensitivity analysis of combustion descriptors for engine diagnostics and control

The sensitivity of combustion phasing and combustion descriptors to ignition timing, load and mixture quality on fuelling a multi-cylinder natural gas engine with bio-derived H-2 and CO rich syngas is addressed. While the descriptors for conventional fuels are well established and are in use for closed loop engine control, presence of H-2 in syngas potentially alters the mixture properties and hence combustion phasing, necessitating the current study. The ability of the descriptors to predict abnormal combustion, hitherto missing in the literature, is also addressed. Results from experiments using multi-cylinder engines and numerical studies using zero dimensional Wiebe function based simulation models are reported. For syngas with 20% H-2 and CO and 2% CH4 (producer gas), an ignition retard of 5 +/- 1 degrees was required compared to natural gas ignition timing to achieve peak load of 72.8 kWe. It is found that, for syngas, whose flammability limits are 0.42-1.93, the optimal engine operation was at an equivalence ratio of 1.12. The same methodology is extended to a two cylinder engine towards addressing the influence of syngas composition, especially H-2 fraction (varying from 13% to 37%), on the combustion phasing. The study confirms the utility of pressure trace derived combustion descriptors, except for the pressure trace first derivative, in describing the MBT operating condition of the engine when fuelled with an alternative fuel. Both experiments and analysis suggest most of the combustion descriptors to be independent of the engine load and mixture quality. A near linear relationship with ignition angle is observed. The general trend(s) of the combustion descriptors for syngas fuelled operation are similar to those of conventional fuels; the differences in sensitivity of the descriptors for syngas fuelled engine operation requires re-calibration of control logic for MBT conditions. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

2-Connecting outerplanar graphs without blowing up the pathwidth

Given a connected outerplanar graph G of pathwidth p, we give an algorithm to add edges to G to get a supergraph of G, which is 2-vertex-connected, outerplanar and of pathwidth O(p). This settles an open problem raised by Biedl 1], in the context of computing minimum height planar straight line drawings of outerplanar graphs, with their vertices placed on a two-dimensional grid. In conjunction with the result of this paper, the constant factor approximation algorithm for this problem obtained by Biedl 1] for 2-vertex-connected outerplanar graphs will work for all outer planar graphs. (C) 2014 Elsevier B.V. All rights reserved.

Reconstruction of Two-Dimensional Spectra from One-Dimensional Projections-Examples from Solid State NMR

The use of Projection Reconstruction (PR) to obtain two-dimensional (2D) spectra from one-dimensional (1D) data in the solid state is illustrated. The method exploits multiple 1D spectra obtained using magic angle spinning and off-magic angle spinning. The spectra recorded under the influence of scaled heteronuclear scalar and dipolar couplings in the presence of homonuclear dipolar decoupling sequences have been used to reconstruct J/D Resolved 2D-NMR spectra. The use of just two 1D spectra is observed sufficient to reconstruct a J-resolved 2D-spectrum while a Separated Local Field (SLF) 2D-NMR spectrum could be obtained from three 1D spectra. The experimental techniques for recording the 10 spectra and procedure of reconstruction are discussed and the reconstructed results are compared with 20 experiments recorded in traditional methods. The application of the technique has been made to a solid polycrystalline sample and to a uniaxially oriented liquid crystal. Implementation of PR-NMR in solid state provides high-resolution spectra as well as leads to significant reduction in experimental time. The experiments are relatively simple and are devoid of several technical complications involved in performing the 2D experiments.

pentahexoctite: A new two-dimensional allotrope of carbon

The ability of carbon to exist in many forms across dimensions has spawned search in exploring newer allotropes consisting of either, different networks of polygons or rings. While research on various 3D phases of carbon has been extensive, 2D allotropes formed from stable rings are yet to be unearthed. Here, we report a new sp(2) hybridized two-dimensional allotrope consisting of continuous 5-6-8 rings of carbon atoms, named as ``pentahexoctite''. The absence of unstable modes in the phonon spectra ensures the stability of the planar sheet. Furthermore, this sheet has mechanical strength comparable to graphene. Electronically, the sheet is metallic with direction-dependent flat and dispersive bands at the Fermi level ensuring highly anisotropic transport properties. This sheet serves as a precursor for stable 1D nanotubes with chirality-dependent electronic and mechanical properties. With these unique properties, this sheet becomes another exciting addition to the family of robust novel 2D allotropes of carbon.

Exact Phase Retrieval for a Class of 2-D Parametric Signals

We address the problem of two-dimensional (2-D) phase retrieval from magnitude of the Fourier spectrum. We consider 2-D signals that are characterized by first-order difference equations, which have a parametric representation in the Fourier domain. We show that, under appropriate stability conditions, such signals can be reconstructed uniquely from the Fourier transform magnitude. We formulate the phase retrieval problem as one of computing the parameters that uniquely determine the signal. We show that the problem can be solved by employing the annihilating filter method, particularly for the case when the parameters are distinct. For the more general case of the repeating parameters, the annihilating filter method is not applicable. We circumvent the problem by employing the algebraically coupled matrix pencil (ACMP) method. In the noiseless measurement setup, exact phase retrieval is possible. We also establish a link between the proposed analysis and 2-D cepstrum. In the noisy case, we derive Cramer-Rao lower bounds (CRLBs) on the estimates of the parameters and present Monte Carlo performance analysis as a function of the noise level. Comparisons with state-of-the-art techniques in terms of signal reconstruction accuracy show that the proposed technique outperforms the Fienup and relaxed averaged alternating reflections (RAAR) algorithms in the presence of noise.

Heat kernels on the AdS(2) cone and logarithmic corrections to extremal black hole entropy

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N = 4 vector multiplet about a Z(N) orbifold of the near-horizon geometry of quarter-BPS black holes in N = 4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over ZN orbifolds of higher-dimensional spheres and hyperboloids.

Dielectric elastomers: Asymptotically-correct three-dimensional displacement field

Asymptotically-accurate dimensional reduction from three to two dimensions and recovery of 3-D displacement field of non-prestretched dielectric hyperelastic membranes are carried out using the Variational Asymptotic Method (VAM) with moderate strains and very small ratio of the membrane thickness to its shortest wavelength of the deformation along the plate reference surface chosen as the small parameters for asymptotic expansion. Present work incorporates large deformations (displacements and rotations), material nonlinearity (hyperelasticity), and electrical effects. It begins with 3-D nonlinear electroelastic energy and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a 2-D nonlinear plate analysis. Major contribution of this paper is a comprehensive nonlinear through-the-thickness analysis which provides a 2-D energy asymptotically equivalent of the 3-D energy, a 2-D constitutive relation between the 2-D generalized strain and stress tensors for the plate analysis and a set of recovery relations to express the 3-D displacement field. Analytical expressions are derived for warping functions and stiffness coefficients. This is the first attempt to integrate an analytical work on asymptotically-accurate nonlinear electro-elastic constitutive relation for compressible dielectric hyperelastic model with a generalized finite element analysis of plates to provide 3-D displacement fields using VAM. A unified software package `VAMNLM' (Variational Asymptotic Method applied to Non-Linear Material models) was developed to carry out 1-D non-linear analysis (analytical), 2-D non-linear finite element analysis and 3-D recovery analysis. The applicability of the current theory is demonstrated through an actuation test case, for which distribution of 3-D displacements are provided. (C) 2014 Elsevier Ltd. All rights reserved.

Spatial filter based light-sheet laser interference technique for three-dimensional nanolithography

We propose a laser interference technique for the fabrication of 3D nano-structures. This is possible with the introduction of specialized spatial filter in a 2 pi cylindrical lens system (consists of two opposing cylindrical lens sharing a common geometrical focus). The spatial filter at the back-aperture of a cylindrical lens gives rise to multiple light-sheet patterns. Two such interfering counter-propagating light-sheet pattern result in periodic 3D nano-pillar structure. This technique overcomes the existing slow point-by-point scanning, and has the ability to pattern selectively over a large volume. The proposed technique allows large-scale fabrication of periodic structures. Computational study shows a field-of-view (patterning volume) of approximately 12: 2mm(3) with the pillar-size of 80 nm and inter-pillar separation of 180 nm. Applications are in nano-waveguides, 3D nano-electronics, photonic crystals, and optical microscopy. (C) 2015 AIP Publishing LLC.

A magnetic micro-manipulator for application of three dimensional forces

Magnetic manipulation finds diverse applications in actuation, characterization, and manipulation of micro-and nano-scale samples. This paper presents the design and development of a novel magnetic micro-manipulator for application of three-dimensional forces on a magnetic micro-bead. A simple analytical model is proposed to obtain the forces of interaction between the magnetic micromanipulator and a magnetic micro-bead. Subsequently, guidelines are proposed to perform systematic design and analysis of the micro-manipulator. The designed micro-manipulator is fabricated and evaluated. The manipulator is experimentally demonstrated to possess an electrical bandwidth of about 1 MHz. The ability of the micro-manipulator to apply both in-plane and out-of-plane forces is demonstrated by actuating permanent-magnet micro-beads attached to micro-cantilever beams. The deformations of the micro-cantilevers are also employed to calibrate the dependence of in-plane and out-of-plane forces on the position of the micro-bead relative to the micro-manipulator. The experimentally obtained dependences are found to agree well with theory. (C) 2015 AIP Publishing LLC.

VAM Applied to Dimensional Reduction of Nonlinear Multifunctional Film-fabric Laminates

This work aims at asymptotically accurate dimensional reduction of non-linear multi-functional film-fabric laminates having specific application in design of envelopes for High Altitude Airships (HAA). The film-fabric laminate for airship envelope consists of a woven fabric core coated with thin films on each face. These films provide UV protection and Helium leakage prevention, while the core provides required structural strength. This problem is both geometrically and materially non-linear. To incorporate the geometric non-linearity, generalized warping functions are used and finite deformations are allowed. The material non-linearity is handled by using hyper-elastic material models for each layer. The development begins with three-dimensional (3-D) nonlinear elasticity and mathematically splits the analysis into a one-dimensional through-the-thickness analysis and a two-dimensional (2-D) plate analysis. The through-the-thickness analysis provides the 2-D constitutive law which is then given as an input to the 2-D reference surface analysis. The dimensional reduction is carried out using Variational Asymptotic Method (VAM) for moderate strains and very small thickness-to-wavelength ratio. It features the identification and utilization of additional small parameters such as ratio of thicknesses and stiffness coefficients of core and films. Closed form analytical expressions for warping functions and 2-D constitutive law of the film-fabric laminate are obtained.

An Optical How Feature and McFIS Based Approach for 3-Dimensional Human Action Recognition

We propose to develop a 3-D optical flow features based human action recognition system. Optical flow based features are employed here since they can capture the apparent movement in object, by design. Moreover, they can represent information hierarchically from local pixel level to global object level. In this work, 3-D optical flow based features a re extracted by combining the 2-1) optical flow based features with the depth flow features obtained from depth camera. In order to develop an action recognition system, we employ a Meta-Cognitive Neuro-Fuzzy Inference System (McFIS). The m of McFIS is to find the decision boundary separating different classes based on their respective optical flow based features. McFIS consists of a neuro-fuzzy inference system (cognitive component) and a self-regulatory learning mechanism (meta-cognitive component). During the supervised learning, self-regulatory learning mechanism monitors the knowledge of the current sample with respect to the existing knowledge in the network and controls the learning by deciding on sample deletion, sample learning or sample reserve strategies. The performance of the proposed action recognition system was evaluated on a proprietary data set consisting of eight subjects. The performance evaluation with standard support vector machine classifier and extreme learning machine indicates improved performance of McFIS is recognizing actions based of 3-D optical flow based features.

Vacancy mediated clipping of multi-layered graphene: A precursor for 1, 2 and 3D carbon structures

Using first principles calculations, we show that the overlapping defects in bi-layer graphene (both AA-and AB-stacked) interact forming inter-layer covalent bonds, giving rise to two-dimensional (2D) clipped structures, without explicit use of functional groups. These clipped structures can be transformed into one-dimensional (1D) double wall nanotubes (DWCNT) or multi-layered three dimensional (3D) bulk structures. These clipped structures show good mechanical strength due to covalent bonding between multi-layers. Clipping also provides a unique way to simultaneously harness the conductivity of both walls of a double wall nanotube through covalently bonded scattering junctions. With additional conducting channels and improved mechanical stability, these clipped structures can lead to a myriad of applications in novel devices. (C) 2015 Elsevier Ltd. All rights reserved.

Separation index of graphs and stacked 2-spheres

In 1987, Kalai proved that stacked spheres of dimension d >= 3 are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension d = 2. In this article, we give a characterisation of stacked 2-spheres using what we call the separation index. Namely, we show that the separation index of a triangulated 2-sphere is maximal if and only if it is stacked. In addition, we prove that, amongst all n-vertex triangulated 2-spheres, the separation index is minimised by some n-vertex flag sphere for n >= 6. Furthermore, we apply this characterisation of stacked 2-spheres to settle the outstanding 3-dimensional case of the Lutz-Sulanke-Swartz conjecture that ``tight-neighbourly triangulated manifolds are tight''. For dimension d >= 4, the conjecture has already been proved by Effenberger following a result of Novik and Swartz. (C) 2015 Elsevier Inc. All rights reserved.