Confinement-deconfinement transition and spin correlations in a generalized Kitaev model

We present a spin model, namely, the Kitaev model augmented by a loop term and perturbed by an Ising Hamiltonian, and show that it exhibits both confinement-deconfinement transitions from spin liquid to antiferromagnetic/spin-chain/ferromagnetic phases and topological quantum phase transitions between gapped and gapless spin-liquid phases. We develop a fermionic resonating-valence-bonds (RVB) mean-field theory to chart out the phase diagram of the model and estimate the stability of its spin-liquid phases, which might be relevant for attempts to realize the model in optical lattices and other spin systems. We present an analytical mean-field theory to study the confinement-deconfinement transition for large coefficient of the loop term and show that this transition is first order within such mean-field analysis in this limit. We also conjecture that in some other regimes, the confinement-deconfinement transitions in the model, predicted to be first order within the mean-field theory, may become second order via a defect condensation mechanism. Finally, we present a general classification of the perturbations to the Kitaev model on the basis of their effect on it's spin correlation functions and derive a necessary and sufficient condition, within the regime of validity of perturbation theory, for the spin correlators to exhibit a long-ranged power-law behavior in the presence of such perturbations. Our results reproduce those of Tikhonov et al. [Phys. Rev. Lett. 106, 067203 (2011)] as a special case.

Temperature dependent transport studies in InN quantum dots grown by droplet epitaxy on silicon nitride/Si substrate

InN quantum dots (QDs) were fabricated on silicon nitride/Si (111) substrate by droplet epitaxy. Single-crystalline structure of InN QDs was verified by transmission electron microscopy, and the chemical bonding configurations of InN QDs were examined by x-ray photoelectron spectroscopy. Photoluminescence measurement shows a slight blue shift compared to the bulk InN, arising from size dependent quantum confinement effect. The interdigitated electrode pattern was created and current-voltage (I-V) characteristics of InN QDs were studied in a metal-semiconductor-metal configuration in the temperature range of 80-300K. The I-V characteristics of lateral grown InN QDs were explained by using the trap model. (C) 2011 American Institute of Physics. [doi:10.1063/1.3651762]

Topology Optimization of Electrostatically Actuated Micromechanical Structures with Accurate Electrostatic Modeling of the Interpolated Material Model

In this paper, we present a novel formulation for performing topology optimization of electrostatically actuated constrained elastic structures. We propose a new electrostatic-elastic formulation that uses the leaky capacitor model and material interpolation to define the material state at every point of a given design domain continuously between conductor and void states. The new formulation accurately captures the physical behavior when the material in between a conductor and a void is present during the iterative process of topology optimization. The method then uses the optimality criteria method to solve the optimization problem by iteratively pushing the state of the domain towards that of a conductor or a void in the appropriate regions. We present examples to illustrate the ability of the method in creating the stiffest structure under electrostatic force for different boundary conditions.

Size dependent bandgap of molecular beam epitaxy grown InN quantum dots measured by scanning tunneling spectroscopy

InN quantum dots (QDs) were grown on Si (111) by epitaxial Stranski-Krastanow growth mode using plasma-assisted molecular beam epitaxy. Single-crystalline wurtzite structure of InN QDs was verified by the x-ray diffraction and transmission electron microscopy. Scanning tunneling microscopy has been used to probe the structural aspects of QDs. A surface bandgap of InN QDs was estimated from scanning tunneling spectroscopy (STS) I-V curves and found that it is strongly dependent on the size of QDs. The observed size-dependent STS bandgap energy shifts with diameter and height were theoretical explained based on an effective mass approximation with finite-depth square-well potential model.

Microscopic study of the 2/5 fractional quantum Hall edge

This paper reports on our study of the edge of the 2/5 fractional quantum Hall state, which is more complicated than the edge of the 1/3 state because of the presence of edge sectors corresponding to different partitions of composite fermions in the lowest two Lambda levels. The addition of an electron at the edge is a nonperturbative process and it is not a priori obvious in what manner the added electron distributes itself over these sectors. We show, from a microscopic calculation, that when an electron is added at the edge of the ground state in the [N(1), N(2)] sector, where N(1) and N(2) are the numbers of composite fermions in the lowest two Lambda levels, the resulting state lies in either [N(1) + 1, N(2)] or [N(1), N(2) + 1] sectors; adding an electron at the edge is thus equivalent to adding a composite fermion at the edge. The coupling to other sectors of the form [N(1) + 1 + k, N(2) - k], k integer, is negligible in the asymptotically low-energy limit. This study also allows a detailed comparison with the two-boson model of the 2/5 edge. We compute the spectral weights and find that while the individual spectral weights are complicated and nonuniversal, their sum is consistent with an effective two-boson description of the 2/5 edge.

Validation of a Modified Eddy Dissipation Concept Model for Stationary and Nonstationary Turbulent Diffusion Flames

A transient flame simulation tool based on unsteady Reynolds average Navier Stokes (RANS) is characterized for stationary and nonstationary flame applications with a motivation of performing computationally affordable flame stability studies. Specifically, the KIVA-3V code is utilized with incorporation of a recently proposed modified eddy dissipation concept for simulating turbulence-chemistry interaction along with a model for radiation loss. Detailed comparison of velocities, turbulent kinetic energies, temperature, and species are made with the experimental data of the turbulent, non-premixed DLR_A CH4/H-2/N-2 jet flame. The comparison shows that the model is able to predict flame structure very well. The effect of some of the modeling assumptions is assessed, and strategies to model a stationary diffusion flame are recommended. Unsteady flame simulation capabilities of the numerical model are assessed by simulating an acoustically excited, experimental, oscillatory H-2-air diffusion flame. Comparisons are made with oscillatory velocity field and OH plots, and the numerical code is observed to predict transient flame structure well.

Chemical and shifted mechanical thresholds in Al-Ge-Te glass system

We report the results of the electrical switching studies performed on the bulk Al20GexTe80-x (2.5 less than or equal to x less than or equal to 15) chalcogenide glasses. The well known topological features, mechanical and chemical thresholds are observed. Mechanical threshold is seen at a mean coordination number of atoms, < r > = 2.50 (x = 5) a clear shift rom the mean field value of < r > = 2.4 whereas the chemical threshold is observed at < r > = 2.65 (x = 12.5) as predicted by the chemically ordered covalent network model These experiments are a sequel to similar experiments on Al20AsxTe80-x glasses in which mechanical threshold was seen at < r > = 2.60 and no chemical threshold was observed These results am well understood by a chemical bond picture developed in this article.

A k-epsilon model for turbulent weld pool convection in gas metal arc welding process

In this paper, we present a modified k - epsilon model capable of addressing turbulent weld-pool convection in a GMAW process, taking into account the morphology of the phase change interface during a Gas Metal Arc Welding (GMAW) process. A three-dimensional turbulence mathematical model has been developed to study the heat transfer and fluid flow within the weld pool by considering the combined effect of three driving forces, viz., buoyancy, Lorentz force and surface tension (Marangoni convection). Mass and energy transports by the droplets are considered through the thermal analysis of the electrode. The falling droplet's heat addition to the molten pool is considered to be a volumetric heat source distributed in an imaginary cylindrical cavity ("cavity model") within the weld pool. This nature of heat source distribution takes into account the momentum and the thermal, energy of the falling droplets. The numerically predicted weld pool dimensions both from turbulence and laminar models are then compared with the experimental post-weld results sectioned across the weld axis. The above comparison enables us to analyze the overall effects of turbulent convection on the nature of heat and fluid flow and hence on the weld pool shape/size during the arc welding processes.

An EDC-based turbulent premixed combustion model

In the present study, a new turbulent premixed combustion model is proposed by integrating the Coherent Flame Model with the modified eddy dissipation concept, and relating the fine structure mass fraction to the flame surface density. First, experimental results of turbulent flame speed available from literature are compared with the predicted results at different turbulence intensities to validate the flame surface density model. It is observed that the model is able to predict the turbulent burning speeds accurately. Then, a comprehensive validation is carried out utilizing data on a turbulent lifted methane flame issuing into a vitiated co-flow. Detailed comparison of temperature and species concentrations between experiment and simulation is performed at different heights of the flame. Overall, the model is found to predict both the spatial variation and peak values of the scalars at various heights satisfactorily.

Quenching across quantum critical points in periodic systems: Dependence of scaling laws on periodicity

We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-1/2 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the (z) over cap direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a positive integer. For a linear quench of the strength of the magnetic field (or chemical potential) at a rate 1/tau across a quantum critical point, we find that the density of defects thereby produced scales as 1/tau(q/(q+1)), deviating from the 1/root tau scaling that is ubiquitous in a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a nonlinear quench as well as by performing numerical simulations. We also show that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of tau, although it may exhibit a crossover at intermediate values of tau. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and the interaction strength.

Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the ``fully frustrated'' Bose-Hubbard model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time-reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.

Prediction of inter-laminar stresses in composite honeycomb sandwich panels under mechanical loading using Variational Asymptotic Method

This work focuses on the formulation of an asymptotically correct theory for symmetric composite honeycomb sandwich plate structures. In these panels, transverse stresses tremendously influence design. The conventional 2-D finite elements cannot predict the thickness-wise distributions of transverse shear or normal stresses and 3-D displacements. Unfortunately, the use of the more accurate three-dimensional finite elements is computationally prohibitive. The development of the present theory is based on the Variational Asymptotic Method (VAM). Its unique features are the identification and utilization of additional small parameters associated with the anisotropy and non-homogeneity of composite sandwich plate structures. These parameters are ratios of smallness of the thickness of both facial layers to that of the core and smallness of 3-D stiffness coefficients of the core to that of the face sheets. Finally, anisotropy in the core and face sheets is addressed by the small parameters within the 3-D stiffness matrices. Numerical results are illustrated for several sample problems. The 3-D responses recovered using VAM-based model are obtained in a much more computationally efficient manner than, and are in agreement with, those of available 3-D elasticity solutions and 3-D FE solutions of MSC NASTRAN. (c) 2012 Elsevier Ltd. All rights reserved.