Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems

In this article, we study the problem of determining an appropriate grading of meshes for a system of coupled singularly perturbed reaction-diffusion problems having diffusion parameters with different magnitudes. The central difference scheme is used to discretize the problem on adaptively generated mesh where the mesh equation is derived using an equidistribution principle. An a priori monitor function is obtained from the error estimate. A suitable a posteriori analogue of this monitor function is also derived for the mesh construction which will lead to an optimal second-order parameter uniform convergence. We present the results of numerical experiments for linear and semilinear reaction-diffusion systems to support the effectiveness of our preferred monitor function obtained from theoretical analysis. (C) 2014 Elsevier Inc. All rights reserved.

Acoustic phonon behavior of PbWO4 and BaWO4 probed by low temperature Brillouin spectroscopy

Temperature dependent acoustic phonon behavior of PbWO4 and BaWO4 using Brillouin spectroscopy has been explained for the first time. Low temperature Brillouin studies on PbWO4 and BaWO4 have been carried out from 320-20 K. In PbWO4, we observe a change in acoustic phonon mode behavior around 180 K. But in the case of BaWO4, we have observed two types of change in acoustic phonon mode behavior at 240 K and 130 K. The change in Brillouin shift omega and the slope d omega/dT are the order parameter for all kinds of phase transitions. Since we do not see hysteresis on acoustic phonon mode behavior in the reverse temperature experiments, these second order phase transitions are no related to structural phase change and could be related to acoustic phonon coupled electronic transitions. In PbWO4 he temperature driven phase transition at 180 K could be due to changes in he environment around he lead vacancy (V-pb(2-)) changes the electronic states. In the case of BaWO4, the phase transition at 240 K shows he decrease in penetration depth of WO3 impurity. So it becomes more metallic. The transition at 130 K could be he same electronic transitions as that of PbWO4 as function of temperature. The sound velocity and elastic moduli of BaWO4 shows that it could be the prominent material for acousto-optic device applications. (C) 2014 Elsevier Ltd. All rights reserved.

Faster computation of the Karhunen-Loeve expansion using its domain independence property

The goal of this work is to reduce the cost of computing the coefficients in the Karhunen-Loeve (KL) expansion. The KL expansion serves as a useful and efficient tool for discretizing second-order stochastic processes with known covariance function. Its applications in engineering mechanics include discretizing random field models for elastic moduli, fluid properties, and structural response. The main computational cost of finding the coefficients of this expansion arises from numerically solving an integral eigenvalue problem with the covariance function as the integration kernel. Mathematically this is a homogeneous Fredholm equation of second type. One widely used method for solving this integral eigenvalue problem is to use finite element (FE) bases for discretizing the eigenfunctions, followed by a Galerkin projection. This method is computationally expensive. In the current work it is first shown that the shape of the physical domain in a random field does not affect the realizations of the field estimated using KL expansion, although the individual KL terms are affected. Based on this domain independence property, a numerical integration based scheme accompanied by a modification of the domain, is proposed. In addition to presenting mathematical arguments to establish the domain independence, numerical studies are also conducted to demonstrate and test the proposed method. Numerically it is demonstrated that compared to the Galerkin method the computational speed gain in the proposed method is of three to four orders of magnitude for a two dimensional example, and of one to two orders of magnitude for a three dimensional example, while retaining the same level of accuracy. It is also shown that for separable covariance kernels a further cost reduction of three to four orders of magnitude can be achieved. Both normal and lognormal fields are considered in the numerical studies. (c) 2014 Elsevier B.V. All rights reserved.

Magnetic frustration and dielectric relaxation in insulating Nd2NiMnO6 double perovskites

We have investigated structural, dielectric, and magnetic properties of polycrystalline double perovskite Nd2NiMnO6 compound. The compound crystallizes in monoclinic P2(1)/n symmetry and is partially B-site disordered depending on the synthesis conditions. It undergoes second-order ferromagnetic transition at 192K and shows glassy behaviour at low temperature. The glassy phase is due to anti-site disorder within the homogeneous sample. Temperature and frequency dependent dielectric measurements reveal colossal values of dielectric constant and is best interpreted using Maxwell-Wagner interfacial polarization model. Impedance spectroscopy has been used to analyse the intrinsic dielectric response. This enabled us to differentiate the conduction process at the grain and grain boundaries. Arrhenius behaviour is favoured at the grain boundary, while variable range hopping mechanism is considered most suitable within the grain region. dc conductivity measurements corroborate variable range hopping conduction. (C) 2015 AIP Publishing LLC.

Simultaneous perturbation methods for adaptive labor staffing in service systems

We consider the problem of optimizing the workforce of a service system. Adapting the staffing levels in such systems is non-trivial due to large variations in workload and the large number of system parameters do not allow for a brute force search. Further, because these parameters change on a weekly basis, the optimization should not take longer than a few hours. Our aim is to find the optimum staffing levels from a discrete high-dimensional parameter set, that minimizes the long run average of the single-stage cost function, while adhering to the constraints relating to queue stability and service-level agreement (SLA) compliance. The single-stage cost function balances the conflicting objectives of utilizing workers better and attaining the target SLAs. We formulate this problem as a constrained parameterized Markov cost process parameterized by the (discrete) staffing levels. We propose novel simultaneous perturbation stochastic approximation (SPSA)-based algorithms for solving the above problem. The algorithms include both first-order as well as second-order methods and incorporate SPSA-based gradient/Hessian estimates for primal descent, while performing dual ascent for the Lagrange multipliers. Both algorithms are online and update the staffing levels in an incremental fashion. Further, they involve a certain generalized smooth projection operator, which is essential to project the continuous-valued worker parameter tuned by our algorithms onto the discrete set. The smoothness is necessary to ensure that the underlying transition dynamics of the constrained Markov cost process is itself smooth (as a function of the continuous-valued parameter): a critical requirement to prove the convergence of both algorithms. We validate our algorithms via performance simulations based on data from five real-life service systems. For the sake of comparison, we also implement a scatter search based algorithm using state-of-the-art optimization tool-kit OptQuest. From the experiments, we observe that both our algorithms converge empirically and consistently outperform OptQuest in most of the settings considered. This finding coupled with the computational advantage of our algorithms make them amenable for adaptive labor staffing in real-life service systems.

Robust design of multiple trailing edge flaps for helicopter vibration reduction: A multi-objective bat algorithm approach

The objective of this study is to determine an optimal trailing edge flap configuration and flap location to achieve minimum hub vibration levels and flap actuation power simultaneously. An aeroelastic analysis of a soft in-plane four-bladed rotor is performed in conjunction with optimal control. A second-order polynomial response surface based on an orthogonal array (OA) with 3-level design describes both the objectives adequately. Two new orthogonal arrays called MGB2P-OA and MGB4P-OA are proposed to generate nonlinear response surfaces with all interaction terms for two and four parameters, respectively. A multi-objective bat algorithm (MOBA) approach is used to obtain the optimal design point for the mutually conflicting objectives. MOBA is a recently developed nature-inspired metaheuristic optimization algorithm that is based on the echolocation behaviour of bats. It is found that MOBA inspired Pareto optimal trailing edge flap design reduces vibration levels by 73% and flap actuation power by 27% in comparison with the baseline design.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Electromechanical Analysis of Tapered Piezoelectric Bimorph at High Electric Field

Piezoelectric bimorph laminar actuator of tapered width exhibits better performance for out-of-plane deflection compared to the rectangular surface area, while consuming equal surface area. This paper contains electromechanical analysis and modeling of a tapered width piezoelectric bimorph laminar actuator at high electric field in static state. The analysis is based on the second order constitutive equations of piezoelectric material, assuming small strain and large electric field to capture its behavior at high electric field. Analytical expressions are developed for block force, output strain energy, output energy density, input electrical energy, capacitance and energy efficiency at high electric field. The analytical expressions show that for fixed length, thickness, and surface area of the actuator, how the block force and output strain energy gets improved in a tapered surface actuator compared to a rectangular surface. Constant thickness, constant length and constant surface area of the actuator ensure constant mass, and constant electrical capacitance. We consider high electric field in both series and parallel electrical connection for the analysis. Part of the analytical results is validated with the experimental results, which are reported in earlier literature.

Broadcast Control Mechanism for Positional Consensus in Multiagent Systems

In this paper, a strategy for controlling a group of agents to achieve positional consensus is presented. The problem is constrained by the requirement that every agent must be given the same control input through a broadcast communication mechanism. Although the control command is computed using state information in a global framework, the control input is implemented by the agents in a local coordinate frame. We propose a novel linear programming (LP) formulation that is computationally less intensive than earlier proposed methods. Moreover, a random perturbation input in the control command that helps the agents to come close to each other even for a large number of agents, which was not possible with an existing strategy in the literature, is introduced. The method is extended to achieve positional consensus at a prespecified location. The effectiveness of the approach is illustrated through simulation results. A comparison between the LP approach and the existing second-order cone programming-based approach is also presented. The algorithm was successfully implemented on a robotic platform with three robots.

Global response sensitivity analysis using probability distance measures and generalization of Sobol's analysis

The study introduces two new alternatives for global response sensitivity analysis based on the application of the L-2-norm and Hellinger's metric for measuring distance between two probabilistic models. Both the procedures are shown to be capable of treating dependent non-Gaussian random variable models for the input variables. The sensitivity indices obtained based on the L2-norm involve second order moments of the response, and, when applied for the case of independent and identically distributed sequence of input random variables, it is shown to be related to the classical Sobol's response sensitivity indices. The analysis based on Hellinger's metric addresses variability across entire range or segments of the response probability density function. The measure is shown to be conceptually a more satisfying alternative to the Kullback-Leibler divergence based analysis which has been reported in the existing literature. Other issues addressed in the study cover Monte Carlo simulation based methods for computing the sensitivity indices and sensitivity analysis with respect to grouped variables. Illustrative examples consist of studies on global sensitivity analysis of natural frequencies of a random multi-degree of freedom system, response of a nonlinear frame, and safety margin associated with a nonlinear performance function. (C) 2015 Elsevier Ltd. All rights reserved.

Ag-doped hydroxyapatite as efficient adsorbent for removal of Congo red dye from aqueous solution: Synthesis, kinetic and equilibrium adsorption isotherm analysis

In the present study a versatile and efficient adsorbent with high adsorption capacity for adsorption of Congo red dye in aqueous solution at ambient temperature without adjusting any pH is presented over the Ag modified calcium hydroxyapatite (CaHAp). CaHAp and Ag-doped CaHAp materials were synthesized using facile aqueous precipitation method. The physico-chemical properties of the materials were determined by powder X-ray diffraction (XRD), Fourier transform infrared (FT-IR) spectroscopy, Transmission electron microscopy (TEM), UV-Visible spectroscopy, N-2 physisorption and acidity was determined by n-butylamine titration and pyridine adsorption methods. XRD analysis confirmed all adsorbents exhibit hexagonal CaHAp structure with P6(3)/m space group. TEM analysis confirms the rod like morphology of the adsorbents and the average length of the rods were in the range of 40-45 nm. Pyridine adsorption results indicate increase in number of Lewis acid sites with Ag doping in CaHAp. Adsorption capacity of CaHAp was found increased with Ag content in the adsorbents. Ag (10): CaHAp adsorbent showed superior adsorption performance among all the adsorbents for various concentrations of Congo red (CR) dye in aqueous solutions. The amount of CR dye adsorbed on Ag (10): CaHAp was found to be 49.89-267.81 mg g(-1) for 50-300 ppm in aqueous solution. A good correlation between adsorption capacity and acidity of the adsorbents was observed. The adsorption kinetic data of adsorbents fitted well with pseudo second-order kinetic model with correlation coefficients ranged from 0.998 to 0.999. The equilibrium adsorption data was found to best fit to the Langmuir adsorption isotherm model. (C) 2015 Elsevier Inc. All rights reserved.

Prediction of electronically nonadiabatic decomposition mechanisms of isolated gas phase nitrogen-rich energetic salt: Guanidium-triazolate

Electronically nonadiabatic decomposition pathways of guanidium triazolate are explored theoretically. Nonadiabatically coupled potential energy surfaces are explored at the complete active space self-consistent field (CASSCF) level of theory. For better estimation of energies complete active space second order perturbation theories (CASPT2 and CASMP2) are also employed. Density functional theory (DFT) with B3LYP functional and MP2 level of theory are used to explore subsequent ground state decomposition pathways. In comparison with all possible stable decomposition products (such as, N-2, NH3, HNC, HCN, NH2CN and CH3NC), only NH3 (with NH2CN) and N-2 are predicted to be energetically most accessible initial decomposition products. Furthermore, different conical intersections between the S-1 and S-0 surfaces, which are computed at the CASSCF(14,10)/6-31G(d) level of theory, are found to play an essential role in the excited state deactivation process of guanidium triazolate. This is the first report on the electronically nonadiabatic decomposition mechanisms of isolated guanidium triazolate salt. (C) 2015 Elsevier B.V. All rights reserved.

EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Electromechanical analysis of piezoelectric bimorph actuator in static state considering the nonlinearity at high electric field

This article contains electromechanical analysis of a piezoelectric bimorph actuator at high electric field by incorporating second-order constitutive equations of piezoelectric material. Tip deflection, block force, block moment, block load, output strain energy, output energy density, input electrical energy, and energy efficiency are analytically derived for the actuator at high electric field. The analysis shows that output energy and energy density increase more rapidly at high electric field, compared to the prediction by the linear model. The analysis shows energy efficiency depends on electric field. Some analytical results are validated with the published experimental results.

A peridynamic theory for linear elastic shells

A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures that have one geometric dimension much smaller than the other two. A new notion of curved bonds is exploited to cater for force transfer between the peridynamic particles describing the shell. Starting with the three dimensional force and deformation states, appropriate surface based force, moment and several deformation states are arrived at. Upon application on the curved bonds, such states yield the necessary force and deformation vectors governing the motion of the shell. By incorporating a shear correction factor, the formulation also accommodates analysis of shells that have higher thickness. In order to attain this, a consistent second order approximation to the complementary energy density is considered and incorporated in peridynamics via constitutive correspondence. Unlike the uncoupled constitution for thin shells, a consequence of a first order approximation, constitutive relations for thick shells are fully coupled in that surface wryness influences the in-plane stress resultants and surface strain the moments. Our proposal on the peridynamic shell theory is numerically assessed against simulations on static deformation of spherical and cylindrical shells, that of flat plates and quasi-static fracture propagation in a cylindrical shell. (C) 2016 Elsevier Ltd. All rights reserved.