A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem

A residual based a posteriori error estimator is derived for a quadratic finite element method (FEM) for the elliptic obstacle problem. The error estimator involves various residuals consisting of the data of the problem, discrete solution and a Lagrange multiplier related to the obstacle constraint. The choice of the discrete Lagrange multiplier yields an error estimator that is comparable with the error estimator in the case of linear FEM. Further, an a priori error estimate is derived to show that the discrete Lagrange multiplier converges at the same rate as that of the discrete solution of the obstacle problem. The numerical experiments of adaptive FEM show optimal order convergence. This demonstrates that the quadratic FEM for obstacle problem exhibits optimal performance.

Effect of a mesh on boundary layer transitions induced by free-stream turbulence and an isolated roughness element

Streamwise streaks, their lift-up and streak instability are integral to the bypass transition process. An experimental study has been carried out to find the effect of a mesh placed normal to the flow and at different wall-normal locations in the late stages of two transitional flows induced by free-stream turbulence (FST) and an isolated roughness element. The mesh causes an approximately 30% reduction in the free-stream velocity, and mild acceleration, irrespective of its wall-normal location. Interestingly, when located near the wall, the mesh suppresses several transitional events leading to transition delay over a large downstream distance. The transition delay is found to be mainly caused by suppression of the lift-up of the high-shear layer and its distortion, along with modification of the spanwise streaky structure to an orderly one. However, with the mesh well away from the wall, the lifted-up shear layer remains largely unaffected, and the downstream boundary layer velocity profile develops an overshoot which is found to follow a plane mixing layer type profile up to the free stream. Reynolds stresses, and the size and strength of vortices increase in this mixing layer region. This high-intensity disturbance can possibly enhance transition of the accelerated flow far downstream, although a reduction in streamwise turbulence intensity occurs over a short distance downstream of the mesh. However, the shape of the large-scale streamwise structure in the wall-normal plane is found to be more or less the same as that without the mesh.

Exploring the origin of ultralow thermal conductivity in layered BiOCuSe

Using first-principles density functional theory calculations, a systematic study of the lattice dynamics and related (e.g., dielectric and anharmonic) properties of BiOCuSe (bismuth-copper oxyselenide), along with a comparison with its isostructural analog LaOCuSe, is performed to find the origin of the ultralow thermal conductivity. in BiOCuSe. From the marked differences in some of these properties of the two materials, the reasons why BiOCuSe is a better thermal insulator than LaOCuSe are elucidated. For this class of oxychalcogenide thermoelectrics, phonon frequencies with symmetries, characters, spectroscopic activities, displacement patterns, and pressure coefficients of different zone-center modes, dielectric constants, dynamical charges, and phonon and Gruneisen dispersions are also determined.

Improved capacity and stability of integrated Li and Mn rich layered-spinel Li1.17Ni0.25Mn1.08O3 cathodes for Li-ion batteries

A Li-rich layered-spinel material with a target composition Li1.17Ni0.25Mn1.08O3 (xLiLi1/3Mn2/3]O-2.(1 - x) LiNi0.5Mn1.5O4, (x = 0.5)) was synthesized by a self-combustion reaction (SCR), characterized by XRD, SEM, TEM, Raman spectroscopy and was studied as a cathode material for Li-ion batteries. The Rietveld refinement results indicated the presence of monoclinic (LiLi1/3Mn2/3]O-2) (52%), spinel (LiNi0.5Mn1.5O4) (39%) and rhombohedral LiNiO2 (9%). The electrochemical performance of this Li-rich integrated cathode material was tested at 30 degrees C and compared to that of high voltage LiNi0.5Mn1.5O4 spinel cathodes. Interestingly, the layered-spinel integrated cathode material exhibits a high specific capacity of about 200 mA h g(-1) at C/10 rate as compared to 180 mA h g(-1) for LiNi0.5Mn1.5O4 in the potential range of 2.4-4.9 V vs. Li anodes in half cells. The layered-spinel integrated cathodes exhibited 92% capacity retention as compared to 82% for LiNi0.5Mn1.5O4 spinel after 80 cycles at 30 degrees C. Also, the integrated cathode material can exhibit 105 mA h g(-1) at 2 C rate as compared to 78 mA h g(-1) for LiNi0.5Mn1.5O4. Thus, the presence of the monoclinic phase in the composite structure helps to stabilize the spinel structure when high specific capacity is required and the electrodes have to work within a wide potential window. Consequently, the Li1.17Ni0.25Mn1.08O3 composite material described herein can be considered as a promising cathode material for Li ion batteries.

Multiobjective fuzzy optimization for sustainable groundwater management using particle swarm optimization and analytic element method

Groundwater management involves conflicting objectives as maximization of discharge contradicts the criteria of minimum pumping cost and minimum piping cost. In addition, available data contains uncertainties such as market fluctuations, variations in water levels of wells and variations of ground water policies. A fuzzy model is to be evolved to tackle the uncertainties, and a multiobjective optimization is to be conducted to simultaneously satisfy the contradicting objectives. Towards this end, a multiobjective fuzzy optimization model is evolved. To get at the upper and lower bounds of the individual objectives, particle Swarm optimization (PSO) is adopted. The analytic element method (AEM) is employed to obtain the operating potentio metric head. In this study, a multiobjective fuzzy optimization model considering three conflicting objectives is developed using PSO and AEM methods for obtaining a sustainable groundwater management policy. The developed model is applied to a case study, and it is demonstrated that the compromise solution satisfies all the objectives with adequate levels of satisfaction. Sensitivity analysis is carried out by varying the parameters, and it is shown that the effect of any such variation is quite significant. Copyright (c) 2015 John Wiley & Sons, Ltd.

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.

Iridium-decorated multiwall carbon nanotubes and its catalytic activity with Shell 405 in hydrazine decomposition

Iridium-functionalized multiwalled carbon nanotubes (Ir-MWNT) are the future catalyst support material for hydrazine fuel decomposition. The present work demonstrates decoration of iridium particle on iron-encapsulated multiwalled carbon nanotubes (MWNT) by wet impregnation method in the absence of any stabilizer. Electron microscopy studies reveal the coated iridium particle size in the range of 5-10 nm. Elemental analysis by energy dispersive X-ray diffraction confirms 21 wt% of Ir coated over MWNT. X-ray photoelectron spectroscopy (XPS) shows 4f(5/2) and 4f(7/2) lines of iridium and confirms the metallic nature. The catalytic activity of Ir-MWNT/Shell 405 combination is performed in 1 N hydrazine micro-thrusters. The thruster performance shows increase in chamber pressure and decrease in chamber temperature when compared to Shell 405 alone. This enhanced performance is due to high thermal conducting nature of MWNTs and the presence of Ir active sites over MWNTs.

Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis

The ultimate bearing capacity of a circular footing, placed over rock mass, is evaluated by using the lower bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The generalized Hoek-Brown (HB) failure criterion, but by keeping a constant value of the exponent, alpha = 0.5, was used. The failure criterion was smoothened both in the meridian and pi planes. The nonlinear optimization was carried out by employing an interior point method based on the logarithmic barrier function. The results for the obtained bearing capacity were presented in a non-dimensional form for different values of GSI, m(i), sigma(ci)/(gamma b) and q/sigma(ci). Failure patterns were also examined for a few cases. For validating the results, computations were also performed for a strip footing as well. The results obtained from the analysis compare well with the data reported in literature. Since the equilibrium conditions are precisely satisfied only at the centroids of the elements, not everywhere in the domain, the obtained lower bound solution will be approximate not true. (C) 2015 Elsevier Ltd. All rights reserved.

Bearing capacity of a circular foundation on layered sand-clay media

The bearing capacity of a circular footing lying over fully cohesive strata, with an overlaying sand layer, is computed using the axisymmetric lower bound limit analysis with finite elements and linear optimization. The effects of the thickness and the internal friction angle of the sand are examined for different combinations of c(u)/(gamma b) and q, where c(u)=the undrained shear strength of the cohesive strata, gamma=the unit weight of either layer, b=the footing radius, and q=the surcharge pressure. The results are given in the form of a ratio (eta) of the bearing capacity with an overlaying sand layer to that for a footing lying directly over clayey strata. An overlaying medium dense to dense sand layer considerably improves the bearing capacity. The improvement continuously increases with decreases in c(u)/(gamma b) and increases in phi and q/(gamma b). A certain optimum thickness of the sand layer exists beyond which no further improvement occurs. This optimum thickness increases with an increase in 0 and q and with a decrease in c(u)/(gamma b). Failure patterns are also drawn to examine the inclusion of the sand layer. (C) 2015 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.

A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.

MnFe2O4-Fe3O4 core-shell nanoparticles as a potential contrast agent for magnetic resonance imaging

In recent years, magnetic core-shell nanoparticles have received widespread attention due to their unique properties that can be used for various applications. We introduce here a magnetic core-shell nanoparticle system for potential application as a contrast agent in magnetic resonance imaging (MRI). MnFe2O4-Fe3O4 core-shell nanoparticles were synthesized by the wet-chemical synthesis method. Detailed structural and compositional charaterization confirmed the formation of a core-shell microstructure for the nanoparticles. Magnetic charaterization revealed the superparamagnetic nature of the as-synthesized core-shell nanoparticles. Average size and saturation magnetization values obtained for the as-synthesized core-shell nanoparticle were 12.5 nm and 69.34 emu g(-1) respectively. The transverse relaxivity value of the water protons obtained in the presence of the core-shell nanoparticles was 184.1 mM(-1) s(-1). To investigate the effect of the core-shell geometry towards enhancing the relaxivity value, transverse relaxivity values were also obtained in the presence of separately synthesized single phase Fe3O4 and MnFe2O4 nanoparticles. Average size and saturation magnetization values for the as-synthesized Fe3O4 nanoparticles were 12 nm and 65.8 emu g(-1) respectively. Average size and saturation magnetization values for the MnFe2O4 nanoparticles were 9 nm and 61.5 emu g(-1) respectively. The transverse relaxivity value obtained in the presence of single phase Fe3O4 and MnFe2O4 nanoparticles was 96.6 and 83.2 mM(-1) s(-1) respectively. All the nanoparticles (core-shell and single phase) were coated with chitosan by a surfactant exchange reaction before determining the relaxivity values. For similar nanoparticle sizes and saturation magnetization values, the highest value of the transverse relaxivity in the case of core-shell nanoparticles clearly illustrated that the difference in the magnetic nature of the core and shell phases in the core-shell nanoparticles creates greater magnetic inhomogeneity in the surrounding medium yielding a high value for proton relaxivity. The MnFe2O4-Fe3O4 core-shell nanoparticles exhibited extremely low toxicity towards the MCF-7 cell line. Taken together, this opens up new avenues for the use of core-shell nanoparticles in MRI.

Amine Functionalized polyaniline grafted to exfoliated graphite oxide: Synthesis, characterization and multi-element sensor studies

An amine functionalized polyaniline (AMPANI) derivative has been grafted onto exfoliated graphite oxide (EGO). The synthesis involved the in-situ chemical oxidative polymerization of functionalized aniline monomer in the presence of EGO with diaminobenzene acting as a bridging ligand to yield EGAMPANI. The synthesized compound was characterized by FT-IR and FT-Raman spectroscopy as well as thermogravimetric and X-ray diffraction analysis. The EGAMPANI was then used to modify a carbon paste electrode (CPE), which was applied for multi-elemental sensing of Pb2+, Cd2+ and Hg2+ ions using differential pulse anodic stripping voltammetty. The limits of detection achieved using the EGAMPANI modified CPE were 22 x 10(-6) M for Hg2+ ion, 1.2 x 10(-6) M for Cd2+ ion and 9.8 x 10(-7) M for Pb2+ ion. (C) 2015 Elsevier B.V. All rights reserved.

Optical-Phonon-Limited High-Field Transport in Layered Materials

An optical-phonon-limited velocity model has been employed to investigate high-field transport in a selection of layered 2-D materials for both, low-power logic switches with scaled supply voltages, and high-power, high-frequency transistors. Drain currents, effective electron velocities, and intrinsic cutoff frequencies as a function of carrier density have been predicted, thus providing a benchmark for the optical-phonon-limited high-field performance limits of these materials. The optical-phonon-limited carrier velocities for a selection of multi-layers of transition metal dichalcogenides and black phosphorus are found to be modest compared to their n-channel silicon counterparts, questioning the utility of biasing these devices in the source-injection dominated regime. h-BN, at the other end of the spectrum, is shown to be a very promising material for high-frequency, high-power devices, subject to the experimental realization of high carrier densities, primarily due to its large optical-phonon energy. Experimentally extracted saturation velocities from few-layer MoS2 devices show reasonable qualitative and quantitative agreement with the predicted values. The temperature dependence of the measured v(sat) is discussed and compared with the theoretically predicted dependence over a range of temperatures.

The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.

The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.