Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.

Dynamics and control of buckling type devices using SMA wire integrated beam

An analysis and design study using Shape Memory Alloy (SMA) wire integrated beam and its buckling shape control are reported. The dynamical system performance is analyzed with a mathematical set-up involving nonlocal and rate sensitive kinetics of phase transformation in the SMA wire. A standard phenomenological constitutive model reported by Brinson (1993) is modified by considering certain consistency conditions in the material property tensors and by eliminating spurious singularity. Considering the inhomogeneity effects, a finite element model of the SMA wire is developed. Simulations are carried out to study the buckling shape control of a beam integrated with SMA wire.

Evaluation of Moderate-Resolution Imaging Spectroradiometer (MODIS) collection 004 (C004) aerosol retrievals at Kanpur, Indo-Gangetic basin

[1] We have compared the spectral aerosol optical depth (AOD, tau lambda) and aerosol fine mode fraction (AFMF) of Collection 004 (C004) derived from Moderate-Resolution Imaging Spectroradiometer (MODIS) on board National Aeronautics and Space Administration's (NASA) Terra and Aqua platforms with that obtained from Aerosol Robotic Network (AERONET) at Kanpur (26.45 degrees N, 80.35 degrees E), India for the period 2001-2005. The spatially-averaged (0.5 degrees x 0.5 degrees centered at AERONET sunphotometer) MODIS Level-2 aerosol parameters (10 km at nadir) were compared with the temporally averaged AERONET-measured AOD (within +/- 30 minutes of MODIS overpass). We found that MODIS systematically overestimated AOD during the pre-monsoon season (March to June, known to be influenced by dust aerosols). The errors in AOD at 0.66 mu m were correlated with the apparent reflectance at 2.1 mu m (rho*(2.1)) which MODIS C004 uses to estimate the surface reflectance in the visible channels (rho(0.47) = rho*(2.1)/ 4, rho(0.66) = rho*(2.1)/ 2). The large errors in AOD (Delta tau(0.66) > 0.3) are found to be associated with the higher values of rho*(2.1) (0.18 to 0.25), where the uncertainty in the ratios of reflectance is large (Delta rho(0.66) +/- 0.04, Delta rho(0.47) +/- 0.02). This could have resulted in lower surface reflectance, higher aerosol path radiance and thus lead to overestimation in AOD. While MODIS-derived AFMF has binary distribution (1 or 0) with too low (AFMF < 0.2) during dust-loading period, and similar to 1 for the rest of the retrievals, AERONET showed range of values (0.4 to 0.9). The errors in tau(0.66) were also high in the scattering angle range 110 degrees - 140 degrees, where the optical effects of nonspherical dust particles are different from that of spherical particles.

A Legendre spectral element model for sloshing and acoustic analysis in nearly incompressible fluids

A new spectral finite element formulation is presented for modeling the sloshing and the acoustic waves in nearly incompressible fluids. The formulation makes use of the Legendre polynomials in deriving the finite element interpolation shape functions in the Lagrangian frame of reference. The formulated element uses Gauss-Lobatto-Legendre quadrature scheme for integrating the volumetric stiffness and the mass matrices while the conventional Gauss-Legendre quadrature scheme is used on the rotational stiffness matrix to completely eliminate the zero energy modes, which are normally associated with the Lagrangian FE formulation. The numerical performance of the spectral element formulated here is examined by doing the inf-sup test oil a standard rectangular rigid tank partially filled with liquid The eigenvalues obtained from the formulated spectral element are compared with the conventional equally spaced node locations of the h-type Lagrangian finite element and the predicted results show that these spectral elements are more accurate and give superior convergence The efficiency and robustness of the formulated elements are demonstrated by solving few standard problems involving free vibration and dynamic response analysis with undistorted and distorted spectral elements. and the obtained results are compared with available results in the published literature (C) 2009 Elsevier Inc All rights reserved

Laser damage studies in nonlinear optical crystal sodium p-nitrophenolate dihydrate

We report the surface laser damage threshold in sodium p-nitrophenolate dihydrate, a nonlinear optical crystal. The experiment is performed with a pulsed Nd:YAG laser in TEM00 mode. The single shot damage thresholds are 11.16 +/- 0.28GWcm(-2) and 1.25 +/- 0.02GWcm(-2) for 1064 nm and 532 nm laser wavelengths respectively. A close correlation between the laser damage threshold and mechanical hardness is observed. A possible mechanism of laser damage is discussed.

Synthesis of Diketopyrrolopyrrole Containing Copolymers: A Study of Their Optical and Photovoltaic Properties

The diketopyrrolopyrrole-based copolymers PDPP-BBT and TDPP-BBT were synthesized and used as donor for bulk heterojunction photovoltaic devices. The photophysical properties of these polymers showed absorption in the range 500-600 nm with a maximum peak around 563 nm, while TDPP-BBT showed broadband absorption in the range 620 - 800 nm with a peak around 656 nm. The power conversion efficiencies (PCE) of the polymer solar cells based on these copolymers and [6,6]-phenyl C61 butyric acid methyl ester (PCBM) were 0.68% (as cast PDPP-BBT:PCBM), 1.51% (annealed PDPP-BBT:PCBM), 1.57% (as cast TDPPBBT: PCBM), and 2.78% (annealed TDPP-BBT:PCBM), under illumination of AM 1.5 (100 mW/cm2). The higher PCE for TDPP-BBT-based polymer solar cells has been attributed to the low band gap of this copolymer as compared to PDPP-BBT, which increases the numbers of photogenerated excitons and corresponding photocurrent of the device. These results indicate that PDPP-BBT and TDPP-BBT act as excellent electron donors for bulk heterojunction devices.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

New rational interpolation functions for finite element analysis of rotating beams

A rotating beam finite element in which the interpolating shape functions are obtained by satisfying the governing static homogenous differential equation of Euler–Bernoulli rotating beams is developed in this work. The shape functions turn out to be rational functions which also depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. These rational functions yield the Hermite cubic when rotation speed becomes zero. The new element is applied for static and dynamic analysis of rotating beams. In the static case, a cantilever beam having a tip load is considered, with a radially varying axial force. It is found that this new element gives a very good approximation of the tip deflection to the analytical series solution value, as compared to the classical finite element given by the Hermite cubic shape functions. In the dynamic analysis, the new element is applied for uniform, and tapered rotating beams with cantilever and hinged boundary conditions to determine the natural frequencies, and the results compare very well with the published results given in the literature.

Magneto-transport and optical properties of diluted magnetic semiconductor Ga1-xMnxSb

We have studied magneto-transport and optical properties of Ga1-xMnxSb crystals (x = 0.01, 0.02, 0.03 and 0.04) grown by horizontal Bridgman method. Negative magnetoresistance and anomalous Hall effect have been observed below 10K. Temperature dependence of magnetization measurement shows a magnetic ordering below 10K which could arise from Ga1-xMnxSb alloy formation. Also, saturation in magnetization observed even at room temperature suggests the existence of ferromagnetic MnSb clusters. Reduction in band gap is observed with increasing Mn concentration in the crystals. Temperature dependence of band gap follows Bose-Einstein's model.

Phase diagram of the system Ca-Ti-O at 1200 K

Phase relations in the system Ca-Ti-O have been established by equilibration of several samples at 1200 K for prolonged periods and identification of phases in quenched samples by optical and scanning electron microscopy, XRD and EDS. Samples representing 20 compositions in the ternary system were analyzed. There was negligible solid solubility of Ca in the phases along the binary Ti-O, and of Ti in CaO. Four ternary oxides were identified: CaTiO3, Ca4Ti3O10 and Ca3Ti2O7 containing tetravalent titanium, and CaTi2O4 containing trivalent titanium. Tie-lines link calcium titanite (CaTi2O4) with the three calcium titanates (CaTiO3, Ca4Ti3O10 and Ca3Ti2O7), CaO, oxygen excess TiO1+delta and stoichiometric TiO. Tie-lines connect CaTiO3 with TiO2-x, Magneli phases TinO2n-1 (28 >= n >= 4), Ti3O5, Ti2O3 and TiO1+delta. CaO was found to coexist with TiO, and Ti-O solid solutions alpha and beta. The phase diagram is useful for understanding the mechanisms and kinetics of direct calciothermic reduction of TiO2 to metal and electrochemical reduction of TiO2 using graphite anode and molten CaCl2 electrolyte.

Influence of surfactant and annealing temperature on optical properties of sol-gel derived nano-crystalline TiO2 thin films

Titanium dioxide thin films have been synthesized by sol-gel spin coating technique on glass and silicon substrates with and without surfactant polyethylene glycol (PEG). XRD and SEM results confirm the presence of nano-crystalline (anatase) phase at an annealing temperature of 300 degrees C. The influence of surfactant and annealing temperature on optical properties of TiO2 thin films has been studied. Optical constants and film thickness were estimated by Swanepoel's (envelope) method and by ellipsometric measurements in the visible spectral range. The optical transmittance and reflectance were found to decrease with an increase in PEG percentage. Refractive index of the films decreased and film thickness increased with the increase in percentage of surfactant. The refractive index of the un-doped TiO2 films was estimated at different annealing temperatures and it has increased with the increasing annealing temperature. The optical band gap of pure TiO2 films was estimated by Tauc's method at different annealing temperature. (C) 2010 Elsevier B.V. All rights reserved.

Single-resolution and multiresolution extended-Kalman-filter-based reconstruction approaches to optical refraction tomography

The problem of reconstruction of a refractive-index distribution (RID) in optical refraction tomography (ORT) with optical path-length difference (OPD) data is solved using two adaptive-estimation-based extended-Kalman-filter (EKF) approaches. First, a basic single-resolution EKF (SR-EKF) is applied to a state variable model describing the tomographic process, to estimate the RID of an optically transparent refracting object from noisy OPD data. The initialization of the biases and covariances corresponding to the state and measurement noise is discussed. The state and measurement noise biases and covariances are adaptively estimated. An EKF is then applied to the wavelet-transformed state variable model to yield a wavelet-based multiresolution EKF (MR-EKF) solution approach. To numerically validate the adaptive EKF approaches, we evaluate them with benchmark studies of standard stationary cases, where comparative results with commonly used efficient deterministic approaches can be obtained. Detailed reconstruction studies for the SR-EKF and two versions of the MR-EKF (with Haar and Daubechies-4 wavelets) compare well with those obtained from a typically used variant of the (deterministic) algebraic reconstruction technique, the average correction per projection method, thus establishing the capability of the EKF for ORT. To the best of our knowledge, the present work contains unique reconstruction studies encompassing the use of EKF for ORT in single-resolution and multiresolution formulations, and also in the use of adaptive estimation of the EKF's noise covariances. (C) 2010 Optical Society of America