Multivariate nonlinear ensemble prediction of daily chaotic rainfall with climate inputs

The basic characteristic of a chaotic system is its sensitivity to the infinitesimal changes in its initial conditions. A limit to predictability in chaotic system arises mainly due to this sensitivity and also due to the ineffectiveness of the model to reveal the underlying dynamics of the system. In the present study, an attempt is made to quantify these uncertainties involved and thereby improve the predictability by adopting a multivariate nonlinear ensemble prediction. Daily rainfall data of Malaprabha basin, India for the period 1955-2000 is used for the study. It is found to exhibit a low dimensional chaotic nature with the dimension varying from 5 to 7. A multivariate phase space is generated, considering a climate data set of 16 variables. The chaotic nature of each of these variables is confirmed using false nearest neighbor method. The redundancy, if any, of this atmospheric data set is further removed by employing principal component analysis (PCA) method and thereby reducing it to eight principal components (PCs). This multivariate series (rainfall along with eight PCs) is found to exhibit a low dimensional chaotic nature with dimension 10. Nonlinear prediction employing local approximation method is done using univariate series (rainfall alone) and multivariate series for different combinations of embedding dimensions and delay times. The uncertainty in initial conditions is thus addressed by reconstructing the phase space using different combinations of parameters. The ensembles generated from multivariate predictions are found to be better than those from univariate predictions. The uncertainty in predictions is decreased or in other words predictability is increased by adopting multivariate nonlinear ensemble prediction. The restriction on predictability of a chaotic series can thus be altered by quantifying the uncertainty in the initial conditions and also by including other possible variables, which may influence the system. (C) 2011 Elsevier B.V. All rights reserved.

Lithium borate-strontium bismuth tantalate glass nanocomposite: a novel material for nonlinear optic and ferroelectric applications

Glass nanocomposites in the system (100 - x)Li2B4O7-xSrBi(2)Ta(2)O(9) (0 less than or equal to x less than or equal to 22.5, in molar ratio) were fabricated via a melt quenching technique followed by controlled heat-treatment. The as-quenched samples were confirmed to be glassy and amorphous by differential thermal analysis (DTA) and X-ray powder diffraction (XRD) techniques, respectively. The phase formation and crystallite size of the heat-treated samples (glass nanocomposites) were monitored by XRD and transmission electron microscopy (TEM). The relative permittivities (epsilon(tau)') of the glass nanocomposites for different compositions were found to lie in between that of the parent host glass (Li2B4O7) and strontium bismuth tantalate (SBT) ceramic in the frequency range 100 Hz-40 MHz at 300 K, whereas the dielectric loss (D) of the glass nanocomposite was less than that of both the parent phases. Among the various dielectric models employed to predict the effective relative permittivity of the glass nanocomposite, the one obtained using the Maxwell's model was in good agreement with the experimentally observed value. Impedance analysis was employed to rationalize the electrical behavior of the glasses and glass nanocomposites. The pyroelectric response of the glasses and glass nanocomposites was monitored as a function of temperature and the pyroelectric coefficient for glass and glass nanocomposite (x = 20) at 300 K were 27 muC m(-2) K-1 and 53 muC m(-2) K-1, respectively. The ferroelectric behavior of these glass nanocomposites was established by P vs. E hysteresis loop studies. The remnant polarization (P-r) of the glass nanocomposite increases with increase in SBT content. The coercive field (E-c) and P-r for the glass nanocomposite (x = 20) were 727 V cm(-1) and 0.527 muC cm(-2), respectively. The optical transmission properties of these glass nanocomposites were found to be composition dependent. The refractive index (n = 1.722), optical polarizability (am = 1.266 6 10 23 cm 3) and third-order nonlinear optical susceptibility (x(3) = 3.046 6 10(-21) cm(3)) of the glass nanocomposite (x = 15) were larger than those of the as-quenched glass. Second harmonic generation (SHG) was observed in transparent glass nanocomposites and the d(eff) for the glass nanocomposite (x = 20) was found to be 0.373 pm V-1.

Nonlinear dynamics of eucaryotic pyruvate dehydrogenase multienzyme complex: Decarboxylation rate, oscillations, and multiplicity

Pyruvate conversion to acetyl-CoA by the pyruvate dehydrogenase (PDH) multienzyme complex is known as a key node in affecting the metabolic fluxes of animal cell culture. However, its possible role in causing possible nonlinear dynamic behavior such as oscillations and multiplicity of animal cells has received little attention. In this work, the kinetic and dynamic behavior of PDH of eucaryotic cells has been analyzed by using both in vitro and simplified in vivo models. With the in vitro model the overall reaction rate (v(1)) of PDH is shown to be a nonlinear function of pyruvate concentration, leading to oscillations under certain conditions. All enzyme components affect v, and the nonlinearity of PDH significantly, the protein X and the core enzyme dihydrolipoamide acyltransferase (E2) being mostly predominant. By considering the synthesis rates of pyruvate and PDH components the in vitro model is expanded to emulate in vivo conditions. Analysis using the in vivo model reveals another interesting kinetic feature of the PDH system, namely, multiple steady states. Depending on the pyruvate and enzyme levels or the operation mode, either a steady state with high pyruvate decarboxylation rate or a steady state with significantly lower decarboxylation rate can be achieved under otherwise identical conditions. In general, the more efficient steady state is associated with a lower pyruvate concentration. A possible time delay in the substrate supply and enzyme synthesis can also affect the steady state to be achieved and lead's to oscillations under certain conditions. Overall, the predictions of multiplicity for the PDH system agree qualitatively well with recent experimental observations in animal cell cultures. The model analysis gives some hints for improving pyruavte metabolism in animal cell culture.

Nonlinear Dynamics of Beams with Stochastic Parameter Variations

The aim of this paper is to investigate the steady state response of beams under the action of random support motions. The study is of relevance in the context of earthquake response of extended land based structures such as pipelines and long span bridges, and, secondary systems such as piping networks in nuclear power plant installations. The following complicating features are accounted for in the response analysis: (a) differential support motions: this is characterized in terms of cross power spectral density functions associated with distinct support motions, (b) nonlinear support conditions, and (c) stochastically inhomogeneous stiffness and mass variations of the beam structure; questions on non-Gaussian models for these variations are considered. The method of stochastic finite elements is combined with equivalent linearization technique and Monte Carlo simulations to obtain response moments.

A Nonlinear Voltage Regulator With One Tunable Parameter for Multimachine Power Systems

This paper proposes a nonlinear voltage regulator with one tunable parameter for multimachine power systems. Based on output feedback linearization, this regulator can achieve simultaneous voltage regulation and small-signal performance objectives. Conventionally output feedback linearization has been used for voltage regulator design by taking infinite bus voltage as reference. Unfortunately, this controller has poor small-signal performance and cannot be applied to multimachine systems without the estimation of the equivalent external reactance seen from the generator. This paper proposes a voltage regulator design by redefining the rotor angle at each generator with respect to the secondary voltage of the step-up transformer as reference instead of a common synchronously rotating reference frame. Using synchronizing and damping torques analysis, we show that the proposed voltage regulator achieves simultaneous voltage regulation and damping performance over a range of system and operating conditions by controlling the relative angle between the generator internal voltage angle delta and the secondary voltage of the step up transformer. The performance of the proposed voltage regulator is evaluated on a single machine infinite bus system and two widely used multimachine test systems.

Geometrically Nonlinear Dynamics of Composite Four-Bar Mechanisms

This work intends to demonstrate the importance of geometrically nonlinear crosssectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the four beam reference curves. For thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses, more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the nonlinear, flexible fourbar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we shall attempt to identify and investigate a few problems where the cross-sectional nonlinearities are significant. This will be carried out by varying stacking sequences and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form nonlinear beam stiffness matrix. Numerical examples will be presented and results from this analysis will be compared with those available in the literature, for linear cross-sectional analysis and isotropic materials as special cases.

Analysis for the Reflected Waves Transmitted on to the Channel by Tall Grounded Objects Using a Special Case

During lightning strike to a tall grounded object (TGO), reflected current waves from TGO are transmitted on to the channel. With regard to these transmitted waves, there seems to be some uncertainties like: 1) will they get reflected at the main wavefront; and 2) if so, what would be their final status. This study makes an attempt to address these issues considering a special case of strike to a TGO involving equal channel core and TGO radii. A macroscopic physical model for the lightning return stroke is adopted for the intended work. Analysis showed that the waves transmitted on to the channel merges with the main wavefront without any sign of reflection. Investigation revealed that: 1) the nonlinear spatio-temporal resistance profile of the channel at the wavefront is mainly responsible for the same; and 2) the distributed source provides additional support. The earlier findings are not limited to the special case of TGO considered. In spite of considering equal TGO and channel core radii, salient features of the model predicted remote electromagnetic fields agree well with the measured data reported in literature.

Nonlinear dielectric behavior in three-component ferroelectric superlattices

Three-component ferroelectric superlattices consisting of alternating layers of SrTiO3, BaTiO3, and CaTiO3 (SBC) with variable interlayer thickness were fabricated on Pt(111)/TiO2/SiO2/Si (100) substrates by pulsed laser deposition. The presence of satellite reflections in x-ray-diffraction analysis and a periodic concentration of Sr, Ba, and Ca throughout the film in depth profile of secondary ion mass spectrometry analysis confirm the fabrication of superlattice structures. The Pr (remnant polarization) and Ps (saturation polarization) of SBC superlattice with 16.4-nm individual layer thickness (SBC16.4) were found to be around 4.96 and 34 μC/cm2, respectively. The dependence of polarization on individual layer thickness and lattice strain were studied in order to investigate the size dependence of the dielectric properties. The dielectric constant of these superlattices was found to be much higher than the individual component layers present in the superlattice configuration. The relatively higher tunability ( ∼ 55%) obtained around 300 K indicates that the superlattice is a potential electrically tunable material for microwave applications at room temperature. The enhanced dielectric properties were thus discussed in terms of the interfacial strain driven polar region due to high lattice mismatch and electrostatic coupling due to polarization mismatch between individual layers.

The R-x, R2-x Planes; Some New Ideas for the Study of Nonlinear Systems

Use of some new planes such as the R-x, R2-x (where R represents in the n-dimensional phase space, the radius vector from the origin to any point on the trajectory described by the system) is suggested for analysis of nonlinear systems of any kind. The stability conditions in these planes are given. For easy understanding of the method, the transformation from the phase plane to the R-x, R2-x planes is brought out for second-order systems. In general, while these planes serve as useful as the phase plane, they have proved to be simpler in determining quickly the general behavior of certain classes of second-order nonlinear systems. A chart and a simple formula are suggested to evaluate time easily from the R-x and R2-x trajectories, respectively. A means of solving higher-order nonlinear systems is also illustrated. Finally, a comparative study of the trajectories near singular points on the phase plane and on the new planes is made.

Dynamical behavior in the nonlinear rheology of surfactant solutions

Several surfactant molecules self-assemble in solution to form long, flexible wormlike micelles which get entangled with each other, leading to viscoelastic gel phases. We discuss our recent work on the rheology of such a gel formed in the dilute aqueous solutions of a surfactant CTAT. In the linear rheology regime, the storage modulus G′(ω) and loss modulus G″(ω) have been measured over a wide frequency range. In the nonlinear regime, the shear stress σ shows a plateau as a function of the shear rate math above a certain cutoff shear rate mathc. Under controlled shear rate conditions in the plateau regime, the shear stress and the first normal stress difference show oscillatory time-dependence. The analysis of the measured time series of shear stress and normal stress has been done using several methods incorporating state space reconstruction by embedding of time delay vectors. The analysis shows the existence of a finite correlation dimension and a positive Lyapunov exponent, unambiguously implying that the dynamics of the observed mechanical instability can be described by that of a dynamical system with a strange attractor of dimension varying from 2.4 to 2.9.

Analysis of oxide and vanadate supports for catalytic hydrogen combustion: Kinetic and mechanistic investigations

Combustion synthesized oxide and vanadate compounds (CeO2, Fe2O3, CeVO4, and FeVO4) were tested for catalytic hydrogen combustion. The compounds were characterized by X-ray diffraction and X-ray photoelectron spectroscopy. All the four compounds showed good activity and stability for catalytic hydrogen combustion and more than 95% conversion was observed over all the compounds within 500 degrees C. The mechanisms for the reaction over the different classes of compounds (cerium-based and iron-based compounds) were proposed on the basis of spectroscopic observations. The main difference in the mechanisms was in the nature of adsorption of H2 over the sites. The elementary processes for the reaction were proposed, corresponding rate expressions were derived, and the rate parameters for the reaction were estimated using nonlinear regression. Langmuir-Hinshelwood and Eley-Rideal mechanisms were also tested for the reaction and the proposed mechanism was compared with these mechanisms. (c) 2011 American Institute of Chemical Engineers AIChE J, 2012

Design and performance analysis of a signal detector based on suprathreshold stochastic resonance

This paper presents the design and performance analysis of a detector based on suprathreshold stochastic resonance (SSR) for the detection of deterministic signals in heavy-tailed non-Gaussian noise. The detector consists of a matched filter preceded by an SSR system which acts as a preprocessor. The SSR system is composed of an array of 2-level quantizers with independent and identically distributed (i.i.d) noise added to the input of each quantizer. The standard deviation sigma of quantizer noise is chosen to maximize the detection probability for a given false alarm probability. In the case of a weak signal, the optimum sigma also minimizes the mean-square difference between the output of the quantizer array and the output of the nonlinear transformation of the locally optimum detector. The optimum sigma depends only on the probability density functions (pdfs) of input noise and quantizer noise for weak signals, and also on the signal amplitude and the false alarm probability for non-weak signals. Improvement in detector performance stems primarily from quantization and to a lesser extent from the optimization of quantizer noise. For most input noise pdfs, the performance of the SSR detector is very close to that of the optimum detector. (C) 2012 Elsevier B.V. All rights reserved.

Analysis for the Reflected Waves Transmitted on to the Channel by Tall Grounded Objects Using a Special Case

During lightning strike to a tall grounded object (TGO), reflected current waves from TGO are transmitted on to the channel. With regard to these transmitted waves, there seems to be some uncertainties like: 1) will they get reflected at the main wavefront; and 2) if so, what would be their final status. This study makes an attempt to address these issues considering a special case of strike to a TGO involving equal channel core and TGO radii. A macroscopic physical model for the lightning return stroke is adopted for the intended work. Analysis showed that the waves transmitted on to the channel merges with the main wavefront without any sign of reflection. Investigation revealed that: 1) the nonlinear spatio-temporal resistance profile of the channel at the wavefront is mainly responsible for the same; and 2) the distributed source provides additional support. The earlier findings are not limited to the special case of TGO considered. In spite of considering equal TGO and channel core radii, salient features of the model predicted remote electromagnetic fields agree well with the measured data reported in literature.

Fracture Analysis of High strength and Ultra high strength Concrete beams by using Finite Element Method

This paper presents the details of nonlinear finite element analysis (FEA) of three point bending specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete (UHSC). Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Cracking strength criterion has been used for simulation of crack propagation by conducting nonlinear FEA. The description about FEA using crack strength criterion has been outlined. Bi-linear tension softening relation has been used for modeling the cohesive stresses ahead of the crack tip. Numerical studies have been carried out on fracture analysis of three point bending specimens. It is observed from the studies that the computed values from FEA are in very good agreement with the corresponding experimental values. The computed values of stress vs crack width will be useful for evaluation of fracture energy, crack tip opening displacement and fracture toughness. Further, these values can also be used for crack growth study, remaining life assessment and residual strength evaluation of concrete structural components.

Studies on lithium L-ascorbate dihydrate: An interesting chiral nonlinear optical crystal

Lithium L-Ascorbate dihydrate (LLA) is a new metal organic nonlinear optical crystal belonging to the saccharide family. Single crystals of LLA were grown from aqueous solution. Solubility of the crystal has a positive temperature coefficient facilitating growth by slow cooling. Rietveld refinement was used to confirm the phase formation. The crystal has prismatic habit with (010), (001) and (10-1) prominent faces. Thermal analysis shows that the crystal is stable up to 102 degrees C. Transmission spectrum of the crystal extends from 302 nm to 1600 nm. Dielectric spectroscopic analysis revealed Cole Cole behaviour and prominent piezoelectric resonance peaks were observed in the range of 100-200 kHz. Second harmonic generation (SHG) conversion efficiency of up to 2.56 times that of a phase matched KDP crystal was achieved when the (010) plate of LLA single crystal was rotated about the +ve c axis, by 9.4 degrees in the clockwise direction. We also observed SHG conical sections which were attributed to noncollinear phase matching. The observation of the third conical section suggests very high birefringence and large nonlinear coefficients. A detailed study of surface laser damage showed that the crystal has high multiple damage thresholds of 9.7 GW cm(-2) and 42 GW cm(-2) at 1064 nm and 532 nm radiation respectively. (C) 2012 Elsevier B.V. All rights reserved.