Stiff-String Basis Functions for Vibration Analysis of High Speed Rotating Beams

A new rotating beam finite element is developed in which the basis functions are obtained by the exact solution of the governing static homogenous differential equation of a stiff string, which results from an approximation in the rotating beam equation. These shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. Using this new element and the Hermite cubic finite element, a convergence study of natural frequencies is performed, and it is found that the new element converges much more rapidly than the conventional Hermite cubic element for the first two modes at higher rotation speeds. The new element is also applied for uniform and tapered rotating beams to determine the natural frequencies, and the results compare very well with the published results given in the literature.

Nonlinear ensemble prediction of chaotic daily rainfall

The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. Many of these approaches aim at only analyzing the chaotic nature and not its prediction. In the present study, an attempt is made to identify chaos using various techniques and prediction is also done by generating ensembles in order to quantify the uncertainty involved. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha, Mahanadi and All-India for the period 1955-2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series. Correlation dimension method is done on th phase randomized and first derivative of the data series to check whether the saturation of the dimension is due to the inherent linear correlation structure or due to low dimensional dynamics. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996-2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are done from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature. (C) 2010 Elsevier Ltd. All rights reserved.

Self-regularized pseudo time-marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non-linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least-square solution is through a regularized Gauss-Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time,recursive integration of the pseudo-dynamical GNM (PD-GNM) update equation addresses the major numerical difficulty associated with the near-zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo-dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo-dynamic ensemble Kalman filter (PD-EnKF). For multiple sets of measurements involving various load cases, we expedite the speed of thePD-EnKF by proposing an inner iteration within every time step. Results using the pseudo-dynamic strategy obtained through PD-EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD-EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small.

Self-regularized pseudo time-marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non-linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least-square solution is through a regularized Gauss-Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time, recursive integration of the pseudo-dynamical GNM (PD-GNM) update equation addresses the major numerical difficulty associated with the near-zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo-dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through apseudo-dynamic ensemble Kalman filter (PD-EnKF). For multiple sets ofmeasurements involving various load cases, we expedite the speed of the PD-EnKF by proposing an inner iteration within every time step. Results using the pseudo-dynamic strategy obtained through PD-EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD-EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small. Copyright (C) 2009 John Wiley & Sons, Ltd.

Probability Distribution of the Eigenvalues of the Random String Equation

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

Hydrologic drought prediction under climate change: Uncertainty modeling with Dempster-Shafer and Bayesian approaches

Representation and quantification of uncertainty in climate change impact studies are a difficult task. Several sources of uncertainty arise in studies of hydrologic impacts of climate change, such as those due to choice of general circulation models (GCMs), scenarios and downscaling methods. Recently, much work has focused on uncertainty quantification and modeling in regional climate change impacts. In this paper, an uncertainty modeling framework is evaluated, which uses a generalized uncertainty measure to combine GCM, scenario and downscaling uncertainties. The Dempster-Shafer (D-S) evidence theory is used for representing and combining uncertainty from various sources. A significant advantage of the D-S framework over the traditional probabilistic approach is that it allows for the allocation of a probability mass to sets or intervals, and can hence handle both aleatory or stochastic uncertainty, and epistemic or subjective uncertainty. This paper shows how the D-S theory can be used to represent beliefs in some hypotheses such as hydrologic drought or wet conditions, describe uncertainty and ignorance in the system, and give a quantitative measurement of belief and plausibility in results. The D-S approach has been used in this work for information synthesis using various evidence combination rules having different conflict modeling approaches. A case study is presented for hydrologic drought prediction using downscaled streamflow in the Mahanadi River at Hirakud in Orissa, India. Projections of n most likely monsoon streamflow sequences are obtained from a conditional random field (CRF) downscaling model, using an ensemble of three GCMs for three scenarios, which are converted to monsoon standardized streamflow index (SSFI-4) series. This range is used to specify the basic probability assignment (bpa) for a Dempster-Shafer structure, which represents uncertainty associated with each of the SSFI-4 classifications. These uncertainties are then combined across GCMs and scenarios using various evidence combination rules given by the D-S theory. A Bayesian approach is also presented for this case study, which models the uncertainty in projected frequencies of SSFI-4 classifications by deriving a posterior distribution for the frequency of each classification, using an ensemble of GCMs and scenarios. Results from the D-S and Bayesian approaches are compared, and relative merits of each approach are discussed. Both approaches show an increasing probability of extreme, severe and moderate droughts and decreasing probability of normal and wet conditions in Orissa as a result of climate change. (C) 2010 Elsevier Ltd. All rights reserved.

Interaction of flux tubes with sound waves

The Landau damping of sound waves in a plasma consisting of ensemble of magnetic flux tubes is discussed. It is shown that sound waves cannot be Landau damped in general but under certain restricted conditions on plasma parameters the possibility of absorption of these waves can exist. The possibility of radiative damping of the acoustic waves along the magnetic filaments is also discussed. It appears that the most plausible mechanism of damping of sound waves in a plasma consisting of magnetic filaments can be due to scattering of a sound wave by the filaments.

Investigations on the Corona performance of a Ceramic disc Insulators integrated with Field Reduction Electrode

This paper presents laboratory investigations on the visible corona and discharge radio noise. Experimental investigations are carried on various types of normal and anti-fog types of ceramic disc insulator at the recently established artificial pollution experimental facility. The results obtained from the experimental investigations show better performance for the disc insulators fitted with field reduction electrodes. In addition to the corona and radio noise investigations the comparisons are also made for the experimental results of the potential distribution across the insulator string (with and without filed reduction electrode) with the simulation results obtained by using Surface Charge Simulation Method.

Linear dynamics and active control of an elastically supported travelling string

In this paper, the linear dynamics and active control of a string travelling with uniform velocity is presented. Discrete elastic supports are introduced along the length of the string. Finite element formulation is adopted to obtain the governing equations of motion. The velocity of translation introduces gyroscopic terms in the system equations. The effect of translation and the discrete elastic supports on the free vibration solution is studied. The solution is utilized in actively controlling the string vibrations due to an initial disturbance. The control, affected in modal space, is optimal with respect to a quadratic performance index. Numerical results are presented to demonstrate the effectiveness of the control strategy in regulating the travelling string vibrations.

Predictive uncertainty of chaotic daily streamflow using ensemble wavelet networks approach

Perfect or even mediocre weather predictions over a long period are almost impossible because of the ultimate growth of a small initial error into a significant one. Even though the sensitivity of initial conditions limits the predictability in chaotic systems, an ensemble of prediction from different possible initial conditions and also a prediction algorithm capable of resolving the fine structure of the chaotic attractor can reduce the prediction uncertainty to some extent. All of the traditional chaotic prediction methods in hydrology are based on single optimum initial condition local models which can model the sudden divergence of the trajectories with different local functions. Conceptually, global models are ineffective in modeling the highly unstable structure of the chaotic attractor. This paper focuses on an ensemble prediction approach by reconstructing the phase space using different combinations of chaotic parameters, i.e., embedding dimension and delay time to quantify the uncertainty in initial conditions. The ensemble approach is implemented through a local learning wavelet network model with a global feed-forward neural network structure for the phase space prediction of chaotic streamflow series. Quantification of uncertainties in future predictions are done by creating an ensemble of predictions with wavelet network using a range of plausible embedding dimensions and delay times. The ensemble approach is proved to be 50% more efficient than the single prediction for both local approximation and wavelet network approaches. The wavelet network approach has proved to be 30%-50% more superior to the local approximation approach. Compared to the traditional local approximation approach with single initial condition, the total predictive uncertainty in the streamflow is reduced when modeled with ensemble wavelet networks for different lead times. Localization property of wavelets, utilizing different dilation and translation parameters, helps in capturing most of the statistical properties of the observed data. The need for taking into account all plausible initial conditions and also bringing together the characteristics of both local and global approaches to model the unstable yet ordered chaotic attractor of a hydrologic series is clearly demonstrated.

Study of temperature distribution along an artificially polluted insulator string

Insulator becomes wet partially or completely, and the pollution layer on it becomes conductive, when collecting pollutants for an extended period during dew, light rain, mist, fog or snow melting. Heavy rain is a complicated factor that it may wash away the pollution layer without initiating other stages of breakdown or it may bridge the gaps between sheds to promote flashover. The insulator with a conducting pollution layer being energized, can cause a surface leakage current to flow (also temperature-rise). As the surface conductivity is non-uniform, the conducting pollution layer becomes broken by dry bands (at spots of high current density), interrupting the flow of leakage current. Voltage across insulator gets concentrated across dry bands, and causes high electric stress and breakdown (dry band arcing). If the resistance of the insulator surface is sufficiently low, the dry band arcs can be propagated to bridge the terminals causing flashover. The present paper concerns the evaluation of the temperature distribution along the surface of an energized artificially polluted insulator string.

String-like propagation of the 5-coordinated defect state in supercooled water: molecular origin of dynamic and thermodynamic anomalies

We find that at low temperature water, large amplitude (similar to 60 degrees) rotational jumps propagate like a string, with the length of propagation increasing with lowering temperature. The strings are formed by mobile 5-coordinated water molecules which move like a Glarum defect (J. Chem. Phys., 1960, 33, 1371), causing water molecules on the path to change from 4-coordinated to 5-coordinated and again back to 4-coordinated water, and in the process cause the tagged water molecule to jump, by following essentially the Laage-Hynes mechanism (Science, 2006, 311, 832-835). The effects on relaxation of the propagating defect causing large amplitude jumps are manifested most dramatically in the mean square displacement (MSD) and also in the rotational time correlation function of the O-H bond of the molecule that is visited by the defect (transient transition to the 5-coordinated state). The MSD and the decay of rotational time correlation function, both remain quenched in the absence of any visit by the defect, as postulated by Glarum long time ago. We establish a direct connection between these propagating events and the known thermodynamic and dynamic anomalies in supercooled water. These strings are found largely in the regions that surround the relatively rigid domains of 4-coordinated water molecules. The propagating strings give rise to a noticeable dynamical heterogeneity, quantified here by a sharp rise in the peak of the four-point density response function, chi(4)(t). This dynamics heterogeneity is also responsible for the breakdown of the Stokes-Einstein relation.

Instabilities of soft elastic microtubes filled with viscous fluids: Pearls, wrinkles, and sausage strings

A linear stability analysis is presented to study the self-organized instabilities of a highly compliant elastic cylindrical shell filled with a viscous liquid and submerged in another viscous medium. The prototype closely mimics many components of micro-or nanofluidic devices and biological processes such as the budding of a string of pearls inside cells and sausage-string formation of blood vessels. The cylindrical shell is considered to be a soft linear elastic solid with small storage modulus. When the destabilizing capillary force derived from the cross-sectional curvature overcomes the stabilizing elastic and in-plane capillary forces, the microtube can spontaneously self-organize into one of several possible configurations; namely, pearling, in which the viscous fluid in the core of the elastic shell breaks up into droplets; sausage strings, in which the outer interface of the mircrotube deforms more than the inner interface; and wrinkles, in which both interfaces of the thin-walled mircrotube deform in phase with small amplitudes. This study identifies the conditions for the existence of these modes and demonstrates that the ratios of the interfacial tensions at the interfaces, the viscosities, and the thickness of the microtube play crucial roles in the mode selection and the relative amplitudes of deformations at the two interfaces. The analysis also shows asymptotically that an elastic fiber submerged in a viscous liquid is unstable for Y = gamma/(G(e)R) > 6 and an elastic microchannel filled with a viscous liquid should rupture to form spherical cavities (pearling) for Y > 2, where gamma, G(e), and R are the surface tension, elastic shear modulus, and radius, respectively, of the fiber or microchannel.

A Coordinated Interdependent Protein Circuitry Stabilizes the Kinetochore Ensemble to Protect CENP-A in the Human Pathogenic Yeast Candida albicans

Unlike most eukaryotes, a kinetochore is fully assembled early in the cell cycle in budding yeasts Saccharomyces cerevisiae and Candida albicans. These kinetochores are clustered together throughout the cell cycle. Kinetochore assembly on point centromeres of S. cerevisiae is considered to be a step-wise process that initiates with binding of inner kinetochore proteins on specific centromere DNA sequence motifs. In contrast, kinetochore formation in C. albicans, that carries regional centromeres of 3-5 kb long, has been shown to be a sequence independent but an epigenetically regulated event. In this study, we investigated the process of kinetochore assembly/disassembly in C. albicans. Localization dependence of various kinetochore proteins studied by confocal microscopy and chromatin immunoprecipitation (ChIP) assays revealed that assembly of a kinetochore is a highly coordinated and interdependent event. Partial depletion of an essential kinetochore protein affects integrity of the kinetochore cluster. Further protein depletion results in complete collapse of the kinetochore architecture. In addition, GFP-tagged kinetochore proteins confirmed similar time-dependent disintegration upon gradual depletion of an outer kinetochore protein (Dam1). The loss of integrity of a kinetochore formed on centromeric chromatin was demonstrated by reduced binding of CENP-A and CENP-C at the centromeres. Most strikingly, Western blot analysis revealed that gradual depletion of any of these essential kinetochore proteins results in concomitant reduction in cellular protein levels of CENP-A. We further demonstrated that centromere bound CENP-A is protected from the proteosomal mediated degradation. Based on these results, we propose that a coordinated interdependent circuitry of several evolutionarily conserved essential kinetochore proteins ensures integrity of a kinetochore formed on the foundation of CENP-A containing centromeric chromatin.

Deformation field in indentation of a granular ensemble

An experimental study has been made of the flow field in indentation of a model granular material. A granular ensemble composed of spherical sand particles with average size of 0.4 mm is indented with a flat ended punch under plane-strain conditions. The region around the indenter is imaged in situ using a high-speed charge-coupled device (CCD) imaging system. By applying a hybrid image analysis technique to image sequences of the indentation, flow parameters such as velocity, velocity gradient, and strain rate are measured at high resolution. The measurements have enabled characterization of the main features of the flow such as dead material zones, velocity jumps, localization of deformation, and regions of highly rotational flow resembling vortices. Implications for validation of theoretical analyses and applications are discussed.