Hybrid stiff-string-polynomial basis functions for vibration analysis of high speed rotating beams

A new finite element is developed for free vibration analysis of high speed rotating beams using basis functions which use a linear combination of the solution of the governing static differential equation of a stiff-string and a cubic polynomial. These new shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. The natural frequencies predicted by the proposed element are compared with an element with stiff-string, cubic polynomial and quintic polynomial shape functions. It is found that the new element exhibits superior convergence compared to the other basis functions.

Field imperfection induced axial secular frequency shifts in nonlinear ion traps

This article develops a simple analytical expression that relates ion axial secular frequency to field aberration in ion trap mass spectrometers. Hexapole and octopole aberrations have been considered in the present computations. The equation of motion of the ions in a pseudopotential well with these superpositions has the form of a Duffing-like equation and a perturbation method has been used to obtain the expression for ion secular frequency as a function of field imperfections. The expression indicates that the frequency shift is sensitive to the sign of the octopole superposition and insensitive to the sign of the hexapole superposition. Further, for weak multipole superposition of the same magnitude, octopole superposition causes a larger frequency shift in comparison to hexapole superposition.

Flow and heat transfer in a stagnation-point flow over a stretching sheet with a magnetic field

The flow and heat transfer problem in the boundary layer induced by a continuous moving surface is important in many manufacturing processes in industry such as the boundary layer along material handling conveyers, the aerodynamic extrusion of plastic sheet, the cooling of an infinite metalic plate in a cooling bath (which may also be electrolyte). Glass blowing, continuous casting and spinning of fibres also involve the flow due to a stretching surface. Sakiadis [1] was the first to study the flow induced by a semi-infinite moving wall in an ambient fluid. On the other hand, Crane [2] first studied the flow over a linearly stretching sheet in an ambient fluid. Subsequently, Crane [3] also investigated the corresponding heat transfer problem. Since then several authors [4-8] have studied various aspects of this problem such as the effects of mass transfer, variable wall temperature, constant heat flux, magnetic field etc. Recently, Andersson [9] has obtained an exact solution of the Navier-Stokes equations for the MHD flow over a linearly stretching sheet in an ambient fluid. Also Chiam [10] has studied the heat transfer with variable thermal conductivity on a stretching sheet when the velocities of the sheet and the free stream are equal.

Precipitation In Small Systems--II. Mean Field Equations More Effective Than Population Balance

Part I (Manjunath et al., 1994, Chem. Engng Sci. 49, 1451-1463) of this paper showed that the random particle numbers and size distributions in precipitation processes in very small drops obtained by stochastic simulation techniques deviate substantially from the predictions of conventional population balance. The foregoing problem is considered in this paper in terms of a mean field approximation obtained by applying a first-order closure to an unclosed set of mean field equations presented in Part I. The mean field approximation consists of two mutually coupled partial differential equations featuring (i) the probability distribution for residual supersaturation and (ii) the mean number density of particles for each size and supersaturation from which all average properties and fluctuations can be calculated. The mean field equations have been solved by finite difference methods for (i) crystallization and (ii) precipitation of a metal hydroxide both occurring in a single drop of specified initial supersaturation. The results for the average number of particles, average residual supersaturation, the average size distribution, and fluctuations about the average values have been compared with those obtained by stochastic simulation techniques and by population balance. This comparison shows that the mean field predictions are substantially superior to those of population balance as judged by the close proximity of results from the former to those from stochastic simulations. The agreement is excellent for broad initial supersaturations at short times but deteriorates progressively at larger times. For steep initial supersaturation distributions, predictions of the mean field theory are not satisfactory thus calling for higher-order approximations. The merit of the mean field approximation over stochastic simulation lies in its potential to reduce expensive computation times involved in simulation. More effective computational techniques could not only enhance this advantage of the mean field approximation but also make it possible to use higher-order approximations eliminating the constraints under which the stochastic dynamics of the process can be predicted accurately.

Particle field imaging using digital in-line holography

Digital holography is the direct recording of holograms using a CCD camera and is an alternative to the use of a film or a plate. In this communication in-line digital holographic microscopy has been explored for its application in particle imaging in 3D. Holograms of particles of about 10 mu m size have been digitally reconstructed. Digital focusing was done to image the particles in different planes along the depth of focus. Digital holographic particle imaging results were compared with conventional optical microscope imaging. A methodology for dynamic analysis of microparticles in 3D using in-line digital holography has been proposed.

Vertical structure and horizontal gradients of aerosol extinction coefficients over coastal India inferred from airborne lidar measurements during the Integrated Campaign for Aerosol, Gases and Radiation Budget (ICARB) field campaign

Quantitative estimates of the vertical structure and the spatial gradients of aerosol extinction coefficients have been made from airborne lidar measurements across the coastline into offshore oceanic regions along the east and west coasts of India. The vertical structure revealed the presence of strong, elevated aerosol layers in the altitude region of similar to 2-4 km, well above the atmospheric boundary layer (ABL). Horizontal gradients also showed a vertical structure, being sharp with the e(-1) scaling distance (D-0H) as small as similar to 150 km in the well-mixed regions mostly under the influence of local source effects. Above the ABL, where local effects are subdued, the gradients were much shallower (similar to 600-800 km); nevertheless, they were steep compared to the value of similar to 1500-2500 km reported for columnar AOD during winter. The gradients of these elevated layers were steeper over the east coast of India than over the west coast. Near-simultaneous radio sonde (Vaisala, Inc., Finland) ascents made over the northern Bay of Bengal showed the presence of convectively unstable regions, first from surface to similar to 750-1000 m and the other extending from 1750 to 3000 m separated by a stable region in between. These can act as a conduit for the advection of aerosols and favor the transport of continental aerosols in the higher levels (> 2 km) into the oceans without entering the marine boundary layer below. Large spatial gradient in aerosol optical and hence radiative impacts between the coastal landmass and the adjacent oceans within a short distance of < 300 km (even at an altitude of 3 km) during summer and the premonsoon is of significance to the regional climate.

Role of predictors in downscaling surface temperature to river basin in India for IPCC SRES scenarios using support vector machine

In this paper, downscaling models are developed using a support vector machine (SVM) for obtaining projections of monthly mean maximum and minimum temperatures (T-max and T-min) to river-basin scale. The effectiveness of the model is demonstrated through application to downscale the predictands for the catchment of the Malaprabha reservoir in India, which is considered to be a climatically sensitive region. The probable predictor variables are extracted from (1) the National Centers for Environmental Prediction (NCEP) reanalysis dataset for the period 1978-2000, and (2) the simulations from the third-generation Canadian Coupled Global Climate Model (CGCM3) for emission scenarios A1B, A2, B1 and COMMIT for the period 1978-2100. The predictor variables are classified into three groups, namely A, B and C. Large-scale atmospheric variables Such as air temperature, zonal and meridional wind velocities at 925 nib which are often used for downscaling temperature are considered as predictors in Group A. Surface flux variables such as latent heat (LH), sensible heat, shortwave radiation and longwave radiation fluxes, which control temperature of the Earth's surface are tried as plausible predictors in Group B. Group C comprises of all the predictor variables in both the Groups A and B. The scatter plots and cross-correlations are used for verifying the reliability of the simulation of the predictor variables by the CGCM3 and to Study the predictor-predictand relationships. The impact of trend in predictor variables on downscaled temperature was studied. The predictor, air temperature at 925 mb showed an increasing trend, while the rest of the predictors showed no trend. The performance of the SVM models that are developed, one for each combination of predictor group, predictand, calibration period and location-based stratification (land, land and ocean) of climate variables, was evaluated. In general, the models which use predictor variables pertaining to land surface improved the performance of SVM models for downscaling T-max and T-min

A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization

While frame-invariant solutions for arbitrarily large rotational deformations have been reported through the orthogonal matrix parametrization, derivation of such solutions purely through a rotation vector parametrization, which uses only three parameters and provides a parsimonious storage of rotations, is novel and constitutes the subject of this paper. In particular, we employ interpolations of relative rotations and a new rotation vector update for a strain-objective finite element formulation in the material framework. We show that the update provides either the desired rotation vector or its complement. This rules out an additive interpolation of total rotation vectors at the nodes. Hence, interpolations of relative rotation vectors are used. Through numerical examples, we show that combining the proposed update with interpolations of relative rotations yields frame-invariant and path-independent numerical solutions. Advantages of the present approach vis-a-vis the updated Lagrangian formulation are also analyzed.

A phase field study of morphological instabilities in multilayer thin films

We studied the microstructural evolution of multiple layers of elastically stiff films embedded in an elastically soft matrix using a phase field model. The coherent and planar film/matrix interfaces are rendered unstable by the elastic stresses due to a lattice parameter mismatch between the film and matrix phases, resulting in the break-up of the films into particles. With an increasing volume fraction of the stiff phase, the elastic interactions between neighbouring layers lead to: (i) interlayer correlations from an early stage; (ii) a longer wavelength for the maximally growing wave; and therefore (iii) a delayed break-LIP. Further, they promote a crossover in the mode of instability from a predominantly anti-symmetric (in phase) one to a symmetric (out of phase) one. We have computed a stability diagram for the most probable mode of break-up in terms of elastic modulus Mismatch and Volume fraction. We rationalize our results in terms of the initial driving force for destabilization, and corroborate our conclusions using simulations in elastically anisotropic systems.

Prediction of Ultimate Capacity of Laterally Loaded Piles in Clay: A Relevance Vector Machine Approach

This study investigates the potential of Relevance Vector Machine (RVM)-based approach to predict the ultimate capacity of laterally loaded pile in clay. RVM is a sparse approximate Bayesian kernel method. It can be seen as a probabilistic version of support vector machine. It provides much sparser regressors without compromising performance, and kernel bases give a small but worthwhile improvement in performance. RVM model outperforms the two other models based on root-mean-square-error (RMSE) and mean-absolute-error (MAE) performance criteria. It also stimates the prediction variance. The results presented in this paper clearly highlight that the RVM is a robust tool for prediction Of ultimate capacity of laterally loaded piles in clay.

Enhancing field emission from a carbon nanotube array by lateral control of electrodynamic force field

Fluctuation of field emission current from carbon nanotubes (CNTs) poses certain difficulties for their use in nanobiomedical X-ray devices and imaging probes. This problem arises due to deformation of the CNTs due to electrodynamic force field and electron-phonon interaction. It is of great importance to have precise control of emitted electron beams very near the CNT tips. In this paper, a new array configuration with stacked array of CNTs is analysed and it is shown that the current density distribution is greatly localised at the middle of the array, that the scatter due to electrodynamic force field is minimised and that the temperature transients are much smaller compared to those in an array with random height distribution.

Partial discharges at low pressures in a dielectric interface between uniform field electrodes

Partial discharges in a gaseous interface due to the presence of a dielectric between two uniform field electrodes in air at different pressures from 0.5 to 685 mm Hg have been studied and measurements of inception and extinction voltages, number of pulses and their charge magnitudes at inception are reported. It has been observed that the extinction voltage can be as low as 70% of the inception voltage suggesting that the working voltage in such cases should be about 30% lower than the observed inception voltage. Small magnitude pulses are found to be more in number than large magnitude pulses. The charge is found to be pressure dependent. The results have been explained on the basis of an equivalent circuit consisting of resistance and capacitance in which the discharge gap functions as a switch.

Has the Crab Pulsar Magnetic-Field Grown After its Birth

We investigate the evolution of rotation period and spindown age of a pulsar whose surface magnetic field undergoes a phase of growth. Application of these results to the Crab pulsar strongly indicates that its parameters cannot be accounted for by the field growth theories.

The relation between polarisation and electric field for trissarcosine calcium chloride

Measurement of the relation between polarisation and electric field for ferroelectric trissarcosine calcium chloride (TSCC) was made in the pressure range up to 6 kbar. The pressure dependence of the spontaneous polarisation and the coercive field were obtained, and the existence of a new pressure-induced phase and the paraelectric- ferroelectric-new phase triple point were found.

On the probability that the determinant of an nxn matrix over a finite field vanishe

An expression is derived for the probability that the determinant of an n x n matrix over a finite field vanishes; from this it is deduced that for a fixed field this probability tends to 1 as n tends to.