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.

Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Auxiliary coils for generating magnetic field gradients for a Faraday magnetometer

A set of coils has been designed and constructed for generating magnetic field gradients for a Faraday magnetometer. We have obtained a gradient of magnitude -1 1 kOe m-' (8.75 x lo5 A m-') in an air gap of 42 mm for a current of 12 A passing through the coils.

Effect of a magnetic field on the flow and blood oxygenation in channels of variable cross-section

The effect of a magnetic field on the flow and oxygenation of an incompressible Newtonian conducting fluid in channels with irregular boundaries has been investigated. The geometric parameter δ, which is a ratio of the mean half width of the channel d to the characteristic length λ along the channel over which the significant changes in the flow quantities occur, has been used for perturbing the governing equations. Closed form solutions of the various order equations are presented for the stream function. The equations for oxygen partial pressure remain nonlinear even after perturbation, therefore a numerical solution is presented. The expressions for shear stress at a wall and pressure distributions are derived. Here the separation in the flow occurs at a higher Reynolds number than the corresponding non-magnetic case. It is found that the magnetic field has an effect on local oxygen concentration but has a little effect on the saturation length.

Composite field approximations for ion traps with apertures on electrodes

This paper presents two approximate analytical expressions for nonlinear electric fields in the principal direction in axially symmetric (3D) and two dimensional (2D) ion trap mass analysers with apertures (holes in case of 3D traps and slits in case of 2D traps) on the electrodes. Considered together (3D and 2D), we present composite approximations for the principal unidirectional nonlinear electric fields in these ion traps. The composite electric field E has the form E = E-noaperture + E-aperture. where E-noaperture is the field within an imagined trap which is identical to the practical trap except that the apertures are missing and E-aperture is the field contribution due to apertures on the two trap electrodes. The field along the principal axis, of the trap can in this way be well approximated for any aperture that is not too large. To derive E-aperture. classical results of electrostatics have been extended to electrodes with finite thickness and different aperture shapes.E-noaperture is a modified truncated multipole expansion for the imagined trap with no aperture. The first several terms in the multipole expansion are in principle exact(though numerically determined using the BEM), while the last term is chosen to match the field at the electrode. This expansion, once Computed, works with any aperture in the practical trap. The composite field approximation for axially symmetric (3D) traps is checked for three geometries: the Paul trap, the cylindrical ion trap (CIT) and an arbitrary other trap. The approximation for 2D traps is verified using two geometries: the linear ion trap (LIT) and the rectilinear ion trap (RIT). In each case, for two aperture sizes (10% and 50% of the trap dimension), highly satisfactory fits are obtained. These composite approximations may be used in more detailed nonlinear ion dynamics Studies than have been hitherto attempted. (C) 2009 Elsevier B.V. All rights reserved.

Reduced complexity two stage vector quantization

We address the issue of complexity for vector quantization (VQ) of wide-band speech LSF (line spectrum frequency) parameters. The recently proposed switched split VQ (SSVQ) method provides better rate-distortion (R/D) performance than the traditional split VQ (SVQ) method, even at the requirement of lower computational complexity. but at the expense of much higher memory. We develop the two stage SVQ (TsSVQ) method, by which we gain both the memory and computational advantages and still retain good R/D performance. The proposed TsSVQ method uses a full dimensional quantizer in its first stage for exploiting all the higher dimensional coding advantages and then, uses an SVQ method for quantizing the residual vector in the second stage so as to reduce the complexity. We also develop a transform domain residual coding method in this two stage architecture such that it further reduces the computational complexity. To design an effective residual codebook in the second stage, variance normalization of Voronoi regions is carried out which leads to the design of two new methods, referred to as normalized two stage SVQ (NTsSVQ) and normalized two stage transform domain SVQ (NTsTrSVQ). These two new methods have complimentary strengths and hence, they are combined in a switched VQ mode which leads to the further improvement in R/D performance, but retaining the low complexity requirement. We evaluate the performances of new methods for wide-band speech LSF parameter quantization and show their advantages over established SVQ and SSVQ methods.

Time dependent rotational flow of a viscous fluid over an infinite porous disk with a magnetic field

Both the semi-similar and self-similar flows due to a viscous fluid rotating with time dependent angular velocity over a porous disk of large radius at rest with or without a magnetic field are investigated. For the self-similar case the resulting equations for the suction and no mass transfer cases are solved numerically by quasilinearization method whereas for the semi-similar case and injection in the self-similar case an implicit finite difference method with Newton's linearization is employed. For rapid deceleration of fluid and for moderate suction in the case of self-similar flow there exists a layer of fluid, close to the disk surface where the sense of rotation is opposite to that of the fluid rotating far away. The velocity profiles in the absence of magnetic field are found to be oscillatory except for suction. For the accelerating freestream, (semi-similar flow) the effect of time is to reduce the amplitude of the oscillations of the velocity components. On the other hand the effect of time for the oscillating case is just the opposite.

Numerical simulation of conductive particle behaviour at the surface of a plate electrode affected by a DC corona field

The electric field in certain electrostatic devices can be modeled by a grounded plate electrode affected by a corona discharge generated by a series of parallel wires connected to a DC high-voltage supply. The system of differential equations that describe the behaviour (i.e., charging and motion) of the conductive particle in such an electric field has been numerically solved, using several simplifying assumptions. Thus, it was possible to investigate the effect of various electrical and mechanical factors on the trajectories of conductive particles. This model has been employed to study the behaviour of coalparticles in fly-ash corona separators.