Application of the method of initial functions for the analysis of composite laminated plates

The method of initial functions has been applied for deriving higher order theories for cross-ply laminated composite thick rectangular plates. The equations of three-dimensional elasticity have been used. No a priori assumptions regarding the distribution of stresses or displacements are needed. Numerical solutions of the governing equations have been presented for simply supported edges and the results are compared with available ones.

Sensing Shape Recovery Using Conductivity Noise in Thin Films of NiTi Shape Memory Alloys

Low frequency fluctuations in the electrical resistivity, or noise, have been used as a sensitive tool to probe into the temperature driven martensite transition in dc magnetron sputtered thin films of nickel titanium shape-memory alloys. Even in the equilibrium or static case, the noise magnitude was more than nine orders of magnitude larger than conventional metallic thin films and had a characteristic dependence on temperature. We observe that the noise while the temperature is being ramped is far larger as compared to the equilibrium noise indicating the sensitivity of electrical resistivity to the nucleation and propagation of domains during the shape recovery. Further, the higher order statistics suggests the existence of long range correlations during the transition. This new characterization is based on the kinetics of disorder in the system and separate from existing techniques and can be integrated to many device applications of shape memory alloys for in-situ shape recovery sensing.

Perturbation expansions and series acceleration procedures: Part-II. Extrapolation techniques

Three new procedures for the extrapolation of series coefficients from a given power series expansion are proposed. They are based on (i) a novel resummation identity, (ii) parametrised Euler transformation (pet) and (iii) a modifiedpet. Several examples taken from the Ising model series expansions, ferrimagnetic systems, etc., are illustrated. Apart from these applications, the higher order virial coefficients for hard spheres and hard discs have also been evaluated using the new techniques and these are compared with the estimates obtained by other methods. A satisfactory agreement is revealed between the two.

On a generalized dynamic model of bi-state social interaction processes

A non-linear model, construed as a generalized version of the models put forth earlier for the study of bi-state social interaction processes, is proposed in this study. The feasibility of deriving the dynamics of such processes is demonstrated by establishing equivalence between the non-linear model and a higher order linear model.

Monte Carlo simulation of Ising chains showing several phase transitions

A Monte Carlo simulation of Ising chains with competing short-range and infiniterange interactions has been carried out. Results show that whenever the system does not enter a metastable state, variation of temperature brings about phase transitions in the Ising chain. These phase transitions, except for two sets of interaction strengths, are generally of higher order and involve changes in the long-range order while the short-range order remains unaffected.

Comparison of Prediction Based LSF Quantization Methods using Split VQ

Further improvement in performance, to achieve near transparent quality LSF quantization, is shown to be possible by using a higher order two dimensional (2-D) prediction in the coefficient domain. The prediction is performed in a closed-loop manner so that the LSF reconstruction error is the same as the quantization error of the prediction residual. We show that an optimum 2-D predictor, exploiting both inter-frame and intra-frame correlations, performs better than existing predictive methods. Computationally efficient split vector quantization technique is used to implement the proposed 2-D prediction based method. We show further improvement in performance by using weighted Euclidean distance.

Understanding Protein Structure from a Percolation Perspective

Underlying the unique structures and diverse functions of proteins area vast range of amino-acid sequences and a highly limited number of folds taken up by the polypeptide backbone. By investigating the role of noncovalent connections at the backbone level and at the detailed side-chain level, we show that these unique structures emerge from interplay between random and selected features. Primarily, the protein structure network formed by these connections shows simple (bond) and higher order (clique) percolation behavior distinctly reminiscent of random network models. However, the clique percolation specific to the side-chain interaction network bears signatures unique to proteins characterized by a larger degree of connectivity than in random networks. These studies reflect some salient features of the manner in which amino acid sequences select the unique structure of proteins from the pool of a limited number of available folds.

Fournier polarography revisited

A theory for Fournier polarography and higher order harmonics is presented. This is valid for reversible systems under semi-infinite diffusion to stationary and expanding plane electrodes. The algorithm is simple, accurate and exploits the identities holding for the interfacial concentrations. The computations — minimal in nature — can be carried out easily and the results given here were evaluated taking into account the presence of harmonics to, at least, the twenty-fifth order.

Effect of amplifier imperfections on active networks

The deviation in the performance of active networks due to practical operational amplifiers (OA) is mainly because of the finite gain bandwidth productBand nonzero output resistanceR_0. The effect ofBandR_0on two OA impedances and single and multi-OA filters are discussed. In filters, the effect ofR_0is to add zeros to the transfer function often making it nonminimum phase. A simple method of analysis has been suggested for 3-OA biquad and coupled biquad circuits. A general method of noise minimization of the generalized impedance converter (GIC), while operating OA's within the prescribed voltage and current limits, is also discussed. The 3-OA biquadratic sections analyzed also exhibit noise behavior and signal handling capacity similar to the GIC. The GIC based structures are found to be better than other configurations both in biquadratic sections and direct realizations of higher order transfer functions.

Recognition and alignment of homologous DNA sequences between minichromosomes and single-stranded DNA promoted by RecA protein

The incorporation of DNA into nucleosomes and higher-order forms of chromatin in vivo creates difficulties with respect to its accessibility for cellular functions such as transcription, replication, repair and recombination. To understand the role of chromatin structure in the process of homologous recombination, we have studied the interaction of nucleoprotein filaments, comprised of RecA protein and ssDNA, with minichromosomes. Using this paradigm, we have addressed how chromatin structure affects the search for homologous DNA sequences, and attempted to distinguish between two mutually exclusive models of DNA-DNA pairing mechanisms. Paradoxically, we found that the search for homologous sequences, as monitored by unwinding of homologous or heterologous duplex DNA, was facilitated by nucleosomes, with no discernible effect on homologous pairing. More importantly, unwinding of minichromosomes required the interaction of nucleoprotein filaments and led to the accumulation of circular duplex DNA sensitive to nuclease P1. Competition experiments indicated that chromatin templates and naked DNA served as equally efficient targets for homologous pairing. These and other findings suggest that nucleosomes do not impede but rather facilitate the search for homologous sequences and establish, in accordance with one proposed model, that unwinding of duplex DNA precedes alignment of homologous sequences at the level of chromatin. The potential application of this model to investigate the role of chromosomal proteins in the alignment of homologous sequences in the context of cellular recombination is considered.

Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The axisymmetric mode

The coupled wavenumbers of a fluid-filled flexible cylindrical shell vibrating in the axisymmetric mode are studied. The coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter e due to the coupling. Using the smallness of Poisson's ratio (v), a double-asymptotic expansion involving e and v 2 is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (for large and small values of E). Different asymptotic expansions are used for different frequency ranges with continuous transitions occurring between them. The wavenumber solutions are continuously tracked as e varies from small to large values. A general trend observed is that a given wavenumber branch transits from a rigidwalled solution to a pressure-release solution with increasing E. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. Only the axisymmetric mode is considered. However, the method can be extended to the higher order modes.

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.

Predicting spin of compact objects from their QPOs: A global QPO model

We establish a unified model to explain Quasi-Periodic-Oscillation (QPO) observed from black hole and neutron star systems globally. This is based on the accreting systems thought to be damped harmonic oscillators with higher order nonlinearity. The model explains multiple properties parallelly independent of the nature of the compact object. It describes QPOs successfully for several compact sources. Based on it, we predict the spin frequency of the neutron star Sco X-1 and the specific angular momentum of black holes GRO J1655-40, GRS 1915+105.

On an asymptotic method of Krylov-Bogoliubov for overdamped nonlinear systems

A general asymptotic method based on the work of Krylov-Bogoliubov is developed to obtain the response of nonlinear over damped systems. A second-order system with both roots real is treated first and the method is then extended to higher-order systems. Two illustrative examples show good agreement with results obtained by numerical integration.

A nonlinear theory of wake development

A simple new series, using an expansion of the velocity profile in parabolic cylinder functions, has been developed to describe the nonlinear evolution of a steady, laminar, incompressible wake from a given arbitrary initial profile. The first term in this series is itself found to provide a very satisfactory prediction of the decay of the maximum velocity defect in the wake behind a flat plate or aft of the recirculation zone behind a symmetric blunt body. A detailed analysis, including higher order terms, has been made of the flat plate wake with a Blasius profile at the trailing edge. The same method yields, as a special case, complete results for the development of linearized wakes with arbitrary initial profile under the influence of arbitrary pressure gradients. Finally, for purposes of comparison, a simple approximate solution is obtained using momentum integral methods, and found to predict satisfactorily the decay of the maximum velocity defect. © 1970 Wolters-Noordhoff Publishing.