Average variation L2-stability criteria for time-varying feedback systems-A unified approach

The problem of developing L2-stability criteria for feedback systems with a single time-varying gain, which impose average variation constraints on the gain is treated. A unified approach is presented which facilitates the development of such average variation criteria for both linear and nonlinear systems. The stability criteria derived here are shown to be more general than the existing results.

Class of linear time-varying discrete systems

A class of linear time-varying discrete systems is considered, and closed-form solutions are obtained in different cases. Some comments on stability are also included.

Antiferroelectriclike polarization behavior in compositionally varying (1-x) Pb(Mg1/3Nb2/3)O3–(x) PbTiO3 multilayers

Compositionally varying multilayers of (1−x) Pb(Mg1/3N2/3)O3–(x) PbTiO3 were fabricated using pulsed laser ablation technique. An antiferroelectriclike polarization hysteresis was observed in these relaxor based multilayer systems. The competition among the intrinsic ferroelectric coupling in the relaxor ferroelectrics and the antiferroelectric coupling among the dipoles at the interface gives rise to an antiferroelectriclike polarization behavior. An increment in the coercive field and the applied field corresponding to the polarization flipping at low temperatures, provide further insight on the competition among the long-range ferroelectric interaction and the interfacial interaction in the polarization behavior of these relaxor multilayers.

Evolution of texture and grain boundary microstructure in two-phase (α + β) brass during recrystallization

The evolution of texture and microstructure during recrystallization is studied for two-phase copper alloy (Cu–40Zn) with a variation of the initial texture and microstructure (hot rolled and solution treated) as well as the mode of rolling (deformation path: uni-directional rolling and cross rolling). The results of bulk texture have been supported by micro-texture and microstructure studies carried out using electron back scatter diffraction (EBSD). The initial microstructural condition as well as the mode of rolling has been found to alter the recrystallization texture and microstructure. The uni-directionally rolled samples showed a strong Goss and BR {236}385 component while a weaker texture similar to that of rolling evolved for the cross-rolled samples in the α phase on recrystallization. The recrystallization texture of the β phase was similar to that of the rolling texture with discontinuous 101 α and {111} γ fiber with high intensity at {111}101. For a given microstructure, the cross-rolled samples showed a higher fraction of coincident site lattice Σ3 twin boundaries in the α phase. The higher fraction of Σ3 boundaries is explained on the basis of the higher propensity of growth accidents during annealing of the cross-rolled samples. The present investigation demonstrates that change in strain path, as introduced during cross-rolling, could be a viable tool for grain boundary engineering of low SFE fcc materials.

Interrelation of grain boundary microstructure and texture in a hot rolled Ni-rich NiTi alloy

This investigation deals with the evolution of grain boundary microstructure and crystallographic texture during hot rolling of a Ni-rich NiTi alloy. Electron backscattered diffraction studies revealed the occurrence of several coincidence site lattice (CSL) boundaries. The origin of these boundaries has been identified. The crystallographic texture of the deformed sample consists mainly of (1 1 1)parallel to normal direction fiber. The texture components on the fiber exhibit some correlation with the type of CSL boundary. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Online Computation of Hysteresis Boundary for Constant Switching Frequency Current-Error Space-Vector-Based Hysteresis Controller for VSI-Fed IM Drives

This paper proposes a current-error space-vector-based hysteresis controller with online computation of boundary for two-level inverter-fed induction motor (IM) drives. The proposed hysteresis controller has got all advantages of conventional current-error space-vector-based hysteresis controllers like quick transient response, simplicity, adjacent voltage vector switching, etc. Major advantage of the proposed controller-based voltage-source-inverters-fed drive is that phase voltage frequency spectrum produced is exactly similar to that of a constant switching frequency space-vector pulsewidth modulated (SVPWM) inverter. In this proposed hysteresis controller, stator voltages along alpha- and beta-axes are estimated during zero and active voltage vector periods using current errors along alpha- and beta-axes and steady-state model of IM. Online computation of hysteresis boundary is carried out using estimated stator voltages in the proposed hysteresis controller. The proposed scheme is simple and capable of taking inverter upto six-step-mode operation, if demanded by drive system. The proposed hysteresis-controller-based inverter-fed drive scheme is experimentally verified. The steady state and transient performance of the proposed scheme is extensively tested. The experimental results are giving constant frequency spectrum for phase voltage similar to that of constant frequency SVPWM inverter-fed drive.

Estimating the Hausdorff-Besicovitch dimension of boundary of basin of attraction in helicopter trim

Helicopter trim involves solution of nonlinear force equilibrium equations. As in many nonlinear dynamic systems, helicopter trim problem can show chaotic behavior. This chaotic behavior is found in the basin of attraction of the nonlinear trim equations which have to be solved to determine the main rotor control inputs given by the pilot. This study focuses on the boundary of the basin of attraction obtained for a set of control inputs. We analyze the boundary by considering it at different magnification levels. The magnified views reveal intricate geometries. It is also found that the basin boundary exhibits the characteristic of statistical self-similarity, which is an essential property of fractal geometries. These results led the authors to investigate the fractal dimension of the basin boundary. It is found that this dimension is indeed greater than the topological dimension. From all the observations, it is evident that the boundary of the basin of attraction for helicopter trim problem is fractal in nature. (C) 2012 Elsevier Inc. All rights reserved.

A MATLAB Code for Three Dimensional Linear Elastostatics using Constant Boundary Elements

Present work presents a code written in the very simple programming language MATLAB, for three dimensional linear elastostatics, using constant boundary elements. The code, in full or in part, is not a translation or a copy of any of the existing codes. Present paper explains how the code is written, and lists all the formulae used. Code is verified by using the code to solve a simple problem which has the well known approximate analytical solution. Of course, present work does not make any contribution to research on boundary elements, in terms of theory. But the work is justified by the fact that, to the best of author’s knowledge, as of now, one cannot find an open access MATLAB code for three dimensional linear elastostatics using constant boundary elements. Author hopes this paper to be of help to beginners who wish to understand how a simple but complete boundary element code works, so that they can build upon and modify the present open access code to solve complex engineering problems quickly and easily. The code is available online for open access (as supplementary file for the present paper), and may be downloaded from the website for the present journal.

Receive Antenna Selection for Time-Varying Channels Using Discrete Prolate Spheroidal Sequences

Receive antenna selection (AS) has been shown to maintain the diversity benefits of multiple antennas while potentially reducing hardware costs. However, the promised diversity gains of receive AS depend on the assumptions of perfect channel knowledge at the receiver and slowly time-varying fading. By explicitly accounting for practical constraints imposed by the next-generation wireless standards such as training, packetization and antenna switching time, we propose a single receive AS method for time-varying fading channels. The method exploits the low training overhead and accuracy possible from the use of discrete prolate spheroidal (DPS) sequences based reduced rank subspace projection techniques. It only requires knowledge of the Doppler bandwidth, and does not require detailed correlation knowledge. Closed-form expressions for the channel prediction and estimation error as well as symbol error probability (SEP) of M-ary phase-shift keying (MPSK) for symbol-by-symbol receive AS are also derived. It is shown that the proposed AS scheme, after accounting for the practical limitations mentioned above, outperforms the ideal conventional single-input single-output (SISO) system with perfect CSI and no AS at the receiver and AS with conventional estimation based on complex exponential basis functions.

Continuum theory of edge states of topological insulators: variational principle and boundary conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

Cumulus clouds and convective boundary layers: a tropical perspective on two turbulent shear flows

This paper is a review prepared for the second Marseille Colloquium on the mechanics of turbulence, held in 2011, 50 years after the first. The review covers recent developments in our understanding of the large-scale dynamics of cumulus cloud flows and of the atmospheric boundary layer in the low-wind convective regime that is often encountered in the tropics. It has recently been shown that a variety of cumulus cloud forms and life cycles can be experimentally realized in the laboratory, with the transient diabatic plume taken as the flow model for a cumulus cloud. The plume is subjected to diabatic heating scaled to be dynamically similar to heat release from phase changes in clouds. The experiments are complemented by exact numerical solutions of the Navier-Stokes-Boussinesq equations for plumes with scaled off-source heating. The results show that the Taylor entrainment coefficient first increases with heating, reaches a positive maximum and then drops rapidly to zero or even negative values. This reduction in entrainment is a consequence of structural changes in the flow, smoothing out the convoluted boundaries in the non-diabatic plume, including the tongues engulfing the ambient flow. This is accompanied by a greater degree of mixedness in the core flow because of lower dilution by the ambient fluid. The cloud forms generated depend strongly on the history of the diabatic heating profile in the vertical direction. The striking effects of heating on the flow are attributable to the operation of the baroclinic torque due to the temperature field. The mean baroclinic torque is shown to peak around a quasi-cylindrical sheet situated midway between the axis of the flow and the edges. This torque is shear-enhancing and folds down the engulfment tongues. The increase in mixedness can be traced to an explosive growth in the enstrophy, triggered by a strong fluctuating baroclinic torque that acts as a source, especially at the higher wave numbers, thus enhancing the mixedness. In convective boundary layers field measurements show that, under conditions prevailing in the tropics, the eddy fluxes of momentum and energy do not follow the Monin-Obukhov similarity. Instead, the eddy momentum flux is found to be linear in the wind speed at low winds; and the eddy heat flux is, to a first approximation, governed by free convection laws, with wind acting as a small perturbation on a regime of free convection. A new boundary layer code, based on heat flux scaling rather than wall-stress scaling, shows promising improvements in predictive skills of a general circulation model.

A numerical approach to determine the sufficiency of given boundary data sets for uniquely estimating interior elastic properties

We consider an inverse elasticity problem in which forces and displacements are known on the boundary and the material property distribution inside the body is to be found. In other words, we need to estimate the distribution of constitutive properties using the finite boundary data sets. Uniqueness of the solution to this problem is proved in the literature only under certain assumptions for a given complete Dirichlet-to-Neumann map. Another complication in the numerical solution of this problem is that the number of boundary data sets needed to establish uniqueness is not known even under the restricted cases where uniqueness is proved theoretically. In this paper, we present a numerical technique that can assess the sufficiency of given boundary data sets by computing the rank of a sensitivity matrix that arises in the Gauss-Newton method used to solve the problem. Numerical experiments are presented to illustrate the method.

A QUADRATIC C degrees INTERIOR PENALTY METHOD FOR LINEAR FOURTH ORDER BOUNDARY VALUE PROBLEMS WITH BOUNDARY CONDITIONS OF THE CAHN-HILLIARD TYPE

We develop a quadratic C degrees interior penalty method for linear fourth order boundary value problems with essential and natural boundary conditions of the Cahn-Hilliard type. Both a priori and a posteriori error estimates are derived. The performance of the method is illustrated by numerical experiments.

Temperature dependent structural and dielectric investigations of PbZr0.5Ti0.5O3 solid solution at the morphotropic phase boundary

PbZr1-xTixO3 ceramics synthesised by low temperature calcination followed by sintering at 1280 degrees C show a Morphotropic Phase Boundary (MPB) for compositions of x=0.44-0.51. The morphotropic phase boundary is wider for samples with smaller grain sizes due to the synthesis route. A Rietveld analysis is performed on a composition of x=0.5 composition to quantify the phase fractions of the tetragonal and monoclinic phases present in the PZT system. Temperature dependent X-ray diffraction and dielectric studies of PbZr0.5Ti0.5O3 composition demonstrated a phase transformation from monoclinic to tetragonal at 270 degrees C followed by a ferroelectric tetragonal to a paraelectric cubic transition at 370 degrees C. Thus, the poling of these ceramics should be performed below 270 degrees C to benefit from the presence of a monoclinic phase. (C) 2012 Elsevier Ltd and Techna Group S.r.l. All rights reserved.