Extrinsic Analog Synthesis using Piecewise Linear Current-Mode Circuits

A methodology is presented for the synthesis of analog circuits using piecewise linear (PWL) approximations. The function to be synthesized is divided into PWL segments such that each segment can be realized using elementary MOS current-mode programmable-gain circuits. A number of these elementary current-mode circuits when connected in parallel, it is possible to realize piecewise linear approximation of any arbitrary analog function with in the allowed approximation error bounds. Simulation results show a close agreement between the desired function and the synthesized output. The number of PWL segments used for approximation and hence the circuit area is determined by the required accuracy and the smoothness of the resulting function.

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.

Laser damage threshold studies on urea L-malic acid: A nonlinear optical crystal

A detailed study of surface laser damage performed on a nonlinear optical crystal, urea L-malic acid, using 7 ns laser pulses at 10 Hz repetition rate from a Q-switched Nd:YAG laser at wavelengths of 532 and 1064 nm is reported. The single shot and multiple shot surface laser damage threshold values are determined to be 26.64±0.19 and 20.60±0.36 GW cm−2 at 1064 nm and 18.44±0.31 and 7.52±0.22 GW cm−2 at 532 nm laser radiation, respectively. The laser damage anisotropy is consistent with the Vickers mechanical hardness measurement performed along three crystallographic directions. The Knoop polar plot also reflects the damage morphology. Our investigation reveals a direct correlation between the laser damage profile and hardness anisotropy. Thermal breakdown of the crystal is identified as the possible mechanism of laser induced surface damage.

Nonlinear dielectric behavior in three-component ferroelectric superlattices

Three-component ferroelectric superlattices consisting of alternating layers of SrTiO3, BaTiO3, and CaTiO3 (SBC) with variable interlayer thickness were fabricated on Pt(111)/TiO2/SiO2/Si (100) substrates by pulsed laser deposition. The presence of satellite reflections in x-ray-diffraction analysis and a periodic concentration of Sr, Ba, and Ca throughout the film in depth profile of secondary ion mass spectrometry analysis confirm the fabrication of superlattice structures. The Pr (remnant polarization) and Ps (saturation polarization) of SBC superlattice with 16.4-nm individual layer thickness (SBC16.4) were found to be around 4.96 and 34 μC/cm2, respectively. The dependence of polarization on individual layer thickness and lattice strain were studied in order to investigate the size dependence of the dielectric properties. The dielectric constant of these superlattices was found to be much higher than the individual component layers present in the superlattice configuration. The relatively higher tunability ( ∼ 55%) obtained around 300 K indicates that the superlattice is a potential electrically tunable material for microwave applications at room temperature. The enhanced dielectric properties were thus discussed in terms of the interfacial strain driven polar region due to high lattice mismatch and electrostatic coupling due to polarization mismatch between individual layers.

The R-x, R2-x Planes; Some New Ideas for the Study of Nonlinear Systems

Use of some new planes such as the R-x, R2-x (where R represents in the n-dimensional phase space, the radius vector from the origin to any point on the trajectory described by the system) is suggested for analysis of nonlinear systems of any kind. The stability conditions in these planes are given. For easy understanding of the method, the transformation from the phase plane to the R-x, R2-x planes is brought out for second-order systems. In general, while these planes serve as useful as the phase plane, they have proved to be simpler in determining quickly the general behavior of certain classes of second-order nonlinear systems. A chart and a simple formula are suggested to evaluate time easily from the R-x and R2-x trajectories, respectively. A means of solving higher-order nonlinear systems is also illustrated. Finally, a comparative study of the trajectories near singular points on the phase plane and on the new planes is made.

The x¿n-x Plane for Analysis of Certain Second-Order Nonlinear Systems

Analysis of certain second-order nonlinear systems, not easily amenable to the phase-plane methods, and described by either of the following differential equations xÿn-2ÿ+ f(x)xÿ2n+g(x)xÿn+h(x)=0 ÿ+f(x)xÿn+h(x)=0 n≫0 can be effected easily by drawing the entire portrait of trajectories on a new plane; that is, on one of the xÿnÿx planes. Simple equations are given to evaluate time from a trajectory on any of these n planes. Poincaré's fundamental phase plane xÿÿx is conceived of as the simplest case of the general xÿnÿx plane.

Techniques for Analysis of Certain Nonlinear Systems

This paper suggests the use of simple transformations like ÿ=kx, kx2 for second-order nonlinear differential equations to effect rapid plotting of the phase-plane trajectories. The method is particularly helpful in determining quickly the trajectory slopes along simple curves in any desired region of the phase plane. New planes such as the tÿ-x, tÿ2-x are considered for the study of some groups of nonlinear time-varying systems. Suggestions for solving certain higher-order nonlinear systems are also made.

Novel nonlinear opticalphenomenain nematic liquid crystals

In normal materials, the nonlinear optical effects arise from nonlinearities in the polarisabilities of the constituent atoms or molecules. On the other hand the nonlinear optical effects in liquid crystals arise from totally different processes. Also they occur at relatively low laser intensities. In a laser field a liquid crystal exhibits many novel and interesting nonlinear optical effects. In addition we also find laser field induced effects that are peculiar to liquid crystals, like structural transformations, orientational transitions, modulated structures and phase transitions, to name a few. Here we dwell upon a few of these interesting and important nonlinear optical phenomena that exist in nematic liquid crystals.

Smooth DMS-FEM: A new approach to solving nearly incompressible nonlinear elasto-static problems

The DMS-FEM, which enables functional approximations with C(1) or still higher inter-element continuity within an FEM-based meshing of the domain, has recently been proposed by Sunilkumar and Roy [39,40]. Through numerical explorations on linear elasto-static problems, the method was found to have conspicuously superior convergence characteristics as well as higher numerical stability against locking. These observations motivate the present study, which aims at extending and exploring the DMS-FEM to (geometrically) nonlinear elasto-static problems of interest in solid mechanics and assessing its numerical performance vis-a-vis the FEM. In particular, the DMS-FEM is shown to vastly outperform the FEM (presently implemented through the commercial software ANSYS (R)) as the former requires fewer linearization and load steps to achieve convergence. In addition, in the context of nearly incompressible nonlinear systems prone to volumetric locking and with no special numerical artefacts (e.g. stabilized or mixed weak forms) employed to arrest locking, the DMS-FEM is shown to approach the incompressibility limit much more closely and with significantly fewer iterations than the FEM. The numerical findings are suggestive of the important role that higher order (uniform) continuity of the approximated field variables play in overcoming volumetric locking and the great promise that the method holds for a range of other numerically ill-conditioned problems of interest in computational structural mechanics. (C) 2011 Elsevier Ltd. All rights reserved.