Multi-Tone Testing of Linear and Nonlinear Analog Circuits using Polynomial Coefficients

A method of testing for parametric faults of analog circuits based on a polynomial representation of fault-free function of the circuit is presented. The response of the circuit under test (CUT) is estimated as a polynomial in the applied input voltage at relevant frequencies in addition to DC. Classification or Cur is based on a comparison of the estimated polynomial coefficients with those of the fault free circuit. This testing method requires no design for test hardware as might be added to the circuit fly some other methods. The proposed method is illustrated for a benchmark elliptic filter. It is shown to uncover several parametric faults causing deviations as small as 5% from the nominal values.

Drag interaction effects in linear sphere-assemblies

Free-fall terminal velocities of single spheres and of single-row assemblies containing up to six spheres, with line of centres of spheres perpendicular to the direction of motion, have been determined in the particle Reynolds numbers range 0.2-4, and interaction effects obtained in the case of assemblies relative to drag on single isolated spheres, are discussed. The observed decrease in the drag on a sphere of an assembly is explained on the basis of theoretical considerations governing flow phenomena in such systems.

Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

Evaluation of solute-solvent interactions from solvent blue-shifts of n → π* transitions of C=O, C=S, NO2 and N=N groups: hydrogen bond energies of various donor-acceptor systems

Effects of non-polar, polar and proton-donating solvents on the n → π* transitions of C=O, C=S, NO2 and N=N groups have been investigated. The shifts of the absorption maxima in non-polar and polar solvents have been related to the electrostatic interactions between solute and solvent molecules, by employing the theory of McRAE. In solvents which can donate protons the solvent shifts are mainly determined by solute-solvent hydrogen bonding. Isobestic points have been found in the n → π* bonds of ethylenetrithio-carbonate in heptane-alcohol and heptane-chloroform solvent systems, indicating the existence of equilibria between the hydrogen bonded and the free species of the solute. Among the different proton-donating solvents studied water produces the largest blue-shifts. The blue-shifts in alcohols decrease in the order 2,2,2-trifluoroethanol, methanol, ethanol, isopropanol and t-butanol, the blue-shift in trifluoroethanol being nearly equal to that in water. This trend is exactly opposite to that for the self-association of alcohols. It is suggested that electron-withdrawing groups not merely decrease the extent of self-association of alcohols, but also increase the ability to donate hydrogen bonds. The approximate hydrogen-bond energies for several donor-acceptor systems have been estimated. In a series of aliphatio ketones and nitro compounds studied, the blue-shifts and consequently the hydrogen bond energies decrease with the decrease in the electron-withdrawing power of the alkyl groups. It is felt that electron-withdrawing groups render the chromophores better proton acceptors, and the alcohols better donors. A linear relationship between n → π* transition frequency and the infrared frequency of ethylenetrithiocarbonate has been found. It is concluded that stabilization of the electronic ground states of solute molecules by electrostatic and/or hydrogen-bond interactions determines the solvent shifts.

A weighted mean square method of linearization in non-linear oscillations

The paper deals with a linearization technique in non-linear oscillations for systems which are governed by second-order non-linear ordinary differential equations. The method is based on approximation of the non-linear function by a linear function such that the error is least in the weighted mean square sense. The method has been applied to cubic, sine, hyperbolic sine, and odd polynomial types of non-linearities and the results obtained are more accurate than those given by existing linearization methods.

Application of D transforms in the analysis of nonlinear distributed parameter systems

The scope of application of Laplace transforms presently limited to the study of linear partial differential equations, is extended to the nonlinear domain by this study. This has been achieved by modifying the definition of D transforms, put forth recently for the study of classes of nonlinear lumped parameter systems. The appropriate properties of the new D transforms are presented to bring out their applicability in the analysis of nonlinear distributed parameter systems.

Improved Conditions For L2-Stability Of Nonstationary Feedback-Systems

Concerning the L2-stability of feedback systems containing a linear time-varying operator, some of the stringent restrictions imposed on the multiplier as well as the linear part of the system, in the criteria presented earlier, are relaxed.

L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

Time-Domain Criteria For L2-Stability Of Nonstationary Feedback-Systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

Rare earth exchanged (Ce3+, La3+ and RE3+) H-Y zeolites as solid acid catalysts for the synthesis of linear alkyl benzenes

Rare earth exchanged H–Y zeolites were prepared by simple ion exchange methods at 353 K and have been characterized using different physicochemical techniques. A strong peak around 58 ppm in the 27Al{1H} MAS NMR spectra of these zeolites suggests a tetrahedral coordination for the framework aluminium. Small peak at or near 0 ppm is due to hexa-coordinated extra-framework aluminium and a shoulder peak near 30 ppm is a penta-coordinated aluminium species; [Al(OH)4]−. The vapor-phase benzene alkylation with 1-decene and 1-dodecene was investigated with these catalytic systems. Under the reaction conditions of 448 K, benzene/olefin molar ratio of 20 and time on stream 3 h, the most efficient catalyst was CeH–Y which showed more than 70% of olefin conversion with 48.5% 2-phenyldecane and 46.8%, 2-phenyldodecane selectivities with 1-decene and 1-dodecene respectively.

A mathematical programming approach to optimal Markovian switching of Poisson arrival streams to queueing systems

Motivated by certain situations in manufacturing systems and communication networks, we look into the problem of maximizing the profit in a queueing system with linear reward and cost structure and having a choice of selecting the streams of Poisson arrivals according to an independent Markov chain. We view the system as a MMPP/GI/1 queue and seek to maximize the profits by optimally choosing the stationary probabilities of the modulating Markov chain. We consider two formulations of the optimization problem. The first one (which we call the PUT problem) seeks to maximize the profit per unit time whereas the second one considers the maximization of the profit per accepted customer (the PAC problem). In each of these formulations, we explore three separate problems. In the first one, the constraints come from bounding the utilization of an infinite capacity server; in the second one the constraints arise from bounding the mean queue length of the same queue; and in the third one the finite capacity of the buffer reflect as a set of constraints. In the problems bounding the utilization factor of the queue, the solutions are given by essentially linear programs, while the problems with mean queue length constraints are linear programs if the service is exponentially distributed. The problems modeling the finite capacity queue are non-convex programs for which global maxima can be found. There is a rich relationship between the solutions of the PUT and PAC problems. In particular, the PUT solutions always make the server work at a utilization factor that is no less than that of the PAC solutions.

Chemical Aspects of the Synergistic Hypergolic Ignition in Hybrid Systems with N2O4 as Oxidizer

Synergistic hypergolic ignition with nitrogen tetroxide ( N2O4) as oxidizer has been observed in hybrid systems comprising of a mixture of magnesium and Schiff bases as fuels. The ignition delays (IDs) measured using a modified device, have been compared with those of magnesium-Schiff base-WFNA systems under identical conditions. The ID has been found to vary with the nature of the substitution in both the benzene rings. A linear relationship emerges when the ignition delays are plotted against the Hammett substitution constants (σ). The preignition products of the reaction of N2O4 with magnesium and benzylidineaniline have been analysed to be Mg(NO3)2, benzenediazonium salt and benzaldehyde. Based on the preignition products isolated, a probable reaction mechanism has been proposed. The previously proposed preignition mechanism for the Schiff base-magnesium-WFNA system has been further supported from the present ignition delay data.

Non-linear Dynamic Analysis of a Piezoelectrically Actuated Flapping Wing

An energy method is used in order to derive the non-linear equations of motion of a smart flapping wing. Flapping wing is actuated from the root by a PZT unimorph in the piezofan configuration. Dynamic characteristics of the wing, having the same size as dragonfly Aeshna Multicolor, are analyzed using numerical simulations. It is shown that flapping angle variations of the smart flapping wing are similar to the actual dragonfly wing for a specific feasible voltage. An unsteady aerodynamic model based on modified strip theory is used to obtain the aerodynamic forces. It is found that the smart wing generates sufficient lift to support its own weight and carry a small payload. It is therefore a potential candidate for flapping wing of micro air vehicles.

MNDO study of coupled strained hydrocarbons: Additivity of exocyclic C---C bond contraction induced by different ring systems

MNDO geometry optimizations were carried out on a series of symmetrically and unsymmetrically coupled strained ring hydrocarbons, R1-R1 and R1–R2 (R1=methyl, cyclopropyl, 1-bicyclo[1.1.0]butyl, 1-bicyclo[1.1.1]pentyl, prismyl, cubyl, 6-tricyclo [3.1.1.03,6]heptyl, and tetrahedryl groups; R2=methyl and cyclopropyl). The remarkable contraction of the C---C bond connecting the strained rings found experimentally in a few cases was reproduced correctly by the calculations. A linear correlation was found between the bond length shortening and the bond angle widening at the corresponding carbon atoms for all the structures considered. The reduction in C---C bond lengths due to various ring systems is additive. The additivity indicates that inter-ring interactions which effect the central bond length are absent and confirms the common electronic origin of bond contraction in these systems, viz. enhanced s-character in the exocyclic bonds of strained rings.

Position and Feed-Rate Control for Contouring Numerical-Control Systems

Numerical control (NC) for contouring operations requires precise control of position and feed rate for approximating the contour by linear moves of the cutter. A control scheme, for generating linear moves with desired slopes for the cutter, is described. This scheme provides for nine successive linear moves, and may be either expanded or implemented in succession, for approximating a contour.