ADC Static Characterization Using Nonlinear Ramp Signal

Static characteristics of an analog-to-digital converter (ADC) can be directly determined from the histogram-based quasi-static approach by measuring the ADC output when excited by an ideal ramp/triangular signal of sufficiently low frequency. This approach requires only a fraction of time compared to the conventional dc voltage test, is straightforward, is easy to implement, and, in principle, is an accepted method as per the revised IEEE 1057. However, the only drawback is that ramp signal sources are not ideal. Thus, the nonlinearity present in the ramp signal gets superimposed on the measured ADC characteristics, which renders them, as such, unusable. In recent years, some solutions have been proposed to alleviate this problem by devising means to eliminate the contribution of signal source nonlinearity. Alternatively, a straightforward step would be to get rid of the ramp signal nonlinearity before it is applied to the ADC. Driven by this logic, this paper describes a simple method about using a nonlinear ramp signal, but yet causing little influence on the measured ADC static characteristics. Such a thing is possible because even in a nonideal ramp, there exist regions or segments that are nearly linear. Therefore, the task, essentially, is to identify these near-linear regions in a given source and employ them to test the ADC, with a suitable amplitude to match the ADC full-scale voltage range. Implementation of this method reveals that a significant reduction in the influence of source nonlinearity can be achieved. Simulation and experimental results on 8- and 10-bit ADCs are presented to demonstrate its applicability.

Data rectification and detection of trend shifts in jet engine path measurements using median filters and fuzzy logic

Filtering methods are explored for removing noise from data while preserving sharp edges that many indicate a trend shift in gas turbine measurements. Linear filters are found to be have problems with removing noise while preserving features in the signal. The nonlinear hybrid median filter is found to accurately reproduce the root signal from noisy data. Simulated faulty data and fault-free gas path measurement data are passed through median filters and health residuals for the data set are created. The health residual is a scalar norm of the gas path measurement deltas and is used to partition the faulty engine from the healthy engine using fuzzy sets. The fuzzy detection system is developed and tested with noisy data and with filtered data. It is found from tests with simulated fault-free and faulty data that fuzzy trend shift detection based on filtered data is very accurate with no false alarms and negligible missed alarms.

An Optimal Fuzzy Logic Controller tuned with Artificial Immune System

In this paper, a method for the tuning the membership functions of a Mamdani type Fuzzy Logic Controller (FLC) using the Clonal Selection Algorithm(CSA) a model of the Artificial Immune System(AIS) paradigm is examined. FLC's are designed for two problems, firstly the linear cart centering problem and secondly the highly nonlinear inverted pendulum problem. The FLC tuned by AIS is compared with FLC tuned by GA. In order to check the robustness of the designed PLC's white noise was added to the system, further, the masses of the cart and the length and mass of the pendulum are changed. The PLC's were also tested in the presence of faulty rules. Finally, Kruskal Wallis test was performed to compare the performance of the GA and AIS. An insight into the algorithms are also given by studying the effect of the important parameters of GA and AIS.

Nonlinear Enzyme Kinetics Can Lead to High Metabolic Flux Control Coefficients: Implications for the Evolution of Dominance

In a classic study, Kacser & Burns (1981, Genetics 97, 639-666) demonstrated that given certain plausible assumptions, the flux in a metabolic pathway was more or less indifferent to the activity of any of the enzymes in the pathway taken singly. It was inferred from this that the observed dominance of most wild-type alleles with respect to loss-of-function mutations did not require an adaptive, meaning selectionist, explanation. Cornish-Bowden (1987, J. theor. Biol. 125, 333-338) showed that the Kacser-Burns inference was not valid when substrate concentrations were large relative to the relevant Michaelis constants. We find that in a randomly constructed functional pathway, even when substrate levels are small, one can expect high values of control coefficients for metabolic flux in the presence of significant nonlinearities as exemplified by enzymes with Hill coefficients ranging from two to six, or by the existence of oscillatory loops. Under these conditions the flux can be quite sensitive to changes in enzyme activity as might be caused by inactivating one of the two alleles in a diploid. Therefore, the phenomenon of dominance cannot be a trivial ''default'' consequence of physiology but must be intimately linked to the manner in which metabolic networks have been moulded by natural selection.

Einstein Relation in n-Channel Inversion Layers of Nonlinear Optical, Optoelectronic and Related Materials: Simplified Theory, Relative Comparison and Suggestion for an Experimental Determination

In this paper, we study the Einstein relation for the diffusivity to mobility ratio (DMR) in n-channel inversion layers of non-linear optical materials on the basis of a newly formulated electron dispersion relation by considering their special properties within the frame work of k.p formalism. The results for the n-channel inversion layers of III-V, ternary and quaternary materials form a special case of our generalized analysis. The DMR for n-channel inversion layers of II-VI, IV-VI and stressed materials has been investigated by formulating the respective 2D electron dispersion laws. It has been found, taking n-channel inversion layers of CdGeAs2, Cd(3)AS(2), InAs, InSb, Hg1-xCdxTe, In1-xGaxAsyP1-y lattice matched to InP, CdS, PbTe, PbSnTe, Pb1-xSnxSe and stressed InSb as examples, that the DMR increases with the increasing surface electric field with different numerical values and the nature of the variations are totally band structure dependent. The well-known expression of the DMR for wide gap materials has been obtained as a special case under certain limiting conditions and this compatibility is an indirect test for our generalized formalism. Besides, an experimental method of determining the 2D DMR for n-channel inversion layers having arbitrary dispersion laws has been suggested.

Field imperfection induced axial secular frequency shifts in nonlinear ion traps

This article develops a simple analytical expression that relates ion axial secular frequency to field aberration in ion trap mass spectrometers. Hexapole and octopole aberrations have been considered in the present computations. The equation of motion of the ions in a pseudopotential well with these superpositions has the form of a Duffing-like equation and a perturbation method has been used to obtain the expression for ion secular frequency as a function of field imperfections. The expression indicates that the frequency shift is sensitive to the sign of the octopole superposition and insensitive to the sign of the hexapole superposition. Further, for weak multipole superposition of the same magnitude, octopole superposition causes a larger frequency shift in comparison to hexapole superposition.

Fuzzy Logic-Based Approaches in Water Resource System Modelling

Recent research in modelling uncertainty in water resource systems has highlighted the use of fuzzy logic-based approaches. A number of research contributions exist in the literature that deal with uncertainty in water resource systems including fuzziness, subjectivity, imprecision and lack of adequate data. This chapter presents a broad overview of the fuzzy logic-based approaches adopted in addressing uncertainty in water resource systems modelling. Applications of fuzzy rule-based systems and fuzzy optimisation are then discussed. Perspectives on the scope for further research are presented.

A probabilistic constrained nonlinear optimization framework to optimize RED parameters

The random early detection (RED) technique has seen a lot of research over the years. However, the functional relationship between RED performance and its parameters viz,, queue weight (omega(q)), marking probability (max(p)), minimum threshold (min(th)) and maximum threshold (max(th)) is not analytically availa ble. In this paper, we formulate a probabilistic constrained optimization problem by assuming a nonlinear relationship between the RED average queue length and its parameters. This problem involves all the RED parameters as the variables of the optimization problem. We use the barrier and the penalty function approaches for its Solution. However (as above), the exact functional relationship between the barrier and penalty objective functions and the optimization variable is not known, but noisy samples of these are available for different parameter values. Thus, for obtaining the gradient and Hessian of the objective, we use certain recently developed simultaneous perturbation stochastic approximation (SPSA) based estimates of these. We propose two four-timescale stochastic approximation algorithms based oil certain modified second-order SPSA updates for finding the optimum RED parameters. We present the results of detailed simulation experiments conducted over different network topologies and network/traffic conditions/settings, comparing the performance of Our algorithms with variants of RED and a few other well known adaptive queue management (AQM) techniques discussed in the literature.

In search of inorganic nonlinear optical materials for second harmonic generation

In a search for inorganic oxide materials showing second-order nonlinear optical (NLO) susceptibility, we investigated several berates, silicates, and a phosphate containing trans-connected MO6, octahedral chains or MO5 square pyramids, where, M = d(0): Ti(IV), Nb(V), or Ta(V), Our investigations identified two new NLO structures: batisite, Na2Ba(TiO)(2)Si4O12, containing trans-connected TiO5 octahedral chains, and fresnoite, Ba2TiOSi2O7, containing square-pyramidal TiO5. Investigation of two other materials containing square-pyramidal TiO5 viz,, Cs2TiOP2O7 and Na4Ti2Si8O22. 4H(2)O, revealed that isolated TiO5, square pyramids alone do not cause a second harmonic generation (SHG) response; rather, the orientation of TiO5 units to produce -Ti-O-Ti-O- chains with alternating long and short Ti-O distances in the fresnoite structure is most likely the origin of a strong SHG response in fresnoite,

Energy-momentum conserving algorithm for nonlinear transient analysis within the framework of hybrid elements

This work deals with the formulation and implementation of an energy-momentum conserving algorithm for conducting the nonlinear transient analysis of structures, within the framework of stress-based hybrid elements. Hybrid elements, which are based on a two-field variational formulation, are much less susceptible to locking than conventional displacement-based elements within the static framework. We show that this advantage carries over to the transient case, so that not only are the solutions obtained more accurate, but they are obtained in fewer iterations. We demonstrate the efficacy of the algorithm on a wide range of problems such as ones involving dynamic buckling, complicated three-dimensional motions, et cetera.

Influence of non-stoichiometric defects on nonlinear absorption and refraction in Nd:Zn co-doped lithium niobate

Nonlinear absorption and refraction phenomena in stoichiometric lithium niobate (SLN) pure and co-doped with Zn and Nd, and congruent lithium niobate (CLN) were investigated using Z-scan technique. Femtosecond laser pulses from Ti:Sapphire laser (800 nm, 110 fs pulse width and 1 kHz repetition rate) were utilized for the experiment. The process responsible for nonlinear behavior of the samples was identified to be three photon absorption (3PA). This is in agreement with the band gap energies of the samples obtained from the linear absorption cut off and the slope of the plot of Ln(1 − TOA) vs. Ln(I0) using Sutherland’s theory (s = 2.1, for 3PA). The nonlinear refractive index (n2) of Zn doped samples was found to be lower than that of pure samples. Our experiments show that there exists a correlation between the nonlinear properties and the stoichiometry of the samples. The values of n2 fall into the same range as those obtained for the materials of similar band gap.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

A study of placement algorithms through trial interchange of logic modules

Based on trial interchanges, this paper develops three algorithms for the solution of the placement problem of logic modules in a circuit. A significant decrease in the computation time of such placement algorithms can be achieved by restricting the trial interchanges to only a subset of all the modules in a circuit. The three algorithms are simulated on a DEC 1090 system in Pascal and the performance of these algorithms in terms of total wirelength and computation time is compared with the results obtained by Steinberg, for the 34-module backboard wiring problem. Performance analysis of the first two algorithms reveals that algorithms based on pairwise trial interchanges (2 interchanges) achieve a desired placement faster than the algorithms based on trial N interchanges. The first two algorithms do not perform better than Steinberg's algorithm1, whereas the third algorithm based on trial pairwise interchange among unconnected pairs of modules (UPM) and connected pairs of modules (CPM) performs better than Steinberg's algorithm, both in terms of total wirelength (TWL) and computation time.