Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

Analysis of small signal stability margins using genetic optimization

Power system small signal stability analysis aims to explore different small signal stability conditions and controls, namely: (1) exploring the power system security domains and boundaries in the space of power system parameters of interest, including load flow feasibility, saddle node and Hopf bifurcation ones; (2) finding the maximum and minimum damping conditions; and (3) determining control actions to provide and increase small signal stability. These problems are presented in this paper as different modifications of a general optimization to a minimum/maximum, depending on the initial guesses of variables and numerical methods used. In the considered problems, all the extreme points are of interest. Additionally, there are difficulties with finding the derivatives of the objective functions with respect to parameters. Numerical computations of derivatives in traditional optimization procedures are time consuming. In this paper, we propose a new black-box genetic optimization technique for comprehensive small signal stability analysis, which can effectively cope with highly nonlinear objective functions with multiple minima and maxima, and derivatives that can not be expressed analytically. The optimization result can then be used to provide such important information such as system optimal control decision making, assessment of the maximum network's transmission capacity, etc. (C) 1998 Elsevier Science S.A. All rights reserved.

Thermal Cycling Stability of Silica Membranes for Gas Separation

Hydrogen is being seen as an alternative energy carrier to conventional hydrocarbons to reduce greenhouse gas emissions. High efficiency separation technologies to remove hydrogen from the greenhouse gas, carbon dioxide, are therefore in growing demand. Traditional thermodynamic separation systems utilise distillation, absorption and adsorption, but are limited in efficiency at compact scales. Molecular sieve silica (MSS) membranes can perform this separation as they have high permselectivity of hydrogen to carbon dioxide, but their stability under thermal cycling is not well reported. In this work we exposed a standard MSS membrane and a carbonised template MSS (CTMSS) membrane to thermal cycling from 100 to 450°C. The standard MSS and carbonised template CTMSS membranes both showed permselectivity of helium to nitrogen dropping from around 10 to 6 in the first set of cycles, remaining stable until the last test. The permselectivity drop was due to small micropore collapse, which occurred via structure movement during cycling. Simulating single stage membrane separation with a 50:50 molar feed of H2:CO2, H2 exiting the permeate stream would start at 79% and stabilise at 67%. Higher selectivity membranes showed less of a purity drop, indicating the margin at which to design a stable membrane separation unit for CO2 capture.

Hydrothermal Stability of Modified Silica Membranes for Gas Separation

A new class of hybrid molecular sieve silica (MSS) membranes is developed and tested against standard and organic templated membranes. The hybrid membrane is synthesized by the standard sol-gel process, integrating a template (methyltriethoxysilane - MTES) and a C6 surfactant (triethylhexylammonium bromide) into the silica film matrix. After hydro treatment under a relative humidity of 96% for 50h, the hybrid membrane shows no changes in its gas separation capabilities or energy of mobility. The structural characteristics and integrity of the hybrid membrane are retained due to a high concentration of organophilic functional groups and alkoxides observed using 29 Si NMR. In contrast, the structural integrity of the membranes prepared with non-templated films deteriorated during the hydro treatment due to a large percentage of silanol groups (Si-OH) which react with water. The hybrid membranes underwent a decrease in the H2/CO2 selectivity of only 1% whereas for the non-templated membrane a 21% decrease was observed. The transport mechanism of the hybrid membranes is activated as permeation increased with temperature. The activation energy for the permeation of H2 is positive while negative for CO2. The H2 permeation obtained was 3x 10 -8 mol.m -2 .s -1 .Pa -1 and permselectivities for H2/CO2 and H2/N2 varied between 1-7 and 31-34, respectively.

Hydrothermal Stability Analysis of Carbonised Template Molecular Sieve Silica Membranes

For fuel cell CO clean up application, the presence of water with silica membranes greatly reduces their selectivity to CO. We show results of a new functional carbonised template membrane of around 13nm thickness which offered hydrothermal stability with no compromise to the membrane’s H2/CO permselectivity of 16. Lost permeance was also regenerated.

The effects of viscous loading of the human forearm flexors on the stability of coordination

This experiment investigated whether the stability of rhythmic unimanual movements is primarily a function of perceptual/spatial orientation or neuro-mechanical in nature. Eight participants performed rhythmic flexion and extension movements of the left wrist for 30 s at a frequency of 2.25 Hz paced by an auditory metronome. Each participant performed 8 flex-on-the-beat trials and 8 extend-on-the-beat trials in one of two load conditions, loaded and unload. In the loaded condition, a servo-controlled torque motor was used to apply a small viscous load that resisted the flexion phase of the movement only. Both the amplitude and frequency of the movement generated in the loaded and unloaded conditions were statistically equivalent. However, in the loaded condition movements in which participants were required to flex-on-the-beat became less stable (more variable) while extend-on-the-beat movements remained unchanged compared with the unload condition. The small alteration in required muscle force was sufficient to result in reliable changes in movement stability even a situation where the movement kinematics were identical. These findings support the notion that muscular constraints, independent of spatial dependencies, can be sufficiently strong to reliably influence coordination in a simple unimanual task.

Modulational Instability in Periodic Quadratic Nonlinear Materials

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

Comparison of BR and QR Eigenvalue Algorithms for Power System Small Signal Stability Analysis

The BR algorithm is a novel and efficient method to find all eigenvalues of upper Hessenberg matrices and has never been applied to eigenanalysis for power system small signal stability. This paper analyzes differences between the BR and the QR algorithms with performance comparison in terms of CPU time based on stopping criteria and storage requirement. The BR algorithm utilizes accelerating strategies to improve its performance when computing eigenvalues of narrowly banded, nearly tridiagonal upper Hessenberg matrices. These strategies significantly reduce the computation time at a reasonable level of precision. Compared with the QR algorithm, the BR algorithm requires fewer iteration steps and less storage space without depriving of appropriate precision in solving eigenvalue problems of large-scale power systems. Numerical examples demonstrate the efficiency of the BR algorithm in pursuing eigenanalysis tasks of 39-, 68-, 115-, 300-, and 600-bus systems. Experiment results suggest that the BR algorithm is a more efficient algorithm for large-scale power system small signal stability eigenanalysis.

A study of the stability of subcycling algorithms in structural dynamics

Algorithms for explicit integration of structural dynamics problems with multiple time steps (subcycling) are investigated. Only one such algorithm, due to Smolinski and Sleith has proved to be stable in a classical sense. A simplified version of this algorithm that retains its stability is presented. However, as with the original version, it can be shown to sacrifice accuracy to achieve stability. Another algorithm in use is shown to be only statistically stable, in that a probability of stability can be assigned if appropriate time step limits are observed. This probability improves rapidly with the number of degrees of freedom in a finite element model. The stability problems are shown to be a property of the central difference method itself, which is modified to give the subcycling algorithm. A related problem is shown to arise when a constraint equation in time is introduced into a time-continuous space-time finite element model. (C) 1998 Elsevier Science S.A.

Structure determination of the three disulfide bond isomers of alpha-conotoxin GI: A model for the role of disulfide bonds in structural stability

The three possible disulfide bonded isomers of alpha-conotoxin GI have been selectively synthesised and their structures determined by H-1 NMR spectroscopy. alpha-Conotoxin GI derives from the venom of Conus geographus and is a useful neuropharmacological tool as it selectively binds to the nicotinic acetylcholine receptor (nAChR), a ligand-gated ion channel involved in nerve signal transmission. The peptide has the sequence ECCNPACGRHYSC-NH2, and the three disulfide bonded isomers are referred to as GI(2-7;3-13), GI(2-13;3-7) and GI(2-3;7-13). The NMR structure for the native isomer GI(2-7;3-13) is of excellent quality, with a backbone pairwise RMSD of 0.16 Angstrom for a family of 35 structures, and comprises primarily a distorted 3(10),, helix between residues 5 to 11. The two non-native isomers exhibit multiple conformers in solution, with the major populated forms being different in structure both from each other and from the native form. Structure-activity relationships for the native GI(2-7;3-13) as well as the role of the disulfide bonds on folding and stability of the three isomers are examined. It is concluded that the disulfide bonds in alpha-conotoxin GI play a crucial part in determining both the structure and stability of the peptide. A trend for increased conformational heterogeneity was observed in the order of GI(2-7;3-13) < GI(2-13;3-7) < GI(2-3;7-13). It was found that the peptide bond joining Cys2 to Cys3 in GI(2-3;7-13) is predominantly trans, rather than cis as theoretically predicted. These structural data are used to interpret the varying nAChR binding of the non-native forms. A model for the binding of native GI(2-7;3-13) to the mammalian nAChR is proposed, with an alpha-subunit binding face made up of Cys2, Asn4, Pro5, Ala6 and Cys7 and a selectivity face, comprised of Arg9 and His10. These two faces orient the molecule between the alpha and delta subunits of the receptor. The structure of the CCNPAC sequence of the native GI(2-7;3-13) is compared to the structure of the identical sequence from the toxic domain of heat-stable enterotoxins, which forms part of the receptor binding region of the enterotoxins, but which has a different disulfide connectivity. (C) 1998 Academic Press Limited.

Thickness and stability of adsorbed film in cylindrical mesopores

The adsorbed film in small cylindrical mesopores is studied by using MCM-41 samples of uniform cylindrical channels as model systems. It is found that at a given relative pressure, the smaller the pore radius, the thicker the adsorbed film is, as postulated by Broekhoff and De Beer. Thermodynamics analysis established that the stability of the adsorbed film is determined by interface curvature and the potential of interaction between adsorbate and adsorbent. A semiempirical equation is proposed to describe the state of stable adsorbed films in cylindrical mesopores. It is also shown to be useful in calculations of pore size distributions of mesoporous solids.

Theory of multidimensional parametric band-gap simultons

Multidimensional spatiotemporal parametric simultons (simultaneous solitary waves) are possible in a nonlinear chi((2)) medium with a Bragg grating structure, where large effective dispersion occurs near two resonant band gaps for the carrier and second-harmonic field, respectively. The enhanced dispersion allows much reduced interaction lengths, as compared to bulk medium parametric simultons. The nonlinear parametric band-gap medium permits higher-dimensional stationary waves to form. In addition, solitons can occur with lower input powers than conventional nonlinear Schrodinger equation gap solitons. In this paper, the equations for electromagnetic propagation in a grating structure with a parametric nonlinearity are derived from Maxwell's equation using a coupled mode Hamiltonian analysis in one, two, and three spatial dimensions. Simultaneous solitary wave solutions are proved to exist by reducing the equations to the coupled equations describing a nonlinear parametric waveguide, using the effective-mass approximation (EMA). Exact one-dimensional numerical solutions in agreement with the EMA solutions are also given. Direct numerical simulations show that the solutions have similar types of stability properties to the bulk case, providing the carrier waves are tuned to the two Bragg resonances, and the pulses have a width in frequency space less than the band gap. In summary, these equations describe a physically accessible localized nonlinear wave that is stable in up to 3 + 1 dimensions. Possible applications include photonic logic and switching devices. [S1063-651X(98)06109-1].