Construction of stability multipliers for non-linear feedback systems

This paper is concerned with the analysis of the absolute stability of a non-linear autonomous system which consists of a single non-linearity belonging to a particular class, in an otherwise linear feedback loop. It is motivated from the earlier Popovlike frequency-domain criteria using the ' multiplier ' eoncept and involves the construction of ' stability multipliers' with prescribed phase characteristics. A few computer-based methods by which this problem can be solved are indicated and it is shown that this constitutes a stop-by-step procedure for testing the stability properties of a given system.

An appendix to the paper "approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic"

The theory of Varley and Cumberbatch [l] giving the intensity of discontinuities in the normal derivatives of the dependent variables at a wave front can be deduced from the more general results of Prasad which give the complete history of a disturbance not only at the wave front but also within a short distance behind the wave front. In what follows we omit the index M in Eq. (2.25) of Prasad [2].

Korteweg-De Vries Equation for Non-Linear Ion-Acoustic Waves in a Plasma with Negative Ions

The theoretical analysis, based on the perturbation technique, of ion-acoustic waves in the vicinity of a Korteweg-de Vries (K-dV) equation derived in a plasma with some negative ions has been made. The investigation shows that the negative ions in plasma with isothermal electrons introduced a critical concentration at which the ion-acoustic wave plays an important role of wave-breaking and forming a precursor while the plasma with non-isothermal electrons has no such singular behaviour of the wave. These two distinct features of ion waves lead to an overall different approach of present study of ion-waves. A distinct feature of non-uniform transition from the nonisothermal case to isothermal case has been shown. Few particular plasma models have been chosen to show the characteristics behaviour of the ion-waves existing in different cases

Non-linear vibrations of non-unifo with concentrated masses

Large amplitude oscillations of cantilevered beams of variable cross-section, with concentrated masses along the span, are studied in this paper. The governing non-linear ordinary differential equation is solved by an averaging technique to obtain approximate solutions. Stability boundaries of the response are also investigated.

Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.

Decoupling in non-linear systems with two degrees of freedom

The problem of decoupling a class of non-linear two degrees of freedom systems is studied. The coupled non-linear differential equations of motion of the system are shown to be equivalent to a pair of uncoupled equations. This equivalence is established through transformation techniques involving the transformation of both the dependent and independent variables. The sufficient conditions on the form of the non-linearity, for the case wherein the transformed equations are linear, are presented. Several particular cases of interest are also illustrated.

Non-linear systems with quadratic and cubic damping - an analytical approach

The possible equivalence of second-order non-linear systems having quadratic and cubic damping with third-order linear systems is studied in this paper. It is shown that this equivalence can be established through transformation techniques under certain constraints on the form of the non-linearity of the given system.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

Mean Flow Measurements in Turbulent Boundary Layers along Mildly Curved Surfaces

An experimental investigation of the mean flow characteristics of two-dimensional turbulent boundary layers over surfaces of mild longitudinal curvature is reported. The study covered both convex and concave walls of \d/Rw I « 0.013 (d being the boundary-layer thickness and Rw being the wall radius). It was found that, whereas the region close to the wall was not affected significantly by wall curvature, the outer region was very sensitive to even mild wall curvature. A detailed study of the wake region using present and other available data suggests a systematic effect of b/Rw on the wake structure. The paper also discusses in detail the effect of mild wall curvature on the boundary-layer development with particular emphasis on the difference in behavior of the boundary layer at short and long distances from the leading edge of the curved wall, an aspect which has not received sufficient attention in previous experimental investigations. An attempt has been made to explain this behavior from a consideration of the structure of turbulence in boundary layers over curved surfaces taken into account.

Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

Trajectory sensitivity modification in optimal linear systems

A new procedure for reducing trajectory sensitivity for the optimal linear regulator is described. The design is achieved without increase in the order of optimization and without the feedback of trajectory sensitivity. The procedure is also used in the input signal design problem for linear system identification by interpreting it as increasing trajectory sensitivity with respect to parameters to be estimated.

Use of transverse beam polarization to probe anomalous V V H interactions at a Linear Collider

We investigate use of transverse beam polarization in probing anomalous coupling of a Higgs boson to a pair of vector bosons, at the International Linear Collider (ILC). We consider the most general form of V V H (V = W/Z) vertex consistent with Lorentz invariance and investigate its effects on the process e(+)e(-) -> f (f) over barH, f being a light fermion. Constructing observables with definite C P and naive time reversal ((T) over tilde) transformation properties, we find that transverse beam polarization helps us to improve on the sensitivity of one part of the anomalous Z Z H Coupling that is odd under C P. Even more importantly it provides the possibility of discriminating from each other, two terms in the general Z Z H vertex, both of which are even under C P and (T) over bar. Use of transversebeam polarization when combined with information from unpolarized and linearly polarized beams therefore, allows one to have completely independent probes of all the different parts of a general ZZH vertex.

Studies on transport phenomena during solidification of an aluminum alloy in the presence of linear electromagnetic stirring

Numerical and experimental studies on transport phenomena during solidification of an aluminum alloy in the presence of linear electromagnetic stirring are performed. The alloy is electromagnetically stirred to produce semisolid slurry in a cylindrical graphite mould placed in the annulus of a linear electromagnetic stirrer. The mould is cooled at the bottom, such that solidification progresses from the bottom to the top of the cylindrical mould. A numerical model is developed for simulating the transport phenomena associated with the solidification process using a set of single-phase governing equations of mass. momentum, energy. and species conservation. The viscosity variation of the slurry, used in the model, is determined experimentally using a rotary viscometer. The set of governing equations is solved using a pressure-based finite volume technique, along with an enthalpy based phase change algorithm. The numerical study involves prediction of temperature, velocity, species and solid fraction distribution in the mould. Corresponding solidification experiments are performed, with time-temperature history recorded at key locations. The microstructures at various temperature measurement locations in the solidified billet are analyzed. The numerical predictions of temperature variations are in good agreement with experiments, and the predicted flow field evolution correlates well with the microstructures observed at various locations.

Thermodynamic characterization of the reversible, two-state unfolding of maltose binding protein, a large two-domain protein

The folding and stability of maltose binding protein (MBP) have been investigated as a function of pH and temperature by intrinsic tryptophan fluorescence, far- and near-UV circular dichroism, and high-sensitivity differential scanning calorimetric measurements. MBP is a monomeric, two-domain protein containing 370 amino acids. The protein is stable in the pH range of 4-10.5 at 25 degrees C. The protein exhibits reversible, two-state, thermal and guanidine hydrochloride-mediated denaturation at neutral pH. The thermostability of MBP is maximal at pH 6, with a Tm of 64.9 degrees C and a deltaHm of 259.7 kcal mol(-1). The linear dependence of deltaHm on Tm was used to estimate a value of deltaCp of 7.9 kcal mol(-1) K(-1) or 21.3 cal (mol of residue)(-1) K(-1). These values are higher than the corresponding deltaCp's for most globular proteins studied to date. However, the extrapolated values of deltaH and deltaS (per mole of residue) at 110 degrees C are similar to those of other globular proteins. These data have been used to show that the temperature at which a protein undergoes cold denaturation depends primarily on the deltaCp (per mol of residue) and that this temperature increases with an increase in deltaCp. The predicted decrease in stability of MBP at low temperatures was experimentally confirmed by carrying out denaturant-mediated unfolding studies at neutral pH at 2 and 28 degrees C.

High pressure clamp for electrical measurements up to 8 GPa and temperature down to 77 K

A compact clamp-type high pressure cell for carrying out electrical conductivity measurements on small solid samples of size 1 mm or less at pressures upto 8 GPa (i.e., 80 kbar) and for use down to 77 K has been designed and fabricated. The pressure generated in the sample region has been calibrated at room temperature against the polymorphic phase transitions of Bismuth and Ytterbium. The pressure relaxation of the clamp at low temperatures has been estimated by monitoring the electrical conductivity behavior of lead. Review of Scientific Instruments is copyrighted by The American Institute of Physics.