Application of Krein’s theorem and bifurcation theory for stability analysis of a bladed rotor

This paper considers the stability and eigenvalue analyses for a bladed rotor which goes under cylindrical and conical whirling. The model consists of a group of flexible blades which are modeled by beams and rigid disk on the elastic bearings. The model is a Hamiltonian system which is perturbed by small dissipative forces. Krein’s theorem reveals that the forward whirling mode and the blade collective motion may cause instability when their frequencies cut themselves in the Campbell diagram. An unstable interaction between the blades and the conical whirling is discovered. The eigenmode and eigenvalue evolutions are determined on the stability boundary. The bifurcation analysis is performed by applying multiple scales method around the stability boundary. It is shown that the damping distribution between the blades and the bearings may shift the unstable mode.     

Stability and Hamiltonian Hopf bifurcation for a nonlinear symmetric bladed rotor

The modal interaction which leads to Hamiltonian Hopf bifurcation is studied for a nonlinear rotating bladed-disk system. The model, which is discussed in the paper, is a Jeffcott rotor carrying a number of planar blades which bend in the plane of the motion. The rigid rotating disk is supported on nonlinear bearings. It is supposed that this dynamical system is a Hamiltonian system which is perturbed by small dissipative and nonlinear forces. Krein’s theorem is employed for obtaining a stability criterion. The nonlinear eigenvalue equations on the stability boundary are turned into ordinary differential equations (ODEs) by differentiating them over the rotating speed. By solving these ODEs, the eigenmodes and the eigenvalues on the stability boundary are obtained. The bifurcation analysis is performed by applying multiple scales method around the boundary. The rotor nonlinear behavior and damping effects are studied for different conditions on the rotating speed and nonlinearity type by the bifurcation equation. It is shown that the damping distribution between the blades and bearings may shift the unstable mode. Depending on the nonlinearity type, subcritical and supercritical Hopf bifurcation are possible.     

In vitro selection and characterization of deoxyribonucleic acid aptamers for digoxin

The low therapeutic index of digoxin necessitates careful monitoring of its serum levels. Most of digoxin immunoassays suffer from interferences with digoxin-like immunoreactive substances. Since aptamers have been shown to be highly specific for their targets, the aim of this study was to develop DNA aptamers for this widely used cardiac glycoside. Digoxin was coated onto the surface of streptavidin magnetic beads. DNA aptamers against digoxin were designed using Systematic Evolution of Ligands by Exponential enrichment method (SELEX) by 11 iterative rounds of incubation of digoxin-coated streptavidin magnetic beads with synthetic DNA library, DNA elution, electrophoresis and PCR amplification. The PCR product was cloned and sequenced. Binding affinity was determined using digoxin–BSA conjugate, coated onto ELISA plate. Inhibitory effect of anti-digoxin aptamer was conducted using isolated guinea-pig atrium. Three aptamers (D1, D2 and D3) were identified. Binding studies of fluorescein-labeled truncated (without primer binding region) D1 and D2 and full length D1 anti-digoxin aptamers were performed and their corresponding dissociation constants values were 8.2 × 10⁻⁹, 44.0 × 10⁻⁹ and 17.8 × 10⁻⁹ M, respectively. This is comparable to what other workers have obtained for interaction of monoclonal antibodies raised against digoxin. There was little difference in binding affinity between full length and truncated anti-digoxin D1 aptamer. D1 anti-digoxin aptamer also inhibited the effects of digoxin on the isolated guinea-pig atrium. D1 anti-digoxin aptamer distinguished between digoxin and ouabain in both tissue study and binding experiments. Our finding indicated that D1 anti-digoxin aptamer can selectively bind to digoxin. Further studies might show its suitability for use in digoxin assays and as a therapeutic agent in life-threatening digoxin toxicity.     

Unsteady Couette flow of viscous fluid under a non-uniform magnetic field

The aim of this letter is to construct the analytic solution for unsteady Couette flow in the presence of an arbitrary non-uniform applied magnetic field. The flow is induced by a generalized velocity given to the lower plate. The perturbed eigenfunction expansion method is employed to develop a series solution for small magnetic field.     

Conformal Ricci Collineations of Static Spherically Symmetric Spacetimes

Conformal Ricei collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating eonformal Rieei eollineations is found when the Rieei tensor is non-degenerate, in which ease the number of independent eonformal Rieei eollineations is 15, the maximum number for four-dimensional manifolds. In the degenerate ease it is found that the static spherically symmetric spaeetimes always have an infinite number of eonformal Rieei eollineations. Some examples are provided which admit non-trivial eonformal Rieei eollineations, and perfect fluid source of the matter.     

Field of a Point Source Within Perfectly Conducting Parallel-Plates in a Homogeneous Biisotropic Medium

The spherical wave scattering response by a perfectly conducting open–ended waveguide in a biisotropic medium is obtained. Interestingly, the vector diffraction problem is reduced to the scattering of a single scalar field, this scalar field being the normal component of either a left–handed or a right–handed Beltrami field. Here, we explicitly consider the scattering of the left–handed field component, that of the other scalar field being analogously tractable. The solution is constructed with the aid of the Wiener–Hopf technique.     

An improved Darcian analysis for chemically reacted Maxwell liquid toward convectively heated moving surface with magnetohydrodynamics

Journal of Thermal Analysis and Calorimetry - Heat transportation analysis subjected to porous medium consideration has increased because of industrial and engineering utilization. Typical examples...     

Carter's fourth invariant of the motion

An interpretation of Carter's fourth invariant of the motion is presented and its significance is discussed.     

Simultaneous spectrophotometric determination of nitrite and nitrate by flow injection analysis.

A new catalytic spectrophotometric method is reported for the simultaneous determination of nitrite and nitrate by flow injection analysis, based on the catalytic effect of nitrite on the redox reaction between pyrogallolsulfonephthalein and potassium bromate in acidic media. Nitrate can also be on-line reduced to nitrite with a modified copper-coated cadmium reduction column. The reaction was monitored spectrophotometrically by measuring the decrease in the absorbance of pyrogallolsulfonephthalein at 465 nm. Various analytical parameters such as effects of acidity, reagent concentrations, flow rates, sample sizes, lengths of the reaction coil and temperatures were studied and were optimized. Under the optimized conditions, the calibration graph was linear for 2.4 to 160 ng ml(-1) of nitrite and 4.0 to 100 ng ml(-1) of nitrate. The influences of potential interfering cations and anions for nitrite and nitrate determination were studied. The method is successfully applied for food and water samples. Up to ten samples can be analyzed per hour.     

Modeling Thin Film Multilayer Broad-Band-Pass Filters in Visible Spectrum

Multilayer thin-film structures have been used to model and analyze the performance of broad-band-pass interference optical filters in visible spectrum. Starting from nine-layer configuration comprising quarter-wave layers, the number of layers is increased to make the pass band smooth with steep slopes and square band-pass characteristics. The layer materials are also varied to improve the performance of the filters. Further, matching layers are also introduced with incident medium and the substrate to reduce the magnitude of ripples in the pass band. Shift in the peak wavelength is also investigated as a function of angle of incidence.