Determination of Metal Ions by High Performance Liquid Chromatography

The mixture of metal ions [Bi(III), Fe(III), Fe(II), Cu(II), Zn(II), Ni(II), Co(II), Pb(II), Cd(II), Mn(II)] were separated in the bonded-phase strong cation exchange column (Vydac-401 SA) and monitored at 540 nm after a postcolumn reaction with 4-(2-pyridylazo)-resorcinol (PAR). Citrate, tartrate, lactate and α-hydroxyisobutyrate buffer were used as eluent and it has been found that the elution order of some metal ions were changed with different eluents. The detection limits and the calibration curves of metal ions were also studied.     

Generalisation of the Routh-Hurwitz criterion and its applications

A generalisation of the Routh-Hurwitz stability criterion for testing the presence of unstable roots of a polynomial with complex coefficients is presented. Numerical examples are given to illustrate the application of the generalisation.     

A recurrence relation for the square root

The behavior of the sequence x_{n + 1} = x_n(3N − x_n²)/2N is studied for N > 0 and varying real x₀. When 0 < x₀ < (3N)^1/2 the sequence converges quadratically to N^1/2. When x₀ > (5N)^1/2 the sequence oscillates infinitely. There is an increasing sequence β_r, with β₋₁ = (3N)^1/2 which converges to (5N)^1/2 and is such that when β_r < x₀ < β_{r + 1} the sequence {x_n} converges to (−1)^rN^1/2. For x₀ = 0, β₋₁, β₀,… the sequence converges to 0. For x₀ = (5N)^1/2 the sequence oscillates: x_n = (−1)ⁿ(5N)^1/2. The behavior for negative x₀ is obtained by symmetry.     

A unified approach to the theory of double injection in solids with traps uniformly and non-uniformly distributed in the energy band gap

A unified theoretical approach is presented for the double injection current-voltage characteristics of a solid with traps uniformly and non-uniformly distributed in the energy band gap. The current-voltage characteristics for various forms of trap distribution functions have been computed for a typical wide-gap semiconductor, and these are discussed in the light of presently available results.     

Real-time stress evolution during Si1-xGex Heteroepitaxy: Dislocations, islanding, and segregation

We have used sensitive real-time measurements of film stress during Si_1-xGe_x molecular beam epitaxy to examine strain relaxation due to coherent island formation, and to probe the kinetics of Ge surface segregation. We first describe our novel curvature-measurement technique for real-time stress determination. Measurements of the relaxation kinetics during high temperature Si₇₉Ge₂₁ growth on Si (001) are reported in which formation of highly regular arrays of [501]-faceted islands produce 20% stress relaxation. An island shape transition is also observed that reduces the effective stress by up to 50% without dislocations. Nonuniform composition profiles due to Ge surface segregation during growth of planar alloy films are determined with submonolayer thickness resolution from the real-time stress evolution. Up to two monolayers of Ge can segregate to the growth surface.     

Modern methods of improving the range accuracy of CTFM sonars

In a CTFM (continuous transmission frequency modulated) sonar, the error in range measurement is usually dominated by the low resolution of the range coding frequency of the system. Modern real time spectrum analysers using 1024 point DFTs (discrete Fourier transforms) can display the range codes of the sonar at a resolution approximately equal to 0.2%. To produce a range code accurate to half of the resolution, the linearity of the CTFM sweep must, however, be kept as low as 0.01%. This requirement creates several difficulties in the design of the frequency sweep when both non-linearity and stability of the voltage-controlled oscillator (VCO) and of the controlling voltage ramp are to be considered. A practical approach for achieving the above specifications is described. Properties of electronic components and of state of the art devices and the restrictions of their operating conditions are discussed. Illustrations are given for two measuring instruments: an underwater sonar system for quantitative assessment of fish population, and a diagnostic sonar.     

Low-Reynolds-number modelling of flows over a backward-facing step

The complex turbulent flow behind a backward-facing step is modelled using a full Reynolds stress closure. In order to develop a closure model that can resolve the complex near-wall flow in the recirculation region and in the recovery region downstream of the reattachment point, the performance of a low and a high Reynolds number version of the full Reynolds stress closure is examined and compared. Furthermore, the effects of redistribution modelling on the calculated flow is studied by comparing the performance of three redistribution models: one return-to-isotropy model and two with mean-strain effects. The results are grid independent and show that the flow downstream of the step is best described by a low-Reynolds-number model that does not depend on the conventional wall function assumption. However, the skin friction behavior is correctly predicted by the stipulation of a wall function. Of the three redistribution models examined, the return-to-isotropy model gives results that are in excellent agreement with measurements. Finally, the calculated results are adversely affected by refining the redistribution models to include meanstrain effects.     

Arterial stenosis murmurs: an analysis of flow and pressure fields

The flow field distal to an arterial stenosis is simulated by a confined turbulent jet with moderate Reynolds numbers. The wall pressure fluctuations are related to the momentum fluctuations of the jet by the Poisson equation. A Green's function was derived to satisfy the boundary conditions on a cylindrical surface. This allows the solution of the Poisson's equation to include only a volume integral of the fluctuating momentum, weighed by the relative distance between the source and the sensor. The velocity fluctuations on the jet centerline and at the middle of the shear layer were measured using a laser Doppler anemometer. The wall pressure fluctuations were detected simultaneously by an array of nine wall-mounted pressure transducers along the axial direction. Cross correlation performed between the velocity and pressure fluctuations reveals that the pressure fluctuations were mostly imposed by the passage of turbulent eddies with a convective velocity that is a function of the jet exit velocity. The Strouhal number, defined by the frequency of the passing large-scale structure, is a function of the initial conditions only very close to the jet exit. Further downstream, where the effect of the initial conditions is lost, the Strouhal number approaches a constant irrespect of the jet Reynolds number. The contribution of a source near the jet exit to wall pressure fluctuation near the reattachment is rather weak due to the rapidly decaying weighting function in the axial direction. However, for sources located within one nozzle diameter from the sensor, the cross-spectral density function has a high magnitude with maximum coherence where the pressure spectral changes its slope.