A note on optimal foldover four-level factorials

The foldover is a quick and useful technique in construction of fractional factorial designs, which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the centered L ₂-discrepancy to assess the optimal foldover plans was studied for four-level design. A new analytical expression and a new lower bound of the centered L ₂-discrepancy for fourlevel combined design under a general foldover plan are respectively obtained. A necessary condition for the existence of an optimal foldover plan meeting this lower bound was described. An algorithm for searching the optimal four-level foldover plans is also developed. Illustrative examples are provided, where numerical studies lend further support to our theoretical results. These results may help to provide some powerful and efficient algorithms for searching the optimal four-level foldover plans.     

Nonlinear stability of an axial electric field: Effect of interfacial charge relaxation

We introduce a nonlinear perturbation technique to third order, to study the stability between two cylindrical inviscid fluids, subjected to an axial electric field. The study takes into account the relaxation of electrical charges at the interface between the two fluids. At first order, a linear dispersion relation is obtained. Analytical and numerical results for the overstability and incipient instability conditions are given. For perfect dielectric fluids, the electric field has a stabilizing influence, while for leaky dielectric fluids, the electric field can have either a stabilizing or a destabilizing influence depending on the conductivity and permittivity ratios of the two fluids. At higher order, a nonlinear dispersion relation (nonlinear Ginzburg–Landau equation) is derived, describing the evolution of wave packets of the problem. For leaky dielectric fluids near the marginal state, a nonlinear diffusion equation (nonlinear incipient instability) is obtained. For perfect dielectric fluids, two cubic nonlinear Schrödinger equations are obtained. One of these equations to determine a nonlinear cutoff electric field separating stable and unstable disturbance, whereas the other is used to analyze the stability of the system. It is found that the nonlinear stability criterion depending on the ratio of permittivity, Such effects can only be explained successfully in the nonlinear sense, as the linear analysis unsuccessful to inform about them.     

Nonlinear electrohydrodynamic instability of a finitely conducting cylinder: Effect of interfacial surface charges

The nonlinear electrohydrodynamic stability of cylindrical interface, supporting surface charge, among two conducting fluids is investigated. The two fluids are subjected to a radial electric field. The analysis based on the multiple scale technique. It is shown that the evolution of the amplitude is governed by two partial differential equations. These equations are combined to yield two alternate Schrödinger equations with cubic nonlinearity. One of which calculates the nonlinear cutoff electric field, separating stable and unstable disturbances, while the other is used to analyze the stability of the system. The stability criteria are analytically discussed and numerically confirmed. Numerical calculations resulted in set of graphs to indicate the stability picture of the considered system.     

Non-linear peristaltic transport of a second-order fluid through a porous medium

The present paper investigates phenomena brought about into the classic peristaltic mechanism by inclusion of non-Newtonian effects through a porous space in a channel. The peristaltic motion of a second-order fluid through a porous medium was studied for the case of a planar channel with harmonically undulating extensible walls. The system of the governing nonlinear PDE is solved by using the perturbation method to second-order in dimensionless wavenumber. The analytic solution has been obtained in the form of a stream function from which the axial pressure gradient has been derived. The flow is investigated in a wave frame of reference moving with velocity of the wave. Numerical calculations are carried out for the pressure rise and frictional force. The features of the flow characteristics are analyzed by plotting graphs and discussed in detail.     

Multiplicative linear search for a brownian target motion

This paper investigates a search problem for a brownian target motion on one of n-intersected real lines in which any information of the target position is not available to the searchers all the time. We have n-searchers start searching for the target from the origin that is the intersection point of these lines. Each of the searchers moves continuously along his line in both directions of the starting point. The purpose of this paper is to formulate a search model and find the condition under which the expected value of the first meeting time between one of the searchers and the target is finite. Also, we show the existence of the optimal search plan which minimizes the expected value of the first meeting time and find it.     

Achieving the Reforms Vision: The Effectiveness of a Specialists‐Led Elementary Science Program

This report describes an evaluation project that aimed to assess the potential of two elementary science specialists, as compared to elementary classroom teachers, to realize the reforms vision for science instruction in elementary classrooms. Participant science specialist background, views of elementary science teaching, and planning and assessment practices were compared to those of regular elementary classroom teachers in the specialist district, as well as in a comparable district not employing specialists. Specialists' views and practices were better aligned with those envisioned by current national reform documents in science education. Despite the constraints imposed by the nature of a program evaluation, the present report provides evidence to suggest that students taught by the science specialists (a) were engaged in open‐ended, inquiry‐oriented, science‐based activities of the kind often advocated, but mostly absent, in elementary school, and (b) demonstrated problem solving and higher order and critical thinking skills. This report is the first to provide empirical support for the advocated “effectiveness” of elementary science specialists in achieving the visions espoused by current reform efforts.     

Growth of Fe-doped ZnO nanorods using aerosol-assisted chemical vapour deposition via in situ doping

In situ Fe doping of ZnO nanorods (NRs) was performed using aerosol assisted chemical vapour deposition (AA-CVD) technique. As the aerosol generator is located outside the reactor, AA-CVD provides the flexibility to control doping parameters, such as doping timing, doping duration and a wider choice of dopant precursors. The Fe dopant aerosol was flowed into the reactor during the growth of ZnO NRs to achieve in situ doping. The X-ray diffraction analysis indicates that the Fe dopants were introduced into the ZnO lattice and present mainly in the form of Fe²⁺. This result is supported by the X-ray photoelectron spectroscopy analysis as the doublet separation is 13.6 eV, although there is a shift of Fe_1/2 and Fe_3/2 peaks to a lower binding energy levels. A strong green emission of PL of Fe-doped ZnO NRs shows that the NRs have poor crystal quality attributed to the Fe-induced defects (recombination centres). The poor photocatalytic performance in degrading Rhodamine B solution of Fe-doped ZnO NRs further proves that the Fe-induced defects were recombination centres rather than traps. Lastly, the growth mechanism of in situ Fe doping of ZnO NRs was discussed.     

LINEAR AMPLIFIER VIA THE SQUEEZED COHERENT STATES SUPERPOSITIONS

Much attention is given for the squeezed coherent states (SCS's) superposition. The s-parameterized charactristic function (CF) for the output field with the superposition of SCS's as input field is given. The s-parameterized quasiprobabilty distribution function (QDF) for the output field with superposition of SCS's as input state are investigated. Various moments are calculated by using the s-parameterized CF for that field. The Glauber second-order coherence function is calculated. The quadrature squeezing for the output field are discussed. Some QDF's of the output fields are plotted as functions of the interaction time. Phase properties of the superpostion of SCS's are studied. The s-parameterized phase distributions obtained by integrating the s-parameterized QDF over radial variable are illustrated.     

Erbium in silicon–germanium quantum wells

Strained Si_1−xGe_x/Si quantum wells have been doped with erbium by implantation. A comparison is made with strained Si_1−xGe_x/Si quantum wells and relaxed Si_1−xGe_x, with x between 10% and 25%, doped with erbium during MBE growth. The erbium concentration was between 1×10¹⁸ and 5×10¹⁸ cm⁻³ throughout the active regions. Transmission electron microscopy, X-ray diffraction, and photoluminescence studies indicate that good regrowth can been achieved after full amorphisation by implantation of the strained quantum wells. The erbium luminescence is more intense in the Si_1−xGe_x/Si layers, but erbium-implanted samples containing Si_1−xGe_x exhibit defect luminescence in the region of 0.9–1.0 eV. These defects are also present when Si_1−xGe_x/Si quantum wells are implanted with an amorphising dose of silicon, and then regrown. They are attributed to small germanium-rich platelets, rather than to erbium-related defects. Electroluminescence is presented from a forward biased erbium-implanted Si_0.87Ge_0.13/Si structure at a drive current density of only 1.8 mA/cm².