The stability of a revolving non-newtonian liquid in the presence of an axial pressure gradient

Summary The effect of cross-viscosity on the stability in fluids has been investigated. It is found that this effect destabilizes the flow of an incompressible non-newtonian liquid between coaxial rotating cylinders when an axial pressure gradient is applied.     

Free vibration of rectangular plates of arbitrary thickness with one or more edges clamped

Frequencies of free vibration of rectangular plates of arbitrary thickness, with different support conditions, are calculated by using the Method of Initial Functions (MIF), proposed by Vlasov. Sixth and fourth order MIF theories are used for the solution. Numerical results are presented for three square plates for three thickness ratios. The support conditions considered are (i) three sides simply supported and one side clamped, (ii) two opposite sides simply supported and the other two sides clamped and (iii) all sides clamped. It is found that the results produced by the MIF method are in fair agreement with those obtained by using other methods. The classical theory gives overestimates of the frequencies and the departures from the MIF results increase for higher modes and larger thickness ratios.     

Cooperative effects in optical double resonance

A theory of optical double resonance which takes into account the cooperative interactions among atoms is formulated. The analytical result for the double resonance spectra in the conventional situation when the probe field is weak, is given. The changes in the nature of the spectra as one sweeps from cooperative to single atom branch are discussed. The cooperative interaction is shown to reduce considerably the asymmetry of the Autler-Towne's doublet.     

Global perspectives for secondary reference materials for analysis of food and related biological samples

Primary, secondary and tertiary reference materials (RM) play an important role in quality controls of analytical measurements. Logistics of preparation and proper use of primary and secondary RMs are presented. Tertiary (i.e. in-house) control materials are useful as substitutes in the absence of recognized primary or secondary RMs. The lack of interdisciplinary interaction during development of RMs (e.g. in specific areas such as foods), has an important impact on limiting the usefulness of certain types of RMs. The abundance of RMs in some countries and regions appears to have little effect on the existing paucity in RMs in other regions, and the underlying causes are outlined. The ability of a laboratory to produce good quality in-house RMs traceable to recognized primary or secondary RMs is a direct measure of its quest for reliable analytical data. Therefore many laboratories should be encouraged to engage in secondary and tertiary RM activities designed to answer specific measurement problems. In this context, assistance (e.g. practical training opportunities) in identifying simple methods of analyses for their efficacy in determining specific analytes is a source of help that can be extended to countries experiencing limitations in laboratory instrumentation.     

Ambiguous chance constrained problems and robust optimization

In this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We focus primarily on the special case where the uncertainty set of the distributions is of the form where ρ_p denotes the Prohorov metric. The ambiguous chance constrained problem is approximated by a robust sampled problem where each constraint is a robust constraint centered at a sample drawn according to the central measure The main contribution of this paper is to show that the robust sampled problem is a good approximation for the ambiguous chance constrained problem with a high probability. This result is established using the Strassen-Dudley Representation Theorem that states that when the distributions of two random variables are close in the Prohorov metric one can construct a coupling of the random variables such that the samples are close with a high probability. We also show that the robust sampled problem can be solved efficiently both in theory and in practice. Research partially supported by NSF grant CCR-00-09972. Research partially supported by NSF grants CCR-00-09972, DMS-01-04282, and ONR grant N000140310514.     

Order Parameter and Refractive Index of Cholesteryl Linoleate

Refractive indices of cholesteryl linoleate are determined at different temperatures and order parameters have been calculated in smectic and cholesteric phases.     

Rearrangement of Rare Earth Defects Under Domain Inversion in LiNbO3

Using high resolution excitation-emission spectroscopy we investigated the changes occurring in the optical transition of Er^3? ions in LiNbO₃ during inversion of the ferroelectric axis. In stoichiometric LiNbO₃ we find that a drastic reconfiguration among the different defect sites takes places favoring those centers which have already been dominant in the as-grown sample. The reconfiguration is attributed to changes in the arrangement of the local charge compensators. Furthermore, we find a small shift of the emission transition energy, which is consistent with an increase of the intrinsic electric field. These findings make the Er^3? ions very suitable probes for 3D imaging of domain structures and for in-situ studies of the dynamics of the domain inversion processes and the defect/domain wall interaction.     

Nonlinear dynamical modelling of chaotic electrostatic ion cyclotron oscillations by jerk equations

Plasma being a nonlinear and complex system, is capable of sustaining a wide spectrum of waves, oscillations and instabilities. These fluctuations interact nonlinearly amongst themselves and also with particles: electrons/ions and thus lead to nonlinear wave-wave or wave-particle interaction. In the presence of coherent waves the particles are accelerated whereas irregular oscillations can give rise to particle heating which is also called stochastic heating. Particle orbits are known to be randomized by the wave fields such that their motion can also become stochastic. For fusion to be sustained one needs a very high temperature plasma for an extended duration. It quite common to deploy external waves like electron cyclotron waves or ion cyclotron waves for plasma heating and current drive. These external waves also work only in certain regimes. Conventional plasma techniques have been able to answer several of the observations of the above processes related to heating transport etc, but nonlinear dynamics as a tool has helped in comprehending the plasma oscillations better. We have for the first time obtained a Third Order nonlinear ordinary differential equation (TONLODE) also known as jerk equation to describe the electrostatic ion cyclotron plasma oscillations in a magnetic field. The interesting feature of this equation is that it does not require an external forcing term to obtain chaotic behaviour.     

An [FeIII34] Molecular Metal Oxide

The dissolution of anhydrous iron bromide in a mixture of pyridine and acetonitrile, in the presence of an organic amine, results in the formation of an [Fe₃₄] metal oxide molecule, structurally characterised by alternate layers of tetrahedral and octahedral Fe^III ions connected by oxide and hydroxide ions. The outer shell of the complex is capped by a combination of pyridine molecules and bromide ions. Magnetic data, measured at temperatures as low as 0.4 K and fields up to 35 T, reveal competing antiferromagnetic exchange interactions; DFT calculations showing that the magnitudes of the coupling constants are highly dependent on both the Fe‐O‐Fe angles and Fe?O distances. The simplicity of the synthetic methodology, and the structural similarity between [Fe₃₄], bulk iron oxides, previous Fe^III–oxo cages, and polyoxometalates (POMs), hints that much larger molecular Fe^III oxides can be made.     

Magnetocaloric effect in high-energy ball-milled Gd5Si2Ge2 and Gd5Si2Ge2/Fe nanopowders

Evolution of structure and magnetocaloric properties in ball-milled Gd₅Si₂Ge₂ and Gd₅Si₂Ge₂/0.1 wt% Fe nanostructured powders were investigated. The high-energy ball-milled powders were composed of very fine grains (70–80 nm). Magnetization decreased with milling time due to decrease in the grain size and randomization of the magnetic moments at the surface. The magnetic entropy change (ΔS_M) was calculated from the isothermal magnetization curves and a maximum value of 0.45 J/kg K was obtained for 32 h milled Gd₅Si₂Ge₂ alloy powder for a magnetic field change of 2 T while it was still low in Fe-contained alloy powders. The thermo-magnetic measurements revealed that the milled powders display distribution of magnetic transitions, which is desirable for practical magnetic refrigerant to cover a wide temperature span.