Synthesis and Properties of NdMCr2O5 (M = Na, K, Cs) and NdMgCr2O5.5 Chromites

NdMCr₂O₅ (M = Na, K, Cs) and NdMgCr₂O_5.5 are prepared by solid-state reactions between appropriate oxides and carbonates and are shown to have a tetragonal structure. The heat capacity of these chromites, measured from 298.15 to 673 K, exhibits sharp changes attributable to second-order phase transitions. The C _p ⁰(T) data are represented by quadratic best fit equations. The electrical resistivity of the chromites is measured between 303 and 493 K. The results attest to semiconducting behavior of the materials in certain temperature ranges.     

Preparation and Properties of Er- and Yb-Activated TeO2–WO3 Glasses

TeO₂–WO₃ glasses coactivated with Er³⁺ and Yb³⁺ are prepared. The effect of Yb content on the efficiency of Er photoluminescence (PL) in the visible and IR spectral regions is studied. The highest PL efficiency is achieved at an Er : Yb atomic ratio of 1 : 1. The PL lifetime for the Er^{3+ 4} I _13/2 level is determined to be 7–9 ms.     

Modeling and Analysis of a Long Thin Conducting Stripline

A long thin conducting stripline embedded in a dielectric and centered between two large conducting plates, i.e., the stripline environment, is considered. The stripline is modeled as infinitely long, infinitely thin, and perfectly conducting by first considering a stripline of finite length, thickness, and conductivity in a dielectric layer. Starting from Maxwell's equations and assuming that the current on the stripline is a propagating wave in length direction, asymptotic expressions for the fields inside and in the neighbourhood of the stripline are deduced. These expressions are used to model the stripline in the stripline environment, which leads to a boundary-value problem for the electric potential. This problem is solved by two different approaches, leading to integral equations for the current and for an auxiliary function describing the electric potential. A relation between the current and the auxiliary function is deduced, which is used to obtain asymptotic expressions for current and impedance. Results are compared with a numerical solution of the integral equation for the current and with results in literature.     

On energy arguments applied to the hydrodynamic impact force

The hydrodynamic impact problem is investigated within the framework of potential-flow theory. The vertical load acting on the rigid body is derived based on either momentum or energy conservation, and using the concept of added mass together with a homogeneous Dirichlet condition for the potential on the free surface as usually done to model an impact problem. It is demonstrated that the use of this simplified dynamic free-surface condition, instead of the fully nonlinear one, has a direct influence on the computation of the loads. In particular, the equivalence of momentum and energy analysis is in general not recovered. The situation is then highlighted by performing an asymptotic analysis of the two-dimensional blunt-body asymmetric impact problem. The asymptotic solution is given explicitly and validated through comparisons with experimental results. The energy distribution is then studied. It is shown that the contradiction between momentum and energy analysis can be removed, provided that the flux of energy through the jets is taken into account in the energy balance. If the simplified free-surface condition is indeed valid in the far-field, nonlinear terms must be retained near the body, in the spray-root domains. To leading order, the energy distribution during the gravity-free inertia stage does not depend on the blunt-body shape. The general analysis based on momentum or energy conservation suggests that this result also applies for arbitrary body shape as soon as a homogeneous Dirichlet condition can be applied as a dynamical free-surface boundary condition. In this case, and for a constant vertical impact velocity, half the work performed by the body would seem to be transferred to the fluid as kinetic energy within the spray.     

Stability of Equilibria in a Four-dimensional Nonlinear Model of a Hydraulic Servomechanism

Starting from plysical laws a four-dimensional nonlinear model for mecano-hydraulic servomechanisms is deduced. The stability of its equilibria is analysed using a theorem of Lyapunov and Malkin to handle the critical case due to the presence of zero in the spectrum of the matrix of the linear part around equilibria. Stability diagrams are drawn and simulation results are presented through phase diagrams.     

Corner flow in free liquid films

A lubrication-flow model for a free film in a corner is presented. The model, written in the hyperbolic coordinate system ξ = x ² −y ², η = 2xy, applies to films that are thin in the η-direction. The lubrication approximation yields two coupled evolution equations for the film thickness and the velocity field which, to lowest order, describes plug flow in the hyperbolic coordinates. A free film in a corner evolving under surface tension and gravity is investigated. The rate of thinning of a free film is compared to that of a film evolving over a solid substrate. Viscous shear and normal stresses are both captured in the model and are computed for the entire flow domain. It is shown that normal stress dominates over shear stress in the far field, while shear stress dominates close to the corner. This revised version was published online in October 2005 with corrected page numbers.     

Ugtracold Alkali Atoms in Optical Lattices: A New Type of Quantum Crystals?

Similarities between alkali gases in optical lattices with non-integer occupation of the lattice sites and quantum crystals are explored. The analogy with the vacancy liquid provides an agternative explanation to the Mott transition for the recent experiment on the phase transition in the lattice. The vacancy liquid can undergo BEC with T _c within experimental reach. Direct and vacancy-assisted mechanisms of the band motion for hyperfine impurities are discussed. The presence of vacancies can resugt in the spatial decomposition of the system into pure hyperfine components. Below BEC for the vacancies, the impurity component resembles ³He in ³He-Hell mixtures.     

The reaction of ceria coatings on mica with H2S: An in-situ X-ray diffraction study

Thin layers of ceria were deposited on the surface of mica platelets in solution. The reaction of such particles with hydrogen sulfide yields a red colored special effect pigment. The ceria layer reacts with H₂S to produce a variety of sulfide and oxysulfide phases. The reaction path discovered in situ by time and temperature resolved X-ray diffraction is CeO₂→CeS₂→C-Ce₂S₃→Ce₁₀S₁₄O. The reaction itself is extremely variable depending on gas flow, heating rates and decomposition atmospheres. Effects on the thin film are recorded by scanning electron microscopy (SEM) and revealed a destruction of the layer once red Ce₁₀S₁₄O was formed. The product layer then reveals the typical nonwetting behaviour of a liquid on a surface.     

Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency

In this paper, two brittle fracture problems are numerically simulated: the failure of a ceramic ring under centrifugal loading and crack branching in a PMMA strip. A three‐dimensional finite element package in which cohesive elements are dynamically inserted has been developed. The cohesive elements' strength is chosen to follow a modified weakest link Weibull distribution. The probability of introducing a weak cohesive element is set to increase with the cohesive element size. This reflects the physically based effect according to which larger elements are more likely to contain defects. The calculations illustrate how the area dependence of the Weibull model can be used to effectively address mesh dependency. On the other hand, regular Weibull distributions have failed to reduce mesh dependency for the examples shown in this paper. The ceramic ring calculations revealed that two distinct phenomena appear depending on the magnitude of the Weibull modulus. For low Weibull modulus, the fragmentation of the ring is dominated by heterogeneities. Whereas many cracks were generated, few of them could propagate to the outer surface. Monte Carlo simulations revealed that for highly heterogeneous rings, the number of small fragments was large and that few large fragments were generated. For high Weibull modulus, signifying that the ring is close to being homogeneous, the fragmentation process was very different. Monte Carlo simulations highlighted that a larger number of large fragments are generated due to crack branching. Copyright © 2003 John Wiley & Sons, Ltd.     

On the role of high-energy electrons in the formation of a plasma-beam discharge structure in a diode with a slit cathode

The spatial structure of visible emission from plasma of a transverse nanosecond pulsed electric discharge in a gas-filled diode with a hollow (slit) cathode has been experimentally studied. A relation is established between the regime of electron energy relaxation and the plasma-beam discharge structure formation. High values of the electron emission coefficient are observed in the experiment, which cannot be explained using the notion of electron emission from a cathode bombarded by fast heavy particles.