Diffusion path during internal displacement reactions in multi-component oxides: Reaction between Fe and (Co,Mg)TiO3 solid solution at 1273 K

The reaction between Fe foil and a disc of ilmenite solid solution (Co-0.48 Ni-0.52) TiO3 was studied at 1273 K. At the metal/oxide interface, the displacement reaction, Fe + (Co,Mg)TiO3 = Co + (Fe,Mg)TiO3 occurs, resulting in an ilmenite solid solution containing three divalent cations. Ferrous ions diffuse into the oxide solid solution and cause the precipitation of Co-Fe alloy as discrete particles inside the oxide matrix. The morphology of the product layer was characterized by SEM. Only two phases, alloy and ilmenite, were detected in the reaction zone. This suggests that the local flux condition imposed by ilmenite stoichiometry (Co + Fe + Mg):Ti = 1:1] was satisfied during the reactive diffusion: (J(Co) + J(Fe) + J(Mg)) = J(Ti). The composition of the alloy and the oxide was determined using EPMA as a function of distance in the direction of diffusion. Although Mg does not participate in the displacement reaction, its composition in the ilmenite phase was found to be position dependent inside the reaction zone. The up-hill diffusion of inert Mg is caused by the development of chemical potential gradients as a result of displacement reaction. The evolution of composition gradients inside the reaction zone and the diffusion path in a ternary composition diagram of the system CoTiO3-FeTiO3-MgTiO3 are discussed. (C) 2010 Elsevier B.V. All rights reserved.

Unsteady compressible flow due to relative rotation and translation of a viscous fluid on a disk

The modification of the axisymmetric viscous flow due to relative rotation of the disk or fluid by a translation of the boundary is studied. The fluid is taken to be compressible, and the relative rotation and translation velocity of the disk or fluid are time-dependent. The nonlinear partial differential equations governing the motion are solved numerically using an implicit finite difference scheme and Newton's linearisation technique. Numerical solutions are obtained at various non-dimensional times and disk temperatures. The non-symmetric part of the flow (secondary flow) describing the translation effect generates a velocity field at each plane parallel to the disk. The cartesian components of velocity due to secondary flow exhibit oscillations when the motion is due to rotation of the fluid on a translating disk. Increase in translation velocity produces an increment in the radial skin friction but reduces the tangential skin friction.

Flow induced by an asymmetrically placed disk rotating coaxially inside a cylindrical casing

In this paper, the flow due to a rotating disk non-symmetrically placed with respect to the height of the enclosing stationary cylinder is analyzed numerically. The full Navier-Stokes equations expressed in terms of stream function and vorticity are solved by successive over-relaxation for different disk radii, its distance from the bottom casing and rotational Reynolds numbers. It is observed that the flow pattern is strongly influenced by the size and the position of the disk. When the disk is very close to the top casing and small in radius, there are two regions of different scales and the vortices in the region of small scale are trapped between the disk and the top casing. Further, the variation of the moment coefficient is determined for different positions and sizes of the rotating disk. The calculations shows that the frictional torque increases rapidly, when the disk approaches the top casing. This finding is of importance for the design of vertical rotating disk reactors applied in chemical vapor deposition.

Swing amplification of nonaxisymmetric perturbations in stars and gas in a sheared galactic disk

We present a study of the growth of local, nonaxisymmetric perturbations in gravitationally coupled stars and gas in a differentially rotating galactic disk. The stars and gas are treated as two isothermal fluids of different velocity dispersions, with the stellar velocity dispersion being greater than that for the gas. We examine the physical effects of inclusion of a low-velocity dispersion component (gas) on the growth of non-axisymmetric perturbations in both stars and gas, as done for the axisymmetric case by Jog & Solomon. The amplified perturbations in stars and gas constitute trailing, material, spiral features which may be identified with the local spiral features seen in all spiral galaxies. The formulation of the two-fluid equations closely follows the one-fluid treatment by Goldreich & Lynden-Bell. The local, linearized perturbation equations in the sheared frame are solved to obtain the results for a temporary growth via swing amplification. The problem is formulated in terms of five dimensionless parameters-namely, the Q-factors for stars and gas, respectively; the gas mass fraction; the shearing rate in the galactic disk; and the length scale of perturbation. By using the observed values of these parameters, we obtain the amplifications and the pitch angles for features in stars and gas for dynamically distinct cases, as applicable for different regions of spiral galaxies. A real galaxy consisting of stars and gas may display growth of nonaxisymmetric perturbations even when it is stable against axisymmetric perturbations and/or when either fluid by itself is stable against non-axisymmetric perturbations. Due to its lower velocity dispersion, the gas exhibits a higher amplification than do the stars, and the amplified gas features are slightly more tightly wound than the stellar features. When the gas contribution is high, the stellar amplification and the range of pitch angles over which it can occur are both increased, due to the gravitational coupling between the two fluids. Thus, the two-fluid scheme can explain the origin of the broad spiral arms in the underlying old stellar populations of galaxies, as observed by Schweizer and Elmegreen & Elmegreen. The arms are predicted to be broader in gas-rich galaxies, as is indeed seen for example in M33. In the linear regime studied here, the arm contrast is shown to increase with radius in the inner Galaxy, in agreement with observations of external galaxies by Schweizer. These results follow directly due to the inclusion of gas in the problem.

Singularity structure and chaotic behavior of the homopolar disk dynamo

We study in great detail a system of three first-order ordinary differential equations describing a homopolar disk dynamo (HDD). This system displays a large variety of behaviors, both regular and chaotic. Existence of periodic solutions is proved for certain ranges of parameters. Stability criteria for periodic solutions are given. The nonintegrability aspects of the HDD system are studied by investigating analytically the singularity structure of the system in the complex domain. Coexisting attractors (including period-doubling sequence) and coexisting strange attractors appear in some parametric regimes. The gluing of strange attractors and the ungluing of a strange attractor are also shown to occur. A period of bifurcation leading to chaos, not observed for other chaotic systems, is shown to characterize the chaotic behavior in some parametric ranges. The limiting case of the Lorenz system is also studied and is related to HDD.

Modeling of concrete cracking-A hybrid technique of using displacement discontinuity element method and direct boundary element method

This paper presents a new approach by making use of a hybrid method of using the displacement discontinuity element method and direct boundary element method to model concrete cracking by incorporating fictitious crack model. Fracture mechanics approach is followed using the Hillerborg's fictitious crack model. A boundary element based substructure method and a hybrid technique of using displacement discontinuity element method and direct boundary element method are compared in this paper. In order to represent the process zone ahead of the crack, closing forces are assumed to act in such a way that they obey a linear normal stress-crack opening displacement law. Plain concrete beams with and without initial crack under three-point loading were analyzed by both the methods. The numerical results obtained were shown to agree well with the results from existing finite element method. The model is capable of reproducing the whole range of load-deflection response including strain-softening and snap-back behavior as illustrated in the numerical examples. (C) 2011 Elsevier Ltd. All rights reserved.

Unsteady mhd flow and heat transfer on a rotating disk in an ambient fluid

An unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid over a rotating infinite disk in an otherwise ambient fluid are studied. The unsteadiness in the flow field is caused by the angular velocity of the disk which varies with time. The magnetic field is applied normal to the disk surface. The new self-similar solution of the Navier-Stokes and energy equations is obtained numerically. The solution obtained here is not only the solution of the Navier-Stokes equations, but also of the boundary layer equations. Also, for a simple scaling factor, it represents the solution of the flow and heat transfer in the forward stagnation-point region of a rotating sphere or over a rotating cone. The asymptotic behaviour of the solution for a large magnetic field or for a large independent variable is also examined. The surface shear stresses in the radial and tangential directions and the surface heat transfer increase as the acceleration parameter increases. Also the surface shear stress in the radial direction and the surface heat transfer decrease with increasing magnetic field, but the surface shear stress in the tangential direction increases. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Asymmetric Warps in Disk Galaxies: Dependence on Dark Matter Halo

Recent observations have shown that most of the warps in the disk galaxies are asymmetric. However there exists no generic mechanism to generate these asymmetries in warps. We have shown that a rich variety of possible asymmetries in the z-distribution of the spiral galaxies can naturally arise due to a dynamical wave interference between the first two bending modes i.e. bowl-shaped mode(m=0) and S-shaped warping mode(m = 1) in the galactic disk embedded in a dark matter halo. We show that the asymmetric warps are more pronounced when the dark matter content within the optical disk is lower as in early-type galaxies.

Origin of Disk Lopsidedness in Spiral Galaxies

In our work we have used the atomic hydrogen [HΙ] gas distribution in the HΙ 21-cm line emission to study the dark matter halo perturbations. For tHΙs analysis, the 2-D HΙ surface density and velocity maps (arcHΙval) of the galaxies in the Eridanus group (obtained using the GMRT) and in the Ursa Major group (obtained from WSRT) were used. In addition a few HΙckson Compact Groups of galaxies were also studied using the GMRT. The HΙ maps of these galaxies were Fourier analysed to estimate the asymmetry in the distribution and motion of gas. The average asymmetry parameter in the 1.5 to 2.5 K′-band scale lengths was found to be ~ 0.27 for the Eridanus group of galaxies wHΙle it was ~ 0.14 for the Ursa Major group of galaxies. The asymmetries in the distribution of HΙ as a function of Hubble type of galaxies were also studied and was found to be directly correlated with the compactness of the groups. In addition, the trend in the asymmetry as a function of the Hubble type of galaxies was opposite to that seen in the field galaxies, i.e., in the group galaxies, the early type galaxies showed more asymmetry than late type. These two aspects indicated that tidal interactions between the galaxies in a group environment to be the major cause of asymmetries. The observed asymmetry parameters were consistent with recent numerical simulations of asymmetries of gas disk caused by fly-by interactions. We have also estimated the perturbation of dark matter halo using the asymmetry parameter obtained from the Fourier series analysis of the surface density maps.

Displacement Amplifying Compliant Mechanisms for Two-axis High-resolution Monolithic Inertial Sensors

Novel designs for two-axis, high-resolution, monolithic inertial sensors are presented in this paper. Monolithic, i.e., joint-less single-piece compliant designs are already common in micromachined inertial sensors such as accelerometers and gyroscopes. Here, compliant mechanisms are used not only to achieve de-coupling between motions along two orthogonal axes but also to amplify the displacements of the proof-mass. Sensitivity and resolution capabilities are enhanced because the amplified motion is used for sensing the measurand. A particular symmetric arrangement of displacement-amplifying compliant mechanisms (DaCMs) leads to de-coupled and amplified motion. An existing DaCM and a new topology-optimized DaCM are presented as a building block in the new arrangement. A spring-mass-lever model is presented as a lumped abstraction of the new arrangement. This model is useful for arriving at the optimal parameters of the DaCM and for performing system-level simulation. The new designs improved the performance by a factor of two or more.

An Objective Evaluation of Displacement-Amplifying Compliant Mechanisms for Sensor Applications

Displacement-amplifying compliant mechanisms (DaCMs) reported in literature are mostly used for actuator applications. This paper considers them for sensor applications that rely on displacement measurement, and evaluates them objectively. The main goal is to increase the sensitivity under constraints imposed by several secondary requirements and practical constraints. A spring-mass-lever model that effectively captures the addition of a DaCM to a sensor is used in comparing eight DaCMs. We observe that they significantly differ in performance criteria such as geometric advantage, stiffness, natural frequency, mode amplification, factor of safety against failure, cross-axis stiffness, etc., but none excel in all. Thus, a combined figure of merit is proposed using which the most suitable DaCM could be selected for a sensor application. A case-study of a micro machined capacitive accelerometer and another case-study of a vision-based force sensor are included to illustrate the general evaluation and selection procedure of DaCMs with specific applications. Some other insights gained with the analysis presented here were the optimum size-scale for a DaCM, the effect on its natural frequency, limits on its stiffness, and working range of the sensor.

Internal displacement reactions in multicomponent oxides: Part I. Line compounds with narrow homogeneity range

Structure and phase transition of LaO1−xF1+2x, prepared by solid-state reaction of La2O3 and LaF3, was investigated by X-ray powder diffraction and differential scanning calorimetry for both positive and negative values of the nonstoichiometric parameter x. The electrical conductivity was investigated as a function of temperature and oxygen partial pressure using AC impedance spectroscopy. Fluoride ion was identified as the migrating species in LaOF by coulometric titration and transport number determined by Tubandt technique and EMF measurements. Activation energy for conduction in LaOF was 58.5 (±0.8) kJ/mol. Conductivity increased with increasing fluorine concentration in the oxyfluoride phase, suggesting that interstitial fluoride ions are more mobile than vacancies. Although the values of ionic conductivity of cubic LaOF are lower, the oxygen partial pressure range for predominantly ionic conduction is larger than that for the commonly used stabilized-zirconia electrolytes. Thermodynamic analysis shows that the oxyfluoride is stable in atmospheres containing diatomic oxygen. However, the oxyfluoride phase can degrade with time at high temperatures in atmospheres containing water vapor, because of the higher stability of HF compared with H2O.

Oxygen displacement in a 107Ag17+ ion irradiated Bi2Sr2CaCu2O8 single crystal

We have studied the magnetic field (H∥c) dependent rf dissipation (Hrf∥a) in an as-grown Bi2Sr2CaCu2O8 single crystal prior to and after irradiation with 250 MeV 107Ag17+ ions. In a comparison of the responses from the as-grown crystal with an air-annealed crystal, features due to oxygen deficient regions acting as weak links in the former are identified. These features disappear immediately after irradiation of the as-grown crystal. We attribute such behavior to the displacement of oxygen from columnar tracks to deficient regions thus eliminating the weak links. Losses from the same irradiated as-grown crystal stored at 300 K for 60 days show that the features similar but not identical to those observed in the pristine state have reappeared implying that the displaced oxygen is in a metastable configuration in the deficient regions and hence is mobile due to thermal effects even at 300 K.

Variation of the gas and radiation content in the sub-Keplerian accretion disk around black holes and its impact to the solutions

We investigate the variation of the gas and the radiation pressure in accretion disks during the infall of matter to the black hole and its effect to the flow. While the flow far away from the black hole might be non-relativistic, in the vicinity of the black hole it is expected to be relativistic behaving more like radiation. Therefore, the ratio of gas pressure to total pressure (beta) and the underlying polytropic index (gamma) should not be constant throughout the flow. We obtain that accretion flows exhibit significant variation of beta and then gamma, which affects solutions described in the standard literature based on constant beta. Certain solutions for a particular set of initial parameters with a constant beta do not exist when the variation of beta is incorporated appropriately. We model the viscous sub-Keplerian accretion disk with a nonzero component of advection and pressure gradient around black holes by preserving the conservations of mass, momentum, energy, supplemented by the evolution of beta. By solving the set of five coupled differential equations, we obtain the thermo-hydrodynamical properties of the flow. We show that during infall, beta of the flow could vary up to similar to 300%, while gamma up to similar to 20%. This might have a significant impact to the disk solutions in explaining observed data, e.g. super-luminal jets from disks, luminosity, and then extracting fundamental properties from them. Hence any conclusion based on constant gamma and beta should be taken with caution and corrected. (C) 2011 Elsevier B.V. All rights reserved.