On the orientation of grain boundaries in cadmium recrystallized during hot deformatio

The authors are grateful to Professor K. P. Abraham for the provision of facilities and encouragement. One of us (PRR) acknowledges the award of a National Associateship by the UGC which facilitated a short-time visit to the Indian Institute of Science.

A geometric approach for determining inner and exterior boundaries of workspaces of planar manipulators

In this paper a method to determine the internal and external boundaries of planar workspaces, represented with an ordered set of points, is presented. The sequence of points are grouped and can be interpreted to form a sequence of curves. Three successive curves are used for determining the instantaneous center of rotation for the second one of them. The two extremal points on the curve with respect to the instantaneous center are recognized as singular points. The chronological ordering of these singular points is used to generate the two envelope curves, which are potentially intersecting. Methods have been presented in the paper for the determination of the workspace boundary from the envelope curves. Strategies to deal with the manipulators with joint limits and various degenerate situations have also been discussed. The computational steps being completely geometric, the method does not require the knowledge about the manipulator's kinematics. Hence, it can be used for the workspace of arbitrary planar manipulators. A number of illustrative examples demonstrate the efficacy of the proposed method.

Investigation of the local Fe magnetic moments at the grain boundaries of the Ca2FeReO6 double perovskite

The local Fe ferromagnetic (FM) moment at the grain boundaries of a ceramic sample of Ca2FeReO6 double perovskite was investigated by means of x-ray magnetic circular dichroism spectroscopy at the Fe L-2,L-3 edges and compared to the overall bulk magnetization. We found that, at the grain boundaries, the Fe FM moments at H=5 T are much smaller than expected and that the MxH curve is harder than in the bulk magnetization. These results suggest a larger degree of Fe/Re antisite disorder at the grain boundaries of this sample, shedding light into the intriguing nonmetallic resistivity behavior despite the reported presence of free carriers. (c) 2007 American Institute of Physics.

Orientation Of Grain-Boundaries In Cadmium Recrystallized During Hot Deformation

The authors are grateful to Professor K. P. Abraham for the provision of facilities and encouragement. One of us (PRR) acknowledges the award of a National Associateship by the UGC which facilitated a short-time visit to the Indian Institute of Science.

Nonclassical rotational inertia in a two-dimensional bosonic solid containing grain boundaries

We study the occurrence of nonclassical rotational inertia (NCRI) arising from superfluidity along grain boundaries in a two-dimensionalbosonic system. We make use of a standard mapping between the zero-temperature properties of this system and the statistical mechanics of interacting vortex lines in the mixed phase of a type-II superconductor. In the mapping, the liquid phase of the vortex system corresponds to the superfluid bosonic phase. We consider numerically obtained polycrystalline configurations of the vortex lines in which the microcrystals are separated by liquidlike grain-boundary regions which widen as the vortex system temperature increases. The NCRI of the corresponding zero-temperature bosonic systems can then be numerically evaluated by solving the equations of superfluid hydrodynamics in the channels near the grain boundaries. We find that the NCRI increases very abruptly as the liquid regions in the vortex system (equivalently, superfluid regions in the bosonic system) form a connected, system-spanning structure with one or more closed loops. The implications of these results for experimentally observed supersolid phenomena are discussed.

Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim

A key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim, particularly when free wake models are used. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero. An appropriate initial estimate of the trim state is needed for successful helicopter trim. This study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed. It is found that the basins of attraction can have fractal boundaries. (C) 2010 Elsevier Ltd. All rights reserved.

Five-fold quasiperiodic tilings generated by inflated rhombuses with identical boundaries: possible application to the growth of quasicrystals

In order to generate normal Penrose tilings by inflation/deflation, decisions have to be made regarding the matching of the rhombuses/tilings with their neighbours. We show here that this decision-making problem can be avoided by adopting a deflation/inflation procedure which uses the decorated rhombuses with identical boundaries. The procedure enables both kinds of inflated rhombuses to match in any orientation along their edges. The tilings so generated are quasiperiodic. These structures appear to have a close relationship with the growth mechanism of quasicrystals.

Moving boundaries due to distributed sources in a slab

Analytical and numerical solutions have been obtained for some moving boundary problems associated with Joule heating and distributed absorption of oxygen in tissues. Several questions have been examined which are concerned with the solutions of classical formulation of sharp melting front model and the classical enthalpy formulation in which solid, liquid and mushy regions are present. Thermal properties and heat sources in the solid and liquid regions have been taken as unequal. The short-time analytical solutions presented here provide useful information. An effective numerical scheme has been proposed which is accurate and simple.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear flow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear how of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Investigation of Surface Grooves from Migrating Grain Boundaries

Visible-light microscopy (VLM) and atomic-force microscopy (AFM) were used to study the progression of grain-boundary grooving and migration in high-purity alumina (Lucalox™). Groove profiles from the same grain boundaries were revisited using AFM following successive heat-treatments. The grooves measured from migrating grain boundaries were found to have asymmetric partial-angles compared to those measured from boundaries that did not migrate during the experiment. For a moving boundary, the grain with the larger partial-angle was consistently found to grow into the grain with the smaller partial-angle. Migrating boundaries were observed to leave behind remnant thermal grooves. The observations indicate that the boundary may be bowing out during the migration process.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear ow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear flow of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Thermodynamic properties and phase boundaries of Co O solutions

The thermodynamic properties of liquid unsaturated Co--O solutions have been determined by electrochemical measurements using (Y sub 2 O sub 3 )ThO sub 2 as solid electrolyte. The cell can be represented as, Pt. MoO sub 2 + Mo | (Y sub 2 O sub 3 )ThO sub 2 | O sub Co , tungsten, Pt, Emf of the cell was measured as a function of oxygen concentration in liquid Co at 1798, 1873 and 1973K. Least-mean squares regression analysis of the experimental data gives for the free energy of solution of diatomic oxygen in liquid Co Delta G exp 0 sub O(Co) = --84935--7.61 T ( plus/minus 400) J/g-atom and self interaction parameter for oxygen epsilon exp O sub O = --97240/T + 40.52 ( plus/minus 1) where the standard state for O is an infinitely dilute solution in which the activity is equal to atomic percent. The present data are discussed in comparison with those reported in the literature and the phase diagram for the Co--O system. 18 ref.--AA.