Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t = 0) steady and then at t > 0 it becomes unsteady. The semi-similar solution of the unsteady Navier-Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier-Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier-Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time. (C) 1999 Elsevier Science Ltd. All rights reserved.

Zero-point entropy in 'spin ice'

Common water ice (ice I-h) is an unusual solid-the oxygen atoms form a periodic structure but the hydrogen atoms are highly disordered due to there being two inequivalent O-H bond lengths'. Pauling showed that the presence of these two bond lengths leads to a macroscopic degeneracy of possible ground states(2,3), such that the system has finite entropy as the temperature tends towards zero. The dynamics associated with this degeneracy are experimentally inaccessible, however, as ice melts and the hydrogen dynamics cannot be studied independently of oxygen motion(4). An analogous system(5) in which this degeneracy can be studied is a magnet with the pyrochlore structure-termed 'spin ice'-where spin orientation plays a similar role to that of the hydrogen position in ice I-h. Here we present specific-heat data for one such system, Dy2Ti2O7, from which we infer a total spin entropy of 0.67Rln2. This is similar to the value, 0.71Rln2, determined for ice I-h, SO confirming the validity of the correspondence. We also find, through application of a magnetic field, behaviour not accessible in water ice-restoration of much of the ground-state entropy and new transitions involving transverse spin degrees of freedom.

A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, ther possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

Persistent passive hopping and juggling is possible even with plastic collisions

We describe simple one-dimensional models of passive (no energy input, no control), generally dissipative, vertical hopping and one-ball juggling. The central observation is that internal passive system motions can conspire to eliminate collisions in these systems. For hopping, two point masses are connected by a spring and the lower mass has inelastic collisions with the ground. For juggling, a lower point-mass hand is connected by a spring to the ground and an upper point-mass ball is caught with an inelastic collision and then re-thrown into gravitational free flight. The two systems have identical dynamics. Despite inelastic collisions between non-zero masses, these systems have special symmetric energy-conserving periodic motions where the collision is at zero relative velocity. Additionally, these special periodic motions have a non-zero sized, one-sided region of attraction on the higher-energy side. For either very large or very small mass ratios, the one-sided region of attraction is large. These results persist for mildly non-linear springs and non-constant gravity. Although non-collisional damping destroys the periodic motions, small energy injection makes the periodic motions stable, with a two-sided region of attraction. The existence of such special energy conserving solutions for hopping and juggling points to possibly useful strategies for both animals and robots. The lossless motions are demonstrated with a table-top experiment.

Analysis of link-layer backoff schemes on point-to-point Markov fading links

Backoff algorithms are typically employed in multiple-access networks (e.g., Ethernet) to recover from packet collisions. In this letter, we propose and carry out the analysis for three types of link-layer backoff schemes, namely, linear backoff, exponential backoff, and geometric backoff, on point-to-point wireless fading links where packet errors occur nonindependently. In such a scenario, the backoff schemes are shown to achieve better energy efficiency without compromising much on the link layer throughput performance.

On an oscillatory point force in a rotating stratified fluid

The forced oscillations due to a point forcing effect in an infinite or contained, inviscid, incompressible, rotating, stratified fluid are investigated taking into account the density variation in the inertia terms in the linearized equations of motion. The solutions are obtained in closed form using generalized Fourier transforms. Solutions are presented for a medium bounded by a finite cylinder when the oscillatory forcing effect is acting at a point on the axis of the cylinder. In both the unbounded and bounded case, there exist characteristic cones emanating from the point of application of the force on which either the pressure or its derivatives are discontinuous. The perfect resonance existing at certain frequencies in an unbounded or bounded homogeneous fluid is avoided in the case of a confined stratified fluid.

The central region of meso-3,4-diphenylhexane-2,5-dione

As with 1,2-diphenylethane (dpe), X-ray crystallographic methods measure the central bond in meso-3,4-diphenylhexane-2,5-done (dphd) as significantly shorter than normal for an sp(3)-sp(3) bond. The same methods measure the benzylic (ethane C-Ph) bonds in dphd as unusually long for sp(3)-sp(2) liaisons. Torsional motions of the phenyl rings about the C-Ph bonds have been proposed as the artifacts behind the result of a 'short' central bond in dpe. While a similar explanation can, presumably, hold for the even 'shorter' central bond in dphd, it cannot account for the 'long' C-Ph bonds. The phenyl groups, departing much from regular hexagonal shape, adopt highly skewed conformations with respect to the plane constituted by the four central atoms. It is thought that-the thermal motions of the phenyl rings, conditioned by the potential wells in which they are ensconced in the unit cell, are largely libratory around their normal axes. In what appears to be a straightforward explanation under the 'rigid-body' concept, it appears that these libratory motions of the phenyl rings, that account, at the same time, for the 'short' central bond, are the artifacts behind the 'long' measurement of the C-Ph bonds. These motions could be superimposed on torsional motions analogous to those proposed in the case of dpe. An inspection of the ORTEP diagram from the 298 K data on dphd clearly suggests these possibilities. Supportive evidence for these qualitative explanations from an analysis of the differences between the mean square displacements of C(1) and C(7)/C(1a) and C(7a) based on the 'rigid-body model' is discussed. (C) 2002 Elsevier Science B.V. All rights reserved.

Landslide susceptibility mapping in the downstream region of Sharavathi river basin, Central Western Ghats

Landslides are hazards encountered during monsoon in undulating terrains of Western Ghats causing geomorphic make over of earth surface resulting in significant damages to life and property. An attempt is made in this paper to identify landslides susceptibility regions in the Sharavathi river basin downstream using frequency ratio method based on the field investigations during July- November 2007. In this regard, base layers of spatial data such as topography, land cover, geology and soil were considered. This is supplemented with the field investigations of landslides. Factors that influence landslide were extracted from the spatial database. The probabilistic model -frequency ratio is computed based on these factors. Landslide susceptibility indices were computed and grouped into five classes. Validation of LHS, showed an accuracy of 89% as 25 of the 28 regions tallied with the field condition of highly vulnerable landslide regions. The landslide susceptible map generated for the downstream would be useful for the district officials to implement appropriate mitigation measures to reduce hazards.