Slow rotation of a sphere in a non-Newtonian fluid with or without suction or injection

The flow generated by the rotation of a sphere in an infinitely extending fluid has recently been studied by Goldshtik. The corresponding problem for non-Newtonian Reiner-Rivlin fluids has been studied by Datta. Bhatnagar and Rajeswari have studied the secondary flow between two concentric spheres rotating about an axis in the non-Newtonian fluids. This last investigation was further generalised by Rajeswari to include the effects of small radial suction or injection. In Part A of the present investigation, we have studied the secondary flow generated by the slow rotation of a single sphere in non-Newtonian fluid obeying the Rivlin-Ericksen constitutive equation. In Part B, the effects of small suction or injection have been studied which is applied in an arbitrary direction at the surface of the sphere. In the absence of suction or injection, the secondary flow for small values of the visco-elastic parameter is similar to that of Newtonian fluids with inclusion of inertia terms in the Oseen approximation. If this parameter exceeds Kc = 18R/219, whereR is the Reynolds number, the breaking of the flow field takes place into two domains, in one of which the stream lines form closed loops. For still higher values of this parameter, the complete reversal of the sense of the flow takes place. When suction or injection is included, the breaking of the flow persists under certain condition investigated in this paper. When this condition is broken, the breaking of the flow is obliterated.

Flow of an electrically conducting non-newtonian fluid between two rotating coaxial cones in the presence of external magnetic field due to an axial current

Bhatnagar and Rathna (Quar. Journ. Mech. Appl. Maths., 1963,16, 329) investigated the flows of Newtonian, Reiner-Rivlin and Rivlin-Ericksen fluids between two rotating coaxial cones. In case of the last two types of fluids, they predicted the breaking of secondary flow field in any meridian plane. We find that such breaking is avoided by the application of a sufficiently strong azimuthal magnetic field arising from a line current along the axis of the cones.

Harmonic and anharmonic oscillations of a cylindrical plasma in the presence of a uniform axial magnetic field and a steady axial current

In the present note we have studied the harmonic and anharmonic oscillations of cylindrical plasma using Lagrangian formalism. In order to study the harmonic oscillations, the equations are linearized and the resulting equation for the displacement has been numerically solved. For situations present in thermonuclear reactors, the presence of axial magnetic field is found necessary to make the periods of oscillation to become comparable with the time required for the thermonuclear reactions to set in. A detailed analysis of the anharmonic oscillations reveals that the significant interaction is between the first and the second mode. The fundamental period of anharmonic oscillation is more than the corresponding period of harmonic oscillations by 9·2%. Graphs have been drawn for the amplitudes of relative variations in density and magnetic field and of the time-varying part of anharmonic oscillation.

Rotation sensitivity of Lau fringes: an analysis based on coherence theory

An analysis based on coherence theory is presented, which explains the experimentally observed rotation sensitivity of the contrast of Lau fringes obtained under spatially incoherent illumination.

Mixed-mode stress intensity factors for arbitrarily oriented cracks in cylindrical shells under axial pull and torsion

Results of photoelastic investigations conducted on cylindrical tubes (made of Araldite material) containing cracks oriented at 0°, 30°, 45°, 60° and 90° to the axis of the tube and subjected to axial and torsional loads are reported. The stress-intensity factors (SIFs) were determined by analysing the crack-tip stress fields. Smith and Smith's method [Engng Fracture Mech.4, 357–366 (1972)] and a new method developed by the authors by modifying Rakesh et al.'s method [Proc. 26th Congress of ISTAM, India (1981)] were employed to evaluate the mixed-mode SIFs.

Isoscalar axial-vector renormalization constant and polarized proton structure function

The isoscalar axial-vector renormalization constant is reevaluated using the QCD sum-rule method. It is found to be substantially different from the anomaly-free octet axial-vector u¯γμγ5+d¯γμγ5-2s¯γμγ5 coupling. Combining this determination with the known values of the isovector coupling GA and the F/D ratio for the octet current, we find the integral of the polarized proton structure function to be Gp=Fgp1(x)dx=0.135, in agreement with recent measurement by the European Muon Collaboration.

Combined free and forced convection along a rotating vertical cylinder

The steady incompressible laminar mixed convection boundary layer flow along a rotating slender vertical cylinder with an isothermal wall has been studied. The transformed coupled nonlinear partial differential equations have been solved numerically using the Keller box method. In general, the rotation of the cylinder, the buoyancy forces and the curvature parameter are found to significantly affect the skin friction, heat transfer, velocity and temperature profiles as well as the pressure distribution. The buoyancy forces cause an overshoot in the axial velocity profile but the rotation and curvature parameters reduce it.

Partially conserved axial-vector current inS-matrix theory

Mandelstam�s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm ? andm ? as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionm?2?m?2=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.

Role of spatial coherence on the rotation sensitivity of Lau fringes: an experimental study

A simple technique involving the use of a rotating and a stationary diffuser has been developed to vary the spatial coherence of light from a He-Ne laser. Using this technique an experimental investigation of the dependence of rotation sensitivity of Lau fringes on the spatial coherence of the illuminating wavefield has been carried out. It is observed that (i) the rotation sensitivity of Lau fringes varies in a well-defined manner as a function of the spatial coherence of the light used; (ii) the extremely good rotation sensitivity of Lau fringes can be used to great advantage (compared to the conventional double slit method) in the measurement of the spatial coherence of a wavefield; (iii) Lau fringes are formed at various levels of spatial coherence and as such it appears that the Lau effect need not be associated with an incoherent optical field

An accurate numerical integration scheme for finite rotations using rotation vector parametrization

A numerical integration procedure for rotational motion using a rotation vector parametrization is explored from an engineering perspective by using rudimentary vector analysis. The incremental rotation vector, angular velocity and acceleration correspond to different tangent spaces of the rotation manifold at different times and have a non-vectorial character. We rewrite the equation of motion in terms of vectors lying in the same tangent space, facilitating vector space operations consistent with the underlying geometric structure. While any integration algorithm (that works within a vector space setting) may be used, we presently employ a family of explicit Runge-Kutta algorithms to solve this equation. While this work is primarily motivated out of a need for highly accurate numerical solutions of dissipative rotational systems of engineering interest, we also compare the numerical performance of the present scheme with some of the invariant preserving schemes, namely ALGO-C1, STW, LIEMIDEA] and SUBCYC-M. Numerical results show better local accuracy via the present approach vis-a-vis the preserving algorithms. It is also noted that the preserving algorithms do not simultaneously preserve all constants of motion. We incorporate adaptive time-stepping within the present scheme and this in turn enables still higher accuracy and a `near preservation' of constants of motion over significantly longer intervals. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

On the relation between rotation increments in different tangent spaces

In computational mechanics, finite rotations are often represented by rotation vectors. Rotation vector increments corresponding to different tangent: spaces are generally related by a linear operator, known as the tangential transformation T. In this note, we derive the higher order terms that are usually left out in linear relation. The exact nonlinear relation is also presented. Errors via the linearized T are numerically estimated. While the concept of T arises out of the nonlinear characteristics of the rotation manifold, it has been derived via tensor analysis in the context of computational mechanics (Cardona and Geradin, 1988). We investigate the operator T from a Lie group perspective, which provides a better insight and a 1-1 correspondence between approaches based on tensor analysis and the standard matrix Lie group theory. (C) 2010 Elsevier Ltd. All rights reserved.

A Vicarious One-Pot Transformation of a Fluorocyclitol to a Polycyclitol: Observation of a Formal 4-Fold Axial-Equatorial Epimerization on a Conformationally Locked Scaffold

A conformationally locked fluoropentol undergoes an interesting transformation to (trans,anti,trans,anti,trans)-perhydro-2,3,4a,6,7,8a-naphthalenehexol essentially under conditions of base-induced transesterification. The proposed rationale for the observed metamorphosis involves a nucleophilic displacement of fluoride, and subsequent stereo- and regioselective anti-Furst-Plattner-type ring-opening of the epoxide thus formed.

Sensitivity of Lau fringes to grating rotation: theoretical analysis

Recently reported experimental results on the rotation sensitivity of Lau fringes to the spatial coherence of the source have been theoretically analyzed and explained on the basis of coherence theory. A theoretical plot of the rotation angle required for the Lau fringes to vanish is obtained as a function of the coherence length of the illumination used in the Lau experiment. The theoretical results compare well with the experimental observations. The analysis as well as the experiment could form the basis for a simple and easy measurement of the coherence length of the illumination in a plane.