Formation and propagation of bands in jerky flow:a coupled lattice map description

There has been revival of interest in Jerky flow from the point of view of dynamical systems. The earliest attempt in this direction was from our group. One of the predictions of the theory is that Jerky flow could be chaotic. This has been recently verified by us. We have recently extended the earlier model to account for the spatial aspect as well. Both these models are in the form of coupled set of nonlinear differential equations and hence, they are complicated in their structure. For this reason we wish to devise a model based on the results of these two theories in the form of coupled lattice map for the description of the formation and propagation of dislocation bands. We report here one such model and its results.

Measurement of complex optical flow with use of an augmented generalized gradient scheme

We present a method for measuring the local velocities and first-order variations in velocities in a timevarying image. The scheme is an extension of the generalized gradient model that encompasses the local variation of velocity within a local patch of the image. Motion within a patch is analyzed in parallel by 42 different spatiotemporal filters derived from 6 linearly independent spatiotemporal kernels. No constraints are imposed on the image structure, and there is no need for smoothness constraints on the velocity field. The aperture problem does not arise so long as there is some two-dimensional structure in the patch being analyzed. Among the advantages of the scheme is that there is no requirement to calculate second or higher derivatives of the image function. This makes the scheme robust in the presence of noise. The spatiotemporal kernels are of simple form, involving Gaussian functions, and are biologically plausible receptive fields. The validity of the scheme is demonstrated by application to both synthetic and real video images sequences and by direct comparison with another recently published scheme Biol. Cybern. 63, 185 (1990)] for the measurement of complex optical flow.

Measurement of complex optical flow with use of an augmented generalized gradient scheme

We present a method for measuring the local velocities and first-order variations in velocities in a time-varying image. The scheme is an extension of the generalized gradient model that encompasses the local variation of velocity within a local patch of the image. Motion within a patch is analyzed in parallel by 42 different spatiotemporal filters derived from 6 linearly independent spatiotemporal kernels. No constraints are imposed on the image structure, and there is no need for smoothness constraints on the velocity field. The aperture problem does not arise so long as there is some two-dimensional structure in the patch being analyzed. Among the advantages of the scheme is that there is no requirement to calculate second or higher derivatives of the image function. This makes the scheme robust in the presence of noise. The spatiotemporal kernels are of simple form, involving Gaussian functions, and are biologically plausible receptive fields. The validity of the scheme is demonstrated by application to both synthetic and real video images sequences and by direct comparison with another recently published scheme [Biol. Cybern. 63, 185 (1990)] for the measurement of complex optical flow.

Nonlinear effects on rotating disk flow in a cylindrical casing

The flow due to a finite disk rotating in an incompressible viscous fluid has been studied. A modified Newton-gradient finite difference scheme is used to obtain the solution of full Navier-Stokes equations numerically for different disk and cylinder sizes for a wide range of Reynolds numbers. The introduction of the aspect ratio and the disk-shroud gap, significantly alters the flow characteristics in the region under consideration, The frictional torque calculated from the flow data reveals that the contribution due to nonlinear terms is not negligible even at a low Reynolds number. For large Reynolds numbers, the flow structure reveals a strong boundary layer character.

A study of over-reflection in Hartmann flow

It is observed that Hartmann flow sustains wave propagation in its centre region for waves whose phase speed is less than the maximum flow speed. Similar to the previous observations it is found that viscous boundary layers around the critical level and at the wall replace the exponential regions and wave sinks required for over-reflection in the inviscid flow. The uniform magnetic field stabilizes the flow for small-wave-number disturbances along thez-direction. Over-reflection is confined to a few ranges of phase speeds for which the two boundary layers are close together rather than widely separated. These ranges correspond exactly to those for which unstable eigenmodes exist. Over-reflection is associated with a wave phase tilt opposite in direction to the shear.

A numerical study of division of flow in open channels

A two-dimensional numerical model which employs the depth-averaged forms of continuity and momentum equations along with k-e turbulence closure scheme is used to simulate the flow at the open channel divisions. The model is generalised to flows of arbitrary geometries and MacCormack finite volume method is used for solving governing equations. Application of cartesian version of the model to analyse the flow at right-angled junction is presented. The numerical predictions are compared with experimental data of earlier investigators and measurements made as part of the present study. Performance of the model in predicting discharge distribution, surface profiles, separation zone parameters and energy losses is evaluated and discussed in detail. To illustrate the application of the numerical model to analyse the flow in acute angled offtakes and streamlined branch entries, a few computational results are presented.

Experimental studies of a distorted turbulent spot in a three-dimensional flow

We report here on the results of a series of experiments carried out on a turbulent spot in a distorted duct to study the effects of a divergence with straight streamlines preceded by a short stretch of transverse streamline curvature, both in the absence of any pressure gradient. It is found that the distortion produces substantial asymmetry in the spot: the angles at which the spot cuts across the local streamlines are altered dramatically (in contradiction of a hypothesis commonly made in transition zone modelling), and the Tollmien-Schlichting waves that accompany the wing tips of the spot are much stronger on the outside of the bend than on the inside. However there is no strong effect on the internal structure of the spot and the eddies therein, or on such propagation characteristics as overall spread rate and the celerities of the leading and trailing edges. Both lateral streamline curvature and non-homogeneity of the laminar boundary layer into which the spot propagates are shown to be strong factors responsible for the observed asymmetry. It is concluded that these factors produce chiefly a geometric distortion of the coherent structure in the spot, but do not otherwise affect its dynamics in any significant way.

Plane wave analysis of conical and exponential pipes with incompressible mean flow

The general equation for one-dimensional wave propagation at low flow Mach numbers (M less-than-or-equals, slant0·2) is derived and is solved analytically for conical and exponential shapes. The transfer matrices are derived and shown to be self-consistent. Comparison is also made with the relevant data available in the literature. The transmission loss behaviour of conical and exponential pipes, and mufflers involving these shapes, are studied. Analytical expressions of the same are given for the case of a stationary medium. The mufflers involving conical and exponential pipes are shown to be inferior to simple expansion chambers (of similar dimensions) at higher frequencies from the point of view of noise abatement, as was observed earlier experimentally.

Performance of a mixed flow pump with varying tip clearance .1.

Measurements of the three-dimensional flow field entering and leaving a mixed flow pump of non-dimensional specific speed k = 1.89 [N-s = 100 r/min (metric)] are discussed as a function of flowrate. Flow reversal at inlet at reduced flows is seen to result in abnormally high total pressures in the casing region, but causes no noticeable discontinuities on the head-flow characteristics. Inlet prerotation is associated with the transport of angular momentum by the reversal eddy and begins with the initiation of flow reversal.

Performance of a mixed flow pump with varying tip clearance .2.

Measurements in a mixed flow pump of non-dimensional specific speed k = 1.89[N-S = 100 r/min (metric)] are analysed to give loss distribution and local hydraulic efficiencies at different flowrates and values of tip clearance. Fairly close agreement is obtained between the relative flow angles leaving the blading as predicted by simple deviation and slip models and derived from the measurements. The head developed is broken up into two parts: that contributed by Coriolis action and that associated with blade circulation. It is suggested that lift coefficients based on blade circulation are of limited value in selecting blade profiles. The variation of pump efficiency with tip clearance is greater than that reported for centrifugal pumps.

Quantitation of spermatogenesis by DNA flow cytometry: Comparative study among six species of mammals

Suspensions of testicular germ cells from six species of mammals were prepared and stained for the DNA content with a fluorochrome (ethidium bromide) adopting a common technique and subjected to DNA flow cytometry. While uniform staining of the germ cells of the mouse, hamster, rat and monkey could be obtained by treating with 0.5% pepsin for 60 min followed by staining with ethidium bromide for 30 min, that of the guinea pig and rabbit required for optimal staining pepsinization for 90 min and treatment with ethidium bromide for 60 min. The procedure adopted here provided a uniform recovery of over 80% of germ cells with each one of the species tested and the cell population distributed itself according to the DNA content (expressed as C values) into 5 major classes-spermatogonia (2C), cells in S-phase, primary spermatocytes (4C), round spermatids (1C), and elongating/elongated spermatids (HC). Comparison of the DNA distribution pattern of the germ cell populations between species revealed little variation in the relative quantities of cells with 2C (8-11%), S-phase (6-9%), and 4C (6-9%) amount of DNA. Though the spermatid cell populations exhibited variations (1C:31-46%, HCI:7-20% and and HC2:11-25%) they represented the bulk of germ cells (70-80%). The overall conversion of 2C to 1C (1C:2C ratio) and meiotic transformation of 4C cells to IC (1C:4C ratio) kinetics were relatively constant between the species studied. The present study clearly demonstrates that DNA flow cytometry can be adopted with ease and assurance to quantify germ cell transformation and as such spermatogenesis by analysing a large number of samples with consistency both within and across the species barrier. Any variation from the norms in germ cell proportions observed following treatment, for e.g. hormonal stimulation or deprivation can then be ascribed due to a specific effect of the hormone/drug on single/multiple steps in germ cell transformation

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.

Free convection in power-law fluids near a three-dimensional stagnation point

Numerical results are presented for the free-convection boundary-layer equations of the Ostwald de-Waele non-Newtonian power-law type fluids near a three-dimensional (3-D) stagnation point of attachment on an isothermal surface. The existence of dual solutions that are three-dimensional in nature have been verified by means of a numerical procedure. An asymptotic solution for very large Prandtl numbers has also been derived. Solutions are presented for a range of values of the geometric curvature parameter c, the power-law index n, and the Prandtl number Pr.