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.

On the spurious increase in particle volume fraction during coarsening simulations

The problem of spurious increase in volume fraction of second-phase particles during computer simulations of coarsening is examined. The origin of this problem is traced to the use of too long a time step (used for numerical integration of growth rates with respect to time) which leads to small particles with large negative growth rates shrinking to negative radii at the end of the time step. Such a shrinkage to negative sizes has the effect of pumping solute into the system. It is therefore suggested that the length of the time step be chosen in accordance with the size of the smallest particle present in the system. It is shown that spurious increase in particle Volume has a significant effect on the particle size distributions in the scaling regime (making them broader and more skewed in the Lifshitz-Slyozov-Wagner model). Its effect on coarsening kinetics, however, is found to be small.

Stability of the viscous flow of a fluid through a flexible tube

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate s((0)), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) correction to the growth rate s((2)) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s((2)) increases proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube

Stability of the viscous flow of a fluid through a flexible tube

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity eta in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity eta(s) occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface. The transition velocity Gamma(t) for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities eta(r) = (eta(s)/eta), the capillary number Lambda = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For eta(r) = 0 and Lambda = 0, the transition velocity Gamma(t) diverges in the limits k much less than 1 and k much greater than 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for Lambda > 0 and eta(r) = 0, though there is an increase in Gamma(t) in the limit k much greater than 1. When the viscosity of the surface is non-zero (eta(r) > 0), however, there is a qualitative change in the Gamma(t) vs. k curves. For eta(r) < 1, the transition velocity Gamma(t) is finite only when k is greater than a minimum value k(min), while perturbations with wavenumber k < k(min) are stable even for Gamma--> infinity. For eta(r) > 1, Gamma(t) is finite only for k(min) < k < k(max), while perturbations with wavenumber k < k(min) or k > k(max) are stable in the limit Gamma--> infinity. As H decreases or eta(r) increases, the difference k(max)- k(min) decreases. At minimum value H = H-min, which is a function of eta(r), the difference k(max)-k(min) = 0, and for H < H-min, perturbations of all wavenumbers are stable even in the limit Gamma--> infinity. The calculations indicate that H-min shows a strong divergence proportional to exp (0.0832 eta(r)(2)) for eta(r) much greater than 1.

Common underlying steering curves for motorcycles in steady turns

We study the steady turn behaviours of some light motorcycle models on circular paths, using the commercial software package ADAMS-Motorcycle. Steering torque and steering angle are obtained for several path radii and a range of steady forward speeds. For path radii much greater than motorcycle wheelbase, and for all motorcycle parameters including tyre parameters held fixed, dimensional analysis can predict the asymptotic behaviour of steering torque and angle. In particular, steering torque is a function purely of lateral acceleration plus another such function divided by path radius. Of these, the first function is numerically determined, while the second is approximated by an analytically determined constant. Similarly, the steering angle is a function purely of lateral acceleration, plus another such function divided by path radius. Of these, the first is determined numerically while the second is determined analytically. Both predictions are verified through ADAMS simulations for various tyre and geometric parameters. In summary, steady circular motions of a given motorcycle with given tyre parameters can be approximately characterised by just one curve for steering torque and one for steering angle.

Lopsidedness in WHISP galaxies I. Rotation curves and kinematic lopsidedness

The frequently observed lopsidedness of the distribution of stars and gas in disc galaxies is still considered as a major problem in galaxy dynamics. It is even discussed as an imprint of the formation history of discs and the evolution of baryons in dark matter haloes. Here, we analyse a selected sample of 70 galaxies from the Westerbork Hi Survey of Spiral and Irregular Galaxies. The Hi data allow us to follow the morphology and the kinematics out to very large radii. In the present paper, we present the rotation curves and study the kinematic asymmetry. We extract the rotation curves of the receding and approaching sides separately and show that the kinematic behaviour of disc galaxies can be classified into five different types: symmetric velocity fields where the rotation curves of the receding and approaching sides are almost identical; global distortions where the rotation velocities of the receding and approaching sides have an offset that is constant with radius; local distortions leading to large deviations in the inner and negligible deviations in the outer parts (and vice versa); and distortions that divide the galaxies into two kinematic systems that are visible in terms of the different behaviour of the rotation curves of the receding and approaching sides, which leads to a crossing and a change in side. The kinematic lopsidedness is measured from the maximum rotation velocities, averaged over the plateau of the rotation curves. This gives a good estimate of the global lopsidedness in the outer parts of the sample galaxies. We find that the mean value of the perturbation parameter denoting the lopsided potential as obtained from the kinematic data is 0.056. Altogether, 36% of the sample galaxies are globally lopsided, which can be interpreted as the disc responding to a halo that was distorted by a tidal encounter. In Paper II, we study the morphological lopsidedness of the same sample of galaxies.

Lopsidedness in WHISP galaxies II. Morphological lopsidedness

The distribution of stars and gas in many galaxies is asymmetric. This so-called lopsidedness is expected to significantly affect the dynamics and evolution of the disc, including the star formation activity. Here, we measure the degree of lopsidedness for the gas distribution in a selected sample of 70 galaxies from the Westerbork Hi Survey of Spiral and Irregular Galaxies. This complements our earlier work (Paper I) where the kinematic lopsidedness was derived for the same galaxies. The morphological lopsidedness is measured by performing a harmonic decomposition of the surface density maps. The amplitude of lopsidedness A(1), the fractional value of the first Fourier component, is typically quite high (about 0.1) within the optical disc and has a constant phase. Thus, lopsidedness is a common feature in galaxies and indicates a global mode. We measure A(1) out to typically one to four optical radii, sometimes even further. This is, on average, four times larger than the distance to which lopsidedness was measured in the past using near-IR as a tracer of the old stellar component, and therefore provides a new, more stringent constraint on the mechanism for the origin of lopsidedness. Interestingly, the value of A(1) saturates beyond the optical radius. Furthermore, the plot of A(1) versus radius shows fluctuations that we argue are due to local spiral features. We also try to explain the physical origin of this observed disc lopsidedness. No clear trend is found when the degree of lopsidedness is compared to a measure of the isolation or interaction probability of the sample galaxies. However, this does not rule out a tidal origin if the lopsidedness is long-lived. In addition, we find that the early-type galaxies tend to be more morphologically lopsided than the late-type galaxies. Both results together indicate that lopsidedness has a tidal origin.

Structure of 2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9-hexadecafluorodecyl 1,10-ditosylate by X-ray crystallography and F-19-NMR spectroscopy

2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9-hexadecafluorodecyl 1,10-ditosylate and its precursors were synthesized and characterized by H-1- and F-19-NMR spectroscopic methods and X-ray crystallography. These compounds are building blocks for the syntheses of the surfactants containing polyperfluoromethylene spacer. The molecule has extended all-trans conformation with molecular symmetry (1) over bar (C-i). There is a reasonably strong C-H ... O interaction in the crystal and there are two F ... F intermolecular contact distances less than the sum of van der Waals radii. (C) 1999 Elsevier Science B.V. All rights reserved.

Studies on strontium substituted rare earth manganites

Sintering, electrical conductivity and thermal expansion behaviour of combustion synthesised strontium substituted rare earth manganites with the general formula Ln(1-x)Sr(x)MnO(3) (Ln = Pr, Nd and Sm; x = 0, 0.16 and 0.25) have been investigated as solid oxide fuel cell cathode materials. The combustion derived rare earth manganites have surface area in the range of 13-40 m(2)/g. Strontium substitution increases the electrical conductivity values in all the rare earth manganites. With the decreasing ionic radii of rare earth ions, the conductivity value decreases. Among the rare earth manganites studied, (Pr/Nd)(0.75)Sr0.25MnO3 show high electrical conductivity ( > 100 S/cm). The thermal expansion coefficients of Pr0.75Sr0.25MnO3 and Nd0.75Sr0.25MnO3 were found to be 10.2 x 10(-6) and 10.7 x 10(-6) K-1 respectively, which is very close to that of the electrolyte (YSZ) used in solid oxide fuel cells. (C) 1999 Elsevier Science B.V. All rights reserved.

Tidally compressed gas in centers of early-type and ultraluminous galaxies

In this paper we propose that the compressive tidal held in the centers of flat-core early-type galaxies and ultraluminous galaxies compresses molecular clouds producing dense gas observed in the centers of these galaxies. The effect of galactic tidal fields is usually considered disruptive in the literature. However, for some galaxies, the mass profile flattens toward the center and the resulting galactic tidal field is not disruptive, but instead it is compressive within the flat-core region. We have used the virial theorem to determine the minimum density of a molecular cloud to be stable and gravitationally bound within the tidally compressive region of a galaxy. We have applied the mechanism to determine the mean molecular cloud densities in the centers of a sample of flat-core, early-type galaxies and ultraluminous galaxies. For early-type galaxies with a core-type luminosity profile, the tidal held of the galaxy is compressive within half the core radius. We have calculated the mean gas densities for molecular gas in a sample of early-type galaxies which have already been detected in CO emission, and we obtain mean densities of [n] similar to 10(3)-10(6) cm(-3) within the central 100 pc radius. We also use our model to calculate the molecular cloud densities in the inner few hundred parsecs of a sample of ultraluminous galaxies. From the observed rotation curves of these galaxies we show that they have a compressive core within their nuclear region. Our model predicts minimum molecular gas densities in the range 10(2)-10(4) cm(-3) in the nuclear gas disks; the smaller values are applicable typically for galaxies with larger core radii. The resulting density values agree well with the observed range. Also, for large core radii, even fairly low-density gas (similar to 10(2) cm(-3)) can remain bound and stable close to the galactic center.

Solid state structural and solution studies on the formation of a flexible cavity for anions by copper(I) and 1,2-bis(diphenylphosphino)ethane

Copper(l) complexes of 1,2-bis(diphenylphosphino)ethane (dppe) with a stoichiometry Cu-2(dppe)(3)(X)(2) [X- = CN- (1), SCN- (2), NO3- (3)] are obtained from direct reactions of CuX and dppe. The complexes are structurally and spectroscopically (NMR and IR) characterized. The structure of the [Cu-2(dPPe)(3)](2+) dication is similar to the structural motif observed in many other complexes with a chelating dppe and a bridging dppe connecting two copper centers. In complexes 1 -3, the anions are confined to the cavity formed by the phosphines which force a monodentate coordination mode despite the predominant bidentate/bridging character of the anions. The coordination angles rather than the thermochemical radii dictate the steric requirement of anions. While the solution behavior of 3, with nitrate, is similar to complexes studied earlier, complexes with pseudohalides exhibit new solution behavior. (C) 2002 Elsevier Science Ltd. All rights reserved.

Spherical piston problem in water

In this paper, we study the propagation of a shock wave in water, produced by the expansion of a spherical piston with a finite initial radius. The piston path in the x, t plane is a hyperbola. We have considered the following two cases: (i) the piston accelerates from a zero initial velocity and attains a finite velocity asymptotically as t tends to infinity, and (ii) the piston decelerates, starting from a finite initial velocity. Since an analytic approach to this problem is extremely difficult, we have employed the artificial viscosity method of von Neumann & Richtmyer after examining its applicability in water. For the accelerating piston case, we have studied the effect of different initial radii of the piston, different initial curvatures of the piston path in the x, t plane and the different asymptotic speeds of the piston. The decelerating case exhibits the interesting phenomenon of the formation of a cavity in water when the deceleration of the piston is sufficiently high. We have also studied the motion of the cavity boundary up to 550 cycles.

Stability of the flow of a fluid through a flexible tube at high Reynolds number

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (ρVR / η), the ratio of the viscosities of the wall and fluid ηr = (ηs/η), the ratio of radii H and the dimensionless velocity Γ = (ρV2/G)1/2. Here ρ is the density of the fluid, G is the coefficient of elasticity of the wall and Vis the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter ε = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate do), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctruations due to the Reynolds strees. There is an O(ε1/2) correction to the growth rate, s(1), due to the presence of a wall layer of thickness ε1/2R where the viscous stresses are O(ε1/2) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Γ and wavenumber k where s(l) = 0. At these points, the wail layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(ε) correction to the growth rate s(2) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s(2) increases [is proportional to] (H − 1)−2 for (H − 1) [double less-than sign] 1 (thickness of wall much less than the tube radius), and decreases [is proportional to] (H−4 for H [dbl greater-than sign] 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube.

Progressively More Prolate Dark Matter Halo In the Outer Galaxy As Traced by Flaring Hi gas

A galactic disk in a spiral galaxy is generally believed to be embedded in an extended dark matter halo, which dominates its dynamics in the outer parts. However, the shape of the halo is not clearly understood. Here we show that the dark matter halo in the Milky Way is prolate in shape. Further, it is increasingly more prolate at larger radii, with the vertical-to-planar axis ratio monotonically increasing to 2.0 at 24 kpc. This is obtained by modeling the observed steeply flaring atomic hydrogen gas layer in the outer Galactic disk, where the gas is supported by pressure against the net gravitational field of the disk and the halo. The resulting prolate-shaped halo can explain several long-standing puzzles in galactic dynamics, for example, it permits long-lived warps thus explaining their ubiquitous nature.

Investigation on the Sources of Reflection at the Junction of Tall Grounded Object and Lightning Channel

During lightning strike to a tall grounded object (TGO), reflections of current waves are known to occur at either ends of the TGO. These reflection modify the channel current and hence, the lightning electromagnetic fields. This study aims to identify the possible contributing factors to reflection at a TGO-channel junction for the current waves ascending on the TGO. Possible sources of reflection identified are corona sheath and discontinuity of resistance and radius. For analyzing the contribution of corona sheath and discontinuity of resistance at the junction, a macroscopic physical model for the return stroke developed in our earlier work is employed. NEC-2D is used for assessing the contribution of abrupt change in radii at a TGO-channel junction. The wire-cage model adopted for the same is validated using laboratory experiments. Detailed investigation revealed the following. The main contributor for reflection at a TGO-channel junction is the difference between TGO and channel core radii. Also, the discontinuity of resistance at a TGO-channel junction can be of some relevance only for the first microsecond regime. Further, corona sheath does not play any significant role in the reflection.