Compressive tidal heating of a disk galaxy in a rich cluster

The restricted three-body method is used to model the effect of the mean tidal field of a cluster of galaxies on the internal dynamics of a disk galaxy falling into the cluster for the first time. In the model adopted the galaxy experiences a tidal field that is compressive within the core of the cluster. The planar random velocities of all components in the disk increase after the galaxy passes through the core of the cluster. The low-velocity dispersion gas clouds experience a relatively larger increase in random velocity than the hotter stellar components. The increase in planar velocities results in a strong anisotropy between the planar and vertical velocity dispersions. It is argued that this will make the disk unstable to the 'fire-hose instability' which leads to bending modes in the disk and which will thicken the disk slightly. The mean tidal fields in rich clusters were probably stronger during the epoch of cluster formation and relaxation than they are in present-day relaxed clusters.

Molecular expression for dielectric friction on a rotating dipole: Reduction to the continuum theory

Recently we presented a microscopic expression for dielectric friction on a rotating dipole. This expression has a rather curious structure, involving the contributions of the transverse polarization modes of the solvent and also of the molecular length scale processes. It is shown here that under proper limiting conditions, this expression reduces exactly to the classical continuum model expression of Nee and Zwanzig [J. Chem. Phys. 52, 6353 (1970)]. The derivation requires the use of the asymptotic form of the orientation‐dependent total pair correlation function, the neglect of the contributions of translational modes of the solvent, and also the use of the limit that the size of the solvent molecules goes to zero. Thus, the derivation can be important in understanding the validity of the continuum model and can also help in explaining the results of a recent computer simulation study of dielectric relaxation in a Brownian dipolar lattice.

Transient Flow of a Compressible Viscous Fluid Near an Infinite Disk

We have consider ed the transient motion of art electrically conducting viscous compressible fluid which is in contact with an insulated infinite disk. The initial motion is considered to be due to the uniform rotation of the disk in an otherwise stationary fluid or due to the uniform rigid rotation of the fluid over a stationary disk. Different cases of transient motion due to finite impulse imparted either to the disk or to the distant fluid have been investigated. Effects of the imposed axial magnetic field and the disk temperature on the transient flow are included. The nonlinear partial differential equations governing the motion are solved numerically using an implicit finite-difference scheme along with the Newton's linearisation technique.

A possible origin of viscosity in Keplerian accretion disks due to secondary perturbation: Turbulent transport without magnetic fields

The origin of hydrodynamic turbulence in rotating shear flow is a long standing puzzle. Resolving it is especially important in astrophysics when the flow's angular momentum profile is Keplerian which forms an accretion disk having negligible molecular viscosity. Hence, any viscosity in such systems must be due to turbulence, arguably governed by magnetorotational instability, especially when temperature T greater than or similar to 10(5). However, such disks around quiescent cataclysmic variables, protoplanetary and star-forming disks, and the outer regions of disks in active galactic nuclei are practically neutral in charge because of their low temperature, and thus are not expected to be coupled with magnetic fields enough to generate any transport due to the magnetorotational instability. This flow is similar to plane Couette flow including the Coriolis force, at least locally. What drives their turbulence and then transport, when such flows do not exhibit any unstable mode under linear hydrodynamic perturbation? We demonstrate that the three-dimensional secondary disturbance to the primarily perturbed flow that triggers elliptical instability may generate significant turbulent viscosity in the range 0.0001 less than or similar to nu(t) less than or similar to 0.1, which can explain transport in accretion flows.

Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such a system, which appears in an astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity in the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved non-normal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this answers the question of the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of the origin of turbulence therein.

Investigation of exchange of energy between zeeman and dipolar reservoirs in the rotating frame in solids

Exchange of energy between Zeeman and dipolar reservoirs in the rotating frame during spin-lock has important implications for the understanding of the Hartmann-Hahn cross polarisation process and is examined here with experiments on ammonium dihydrogen phosphate. It is observed that energy exchange between the two reservoirs takes place indicating that the relative magnitude of the dipolar coupling in relation to the applied r.f. field may have a role to play in determining the rate of exchange of energy between the two reservoirs.

Variable density approach for rotating shallow shell of variable thickness

A new approach based on variable density in conjunction with shallow shell theory is proposed to analyse rotating shallow shell of variable thickness. Coupled non-linear ordinary differential equations governing shallows shells of variable thickness are first derived before applying the variable density approach. Results obtained from the new approach compare well with FEM calculation for a wide range of profiles considered in this paper.

Investigation of the characteristics of an SF6 rotating arc by a mathematical model

A mathematical model has been developed for predicting the performance of rotating arcs in SF6 gas by considering the energy balance and force balance equations. The finite difference technique has been adopted for the computer simulation of the arc characteristics. This method helps in considering the spatial variation of the transport and radiative properties of the arc. All the three heat loss mechanisms-conduction, convection, and radiation-have been considered. Results obtained over a 10 ms (half cycle of 50 Hz wave) current flow period for 1.4 kA (peak) and 4.2 kA (peak), show that the proposed arc model gives the expected behavior of the arc over the range of currents studied.

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.

Singularity structure and chaotic behavior of the homopolar disk dynamo

We study in great detail a system of three first-order ordinary differential equations describing a homopolar disk dynamo (HDD). This system displays a large variety of behaviors, both regular and chaotic. Existence of periodic solutions is proved for certain ranges of parameters. Stability criteria for periodic solutions are given. The nonintegrability aspects of the HDD system are studied by investigating analytically the singularity structure of the system in the complex domain. Coexisting attractors (including period-doubling sequence) and coexisting strange attractors appear in some parametric regimes. The gluing of strange attractors and the ungluing of a strange attractor are also shown to occur. A period of bifurcation leading to chaos, not observed for other chaotic systems, is shown to characterize the chaotic behavior in some parametric ranges. The limiting case of the Lorenz system is also studied and is related to HDD.

Direct Cartesian-Space Solutions of Generalized Bloch Equations in the Rotating Frame

Analytical solutions of the generalized Bloch equations for an arbitrary set of initial values of the x, y, and z magnetization components are given in the rotating frame. The solutions involve the decoupling of the three coupled differential equations such that a third-order differential equation in each magnetization variable is obtained. In contrast to the previously reported solutions given by Torrey, the present attempt paves the way for more direct physical insight into the behavior of each magnetization component. Special cases have been discussed that highlight the utility of the general solutions. Representative trajectories of magnetization components are given, illustrating their behavior with respect to the values of off-resonance and initial conditions. (C) 1995 Academic Press, Inc.

Violin string shape functions for finite element analysis of rotating Timoshenko beams

Violin strings are relatively short and stiff and are well modeled by Timoshenko beam theory. We use the static part of the homogeneous differential equation of violin strings to obtain new shape functions for the finite element analysis of rotating Timoshenko beams. For deriving the shape functions, the rotating beam is considered as a sequence of violin strings. The violin string shape functions depend on rotation speed and element position along the beam length and account for centrifugal stiffening effects as well as rotary inertia and shear deformation on dynamic characteristics of rotating Timoshenko beams. Numerical results show that the violin string basis functions perform much better than the conventional polynomials at high rotation speeds and are thus useful for turbo machine applications. (C) 2011 Elsevier B.V. All rights reserved.

Rotating anisotropic disc of uniform strength

A procedure to design a constant thickness composite disc of uniform strength by radially tailoring the anisotropic elastic constants is proposed. A special case of an isotropic disc with radially varying modulus is also examined. Analytical results are also compared with FEM calculations for two cases of radially varying anisotropy and for an isotropic disc with variable modulus. (C) 1999 Elsevier Science Ltd. All rights reserved.

Physics based basis function for vibration analysis of high speed rotating beams

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.