Anisotropic relativistic stellar models

We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the anisotropy factor. The energy density and both radial and tangential pressures are finite and positive inside the anisotropic star. Numerical results show that the basic physical parameters (mass and radius) of the model can describe realistic astrophysical objects like neutron stars.     

Suppression of Rayleigh-Taylor instability by gyroviscosity and sheared axial flow in imploding plasma pinches

The synergistic stabilizing effect of gyroviscosity and sheared axial flow on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible viscid magneto-hydrodynamic equations.The gyroviscosity(or finite Larmor radius) effects are introduced in the momentum equation through an anisotropic ion stress tensor.Dispersion relation with the effect of a density discontinuity is derived.The results indicate that the short-wavelength modes of the Rayleigh-Taylor instability are easily stabilized by the gyroviscosity effects.The long wavelength modes are stabilized by the sufficient sheared axial flow.However,the synergistic effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability.This synergistic effect can compress the Rayleigh-Taylor instability to a narrow wave number region.Even with a sufficient gyroviscosity and large enough flow velocity,the synergistic effect can completely suppressed the Rayleigh-Taylor instability in whole wave number region.     

Dynamical instability and the expansion-free condition

We study the dynamical instability of a spherically symmetric anisotropic fluid which collapses adiabatically under the condition of vanishing expansion scalar. The Newtonian and post Newtonian regimes are considered in detail. It is shown that within those two approximations the adiabatic index Γ₁, measuring the fluid stiffness, does not play any role. Instead, the range of instability is determined by the anisotropy of the fluid pressures and the radial profile of the energy density, independently of its stiffness, in a way which is fully consistent with results previously obtained from the study on the Tolman mass.     

Gravitational loss-cone instability

We study physical corollaries of the existing analogy between the simplest plasma traps (mirror traps) and star clusters surrounding massive black holes or dense galactic nuclei. There is a loss cone in the system through which plasma particles with low velocities transverse to the trap axis or, similarly, stars with low angular momenta (destroyed or absorbed by the central body) escape. The consequences of the “beam-like” deformation of the plasma distribution function in a trap are well known: a peculiar loss-cone instability producing a plasma flow into the loss cone develops as a result. We show that a similar gravitational loss-cone instability can also arise under certain conditions in the galactic case of interest to us. This instability is related to the slow precessional motions of highly elongated (nearly radial) stellar orbits and the main condition for its growth is that the precession of such orbits be retrograde (in the direction opposite to the orbital rotation of stars). Only under this condition do oscillations that can become unstable in the presence of a loss cone arise instead of the radial orbit instability (a variety of the Jeans instability in systems with highly elongated orbits) that takes place in the case of prograde precession. The instability produces a stream of stars onto the galactic center, i.e., serves as a mechanism of fueling the nuclear activity of galaxies. For a mathematical analysis, we have obtained relatively simple characteristic equations that describe small perturbations in a sphere of radially highly elongated stellar orbits. These characteristic equations are derived through a number of successive simplifications from a general linearized system of equations, including the collisionless Boltzmann kinetic equation and the Poisson equation (in action-angle variables). The central point of our analysis of the characteristic equations is preliminary detection of neutral modes (or proof of their absence in the case of stability).     

Effect of Hall Current on the Magnetogravitational Instability of Anisotropic Plasma with Generalized Polytrope Law

The effect of Hall current on the propagation of small perturbations through self gravitating anisotropic collisionless pressure plasma with generalized polytrope law is investigated. The poly-trope law for pressure components parallel and perpendicular to the direction of magnetic field is utilized in the analysis. The effect of Hall current and finite conductivity is introduced in the generalized Ohm's law. Using the polytrope law and Ohm's law dispersion relations are obtained from linearized perturbation equations for wave propagation along and perpendicular to the direction of magnetic field. The dispersion relations incorporating polytrope indices are able to represent the Chew, Goldberger and Low approximation with double adiabatic equation of state for the anisotropic pressure and the magnetohydrodynamic set of equations with isothermal equation of state for the isotropic pressure. The effect of Hall current, finite conductivity and polytrope indices is discussed on the well known hose and gravitational instability. It is found that Jeans' criterion depends on polytrope indices and the condition of gravitational instability is determined for different special cases of interest.     

Magnetohydrodynamics and Plasma Cosmology

We study the linear magnetohydrodynamic (MHD) equations, both in the Newtonian and the general-relativistic limit, as regards a viscous magnetized fluid of finite conductivity and discuss instability criteria. In addition, we explore the excitation of cosmological perturbations in anisotropic spacetimes, in the presence of an ambient magnetic field. Acoustic, electromagnetic (e/m) and fast-magnetosonic modes, propagating normal to the magnetic field, can be excited, resulting in several implications of cosmological significance.     

Quasi-periodic solutions of the integrable dynamical systems related to Hill's equation

We present finite-gap solutions to the Garnier system and to the g-dimensional anisotropic harmonic oscillator in a radial quartic potential. The relationship between these solutions and solutions of Neumann-type dynamical systems is discussed.     

Modulational instability in systems with integrating nonlinearity

A new type of modulational instability for coherent as well as partially coherent light in systems with integrating nonlinearity caused by an irreversible process is investigated both experimentally and theoretically. In such systems plane waves never reach the stationary limit and exhibit a nontrivial time dependence resulting in new features of the modulational instability. For example, the modulational frequency of the nonexponentially increasing perturbation with maximum gain decreases while the wave is propagating. The threshold for vanishing modulational instability due to a finite degree of spatial coherence depends only on system parameters and not on the light intensity.     

Temperature effects on capillary instabilities in a thin nematic liquid crystalline fiber embedded in a viscous matrix

Linear stability analysis of capillary instabilities in a thin nematic liquid crystalline cylindrical fiber embedded in an immiscible viscous matrix is performed by formulating and solving the governing nemato-capillary equations, that include the effect of temperature on the nematic ordering as well as the effect of the nematic orientation. A representative axial nematic orientation texture with the planar easy axis at the fiber surface is studied. The surface disturbance is expressed in normal modes, which include the azimuthal wave number m to take into account non-axisymmetric modes. Capillary instabilities in nematic fibers reflect the anisotropic nature of liquid crystals, such as the ordering and orientation contributions to the surface elasticity and surface normal and bending stresses. Surface gradients of normal and bending stresses provide additional anisotropic contributions to the capillary pressure that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic ordering and orientation, i.e. the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or non-axisymmetric. In addition, when the interface curvature effects are accounted for as contributions of the work of interfacial bending and torsion to the total energy of the system, the higher-order bending moment contribution to the surface stress tensor is critical in stabilizing the fiber instabilities. For the planar easy axis, the nematic ordering contribution to the surface energy, which renormalizes the effect of the fiber shape, plays a crucial role to determine the instability mechanisms. Moreover, the unstable modes, which are most likely observed, can be driven by the dependence of surface energy on the surface area. Low-ordering fibers display the classical axisymmetric mode, since the surface energy decreases by decreasing the surface area. Decreasing temperature gives rise to the encounter with a local maximum or to monotonic increase of the characteristic length of the axisymmetric mode. Meanwhile, in the presence of high surface ordering, non-axisymmetric finite wavelength instabilities emerge, with higher modes growing faster since the surface energy decreases by increasing the surface area. As temperature decreases, the pitches of the chiral microstructures become smaller. However, this non-axisymmetric instability mechanism can be regulated by taking account of the surface bending moment, which contains higher order variations in the interface curvatures. More and more non-axisymmetric modes emerge as temperature decreases, but, at constant temperature, only a finite number of non-axisymmetric modes are unstable and a single fastest growing mode emerges with lower and higher unstable modes growing slower. For nematic fibers, the classical fiber-to-droplet transformation is one of several possible instability pathways, while others include chiral microstructures. The capillary instabilities' growth rate of a thin nematic fiber in a viscous matrix is suppressed by increasing either the fiber or matrix viscosity, but the estimated droplet sizes after fiber breakup in axisymmetric instabilities decrease with increasing the matrix viscosity. Received 15 April 2002 and Received in final form 3 October 2002 RID="a" ID="a"e-mail: alejandro.rey@mcgill.ca     

Wave Instabilities of a Collisionless Plasma in Fluid Approximation

Wave properties and instabilities in a magnetized, anisotropic, collisionless, rarefied hot plasma in fluid approx‐imation are studied, using the 16‐moments set of the transport equations obtained from the Vlasov equations. These equations differ from the CGL‐MHD fluid model (single fluid equations by Chew, Goldberger, and Low [5,9]) by including two anisotropic heat flux evolution equations, where the fluxes invalidate the double polytropic CGL laws. We derived the general dispersion relation for linear compressible wave modes. Besides the classic incompressible fire hose modes there appear four types of compressible wave modes: two fast and slow mirror modes – strongly modified compared to the CGL model – and two thermal modes. In the presence of initial heat fluxes along the magnetic field the wave properties become different for the waves running forward and backward with respect to the magnetic field. The well known discrepancies between the results of the CGL‐MHD fluid model and the kinetic theory are now removed: i) The mirror slow mode instability criterion is now the same as that in the kinetic theory. ii) Similarly, in kinetic studies there appear two kinds of fire hose instabilities ‐ incompressible and compressible ones. These two instabilities can arise for the same plasma parameters, and the instability of the new compressible oblique fire hose modes can become dominant. The compressible fire hose instability is the result of the resonance coupling of three retrograde modes ‐ two thermal modes and a fast mirror mode. The results can be applied to the theory of solar and stellar coronal and wind models (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental observation and characterization of the magnetorotational instability

Differential rotation occurs in conducting flows in accretion disks and planetary cores. In such systems, the magnetorotational instability can arise from coupling Lorentz and centrifugal forces to cause large radial angular momentum fluxes. We present the first experimental observation of the magnetorotational instability. Our system consists of liquid sodium between differentially rotating spheres, with an imposed coaxial magnetic field. We characterize the observed patterns, dynamics, and torque increases, and establish that this instability can occur from a hydrodynamic turbulent background.     

Wave based analysis of the Green's function for a layered cylindrical shell

Cylindrical shells composed of concentric layers may be designed to affect the way that elastic waves are generated and propagated, particularly when some layers are anisotropic. To aid the design process, the present work develops a wave based analysis of the Green's function for a layered cylindrical shell in which the response is given as a sum of waves propagating in the axial coordinate. The analysis assumes linear Hookean materials for each layer. It uses finite element discretizations in the radial coordinate and Fourier series expansions in the circumferential coordinate, leading to linear equations in the axial wavenumber domain that relate shell displacements and forces. Inversion to the axial domain is accomplished via a state-space formulation that is evaluated using residue integration. The resulting expression for the Green's function for each circumferential harmonic is a summation over the natural waves of the shell. The finite element discretization in the radial direction allows the approach to be used for arbitrarily thick shells. The approach is benchmarked to results from an isotropic shell and numerical examples are given for a shell composed of a fiber-reinforced material. The numerical examples illustrate the effect of fiber orientation on the Green's function.     

Observations of an ion-driven instability in non-neutral plasmas confined on magnetic surfaces

The first detailed experimental study of an instability driven by the presence of a finite ion fraction in an electron-rich non-neutral plasma confined on magnetic surfaces is presented. The instability has a poloidal mode number m=1, implying that the parallel force balance of the electron fluid is broken and that the instability involves rotation of the entire plasma, equivalent to ion-resonant instabilities in Penning traps and toroidal field traps. The mode appears when the ion density exceeds approximately 10% of the electron density. The measured frequency decreases with increasing magnetic field strength, and increases with increasing radial electric field, showing that the instability is linked to the E x B flow of the electron plasma. The frequency does not, however, scale exactly with E/B, and it depends on the ion species that is introduced, implying that the instability consists of interacting perturbations of ions and electrons.     

Developments of the theory of spin fluctuations and spin fluctuation-induced superconductivity

Theory of spin fluctuations as developed in the past 30 years have played important roles in the theory of magnetism in metals, particularly in elucidating the properties around the magnetic instability or quantum critical points. Recently the theory has been extended to deal with the spin fluctuaion-mediated superconductivity with anisotropic order parameters in strongly correlated electron systems. These theoretical developments are briefly reviewed and the high temperature superconductivity of cuprates and organic and heavy electron superconductors are discussed in the light of these theories.     

Finite Larmor radius effect on thermosolutal instability of a plasma in porous medium

The thermosolutal instability of a plasma in porous medium is considered in the presence of finite Larmor radius effect. The finite Larmor radius, stable solute gradient and magnetic field introduce oscillatory modes in the systems which were nonexistent in their absence. For stationary convection, the finite Larmor radius and stable solute gradient have stabilizing effects on the thermosolutal instability in porous medium. In presence of finite Larmor radius effect, the medium permeability has a destabilizing (or stabilizing) effect and the magnetic field has a stabilizing (or destabilizing) effect under certain condition whereas in the absence of finite Larmor radius effect, the medium permeability and the magnetic field have destabilizing and stabilizing effects, respectively, on thermosolutal instability of a plasma in porous medium. The sufficient conditions for nonexistence of overstability are obtained.The financial assistance to Mr. Sunil in the form of Senior Research Fellowship of the Council of Scientific and Industrial Research (CSIR), New Delhi is gratefully acknowledged.     

Quarkonium correlators and spectral functions at zero and finite temperature from the Fermilab action

We study charmonium and bottomonium systems at zero and finite temperatures using lattice QCD with the Fermilab action on anisotropic lattices.Arrival of the final proofs: 18 July 2005PACS: 11.15.Ha, 11.10.Wx, 12.38.Mh, 25.75.Nq     

Synergetic Effects of Runaway Electron and Vertical Instability on the Wall Damage on HL-2A Tokamak

1 Generation of vertical instability Tokamak experiments show that the energy confinement time and performance are better, and the larger plasma current can be achieved for non-circular cross-sectional shape of plasma than circular cross-section. However, the external magnetic fields which are used to produce the non-circular cross sectional shape also cause the confined plasma to become unstable to small vertical displacement. In general, the ratio of elongation k is larger, the possibility of instability is more. In practice, this vertical displacement mode stabilized by feedback control system or other provided external radial magnetic field to balance out the plasma motion. Under some of situations the control system may be fail due to rapid growth rate of instability exceeding the ability of controlling. The plasma will then move vertically upwards or downwards depending upon the characteristics of instability and control failure.     

Scaling approach to anisotropic magnetic systems statics

Scaling laws are stated for anisotropic magnetic systems, where the anisotropy parameters are either scaled or held fixed. Combining the two ways of scaling, the critical behavior of thermodynamic quantities in anisotropic systems is determined. Particular attention is drawn to the temperature range where the anisotropy becomes important, and to the dependence there of the different quantities on the anisotropy parameters. In a transverse magnetic field the phase transition of an anisotropic magnet takes place along aλ-line. Assuming the singular part of the free enthalpy to depend on the distance from theλ-line, anomalous corrections to the transverse susceptibility and magnetization are calculated. For an experimental verification of many of the results, experiments including a variation of the anisotropy parameters or a finite transverse field are necessary.     

Magnetogravitational Instability of Anisotropic Plasma with Finite Ion Larmor and Generalized Polytrope Law

The effect of finite ion Larmor radius corrections on the propagation of small perturbations through self gravitating, anisotropic system with generalized polytrope law is investigated. The polytrope laws are considered for the pressure components in parallel and perpendicular directions to the magnetic field. The polytrope model proposed by Abraham-Shranuer can be reduced to CGL equations with double adiabatic equations of state and MHD set of equations with isothermal equation of state. The effects of FLR and polytrope indices are discussed on the gravitational, firehose and mirror instability. The critical Jeans wave numbers are found to depend on polytropic indices and derived for CGL and MHD cases. The FLR corrections are found effective in shorter wave length region and produce stabilizing influence. The condition of mirror instability is uninfluenced by FLR but dependent on polytropic indices.