A new formulation of the viscosity in planetary rings

We present a new formulation of the viscosity in planetary rings, where particles interact through their gravitational forces and direct collisions. In the previous studies on the viscosity in self-gravitating rings, the viscosity consists of three components, which are defined separately in different ways. The complex definitions make it difficult to evaluate the viscosity in N-body simulation of rings. In our new formulation, the viscosity is expressed in terms of changes in orbital elements of particles due to particle interactions. This makes the expression of the viscosity simple. The new formulation gives a simple way to evaluate the viscosity in N-body simulation. We find that for practical evaluation of the viscosity of planetary rings, only energy dissipation at direct inelastic collisions is needed.For tenuous particle disks (i.e., optically thin disks), we further derive a formula of the viscosity. The formula requires only a numerical coefficient that can be obtained from three-body calculation. Since planetesimal disks are also tenuous, the viscosity in planetesimal disks can be also obtained from this formula. In a subsequent paper, we will evaluate this coefficient through three-body calculation and obtain the viscosity for a wide range of parameters such as the restitution coefficient and the radial location in rings.     

含粘滞性弱磁化吸积盘的轴对称脉动不稳定性

本文讨论了一种含扩散型粘滞的弱磁化等温吸积盘模型，在此模型中研究了扩散型粘滞、垂向磁场Bz和环向磁场B对轴对称脉动不稳定性的影响．结果表明，对于轴对称扰动，一般情况下盘内存在四种轴对称振荡模式．其中二种模式是脉动不稳定的，粘滞和磁场对它们表现为非稳因素；而另外二种模式是稳定的，粘滞和磁场对它们表现为致稳因素．此外我们还注意到，Bz和B主要影响近轴向的脉动不稳定性，扩散型弱粘滞主要影响径向脉动不稳定性．     

Five dimensional bulk viscous cosmological model with wet dark fluid in general relativity

In this paper, we have constructed a five dimensional LRS Bianchi type I cosmological model with wet dark fluid (WDF) in general relativity with the matter field described as bulk viscosity. It is found that in presence of bulk viscosity an inflationary effective stiff fluid cosmological model is obtained, whereas in absence of bulk viscosity the wet dark fluid degenerate to stiff fluid. Some physical and geometrical properties of the model are also discussed.     

String cosmology with magnetized bulk viscous fluid in Bianchi I universe

The objective of the present paper is to study an anisotropic Bianchi-I cosmological model filled with bulk viscous fluid and magnetic field in string cosmology. The magnetic field is due to an electric current produced along the x-axis. The expansion in the model is considered to be proportional to one of the components of the shear tensor. We obtain two different quadrature forms of volume scale factor by considering two different relations between bulk viscosity and expansion scalar. We discuss the behavior of the classical potential with respect to the volume scale factor in the presence or absence of magnetic field and bulk viscosity in each case. We observe the role of bulk viscosity on the classical potential and also on the choices of bulk viscous pressure. By introduction of magnetic field or bulk viscosity or both into the model it results in changes in the potential as well as in volume scale factors. The physical and geometrical aspects of the solutions are discussed in detail.     

Artificial viscosity in simulation of shock waves by smoothed particle hydrodynamics

This paper reconsiders artificial viscosity in smoothed particle hydrodynamics in order to prevent interparticle penetration, unwanted heating, and unphysical solutions. The coefficients in the Monaghan’s standard artificial viscosity are considered as a time variable, and we propose a restriction on them such that we avoid the undesired effects in the subsonic regions. We use the shock formation in adiabatic and isothermal cases to study the ability of this modified artificial viscosity recipe. Our computer experiments show that the proposal appears to work and the accuracy of this restriction is acceptable.     

Viscous inflationary universe models

The research on viscous cosmological models is reviewed and carried further. Inflationary cosmological models of Bianchi type-I with shear, bulk, and nonlinear viscosity are studied. The inflation field energy is represented by a two-components cosmic fluid consisting of a vacuum fluid and a Zel'dovich fluid. It is shown that there exist models in which the viscous Zel'dovich fluid removes the initial singularity of the corresponding viscosity free models. The mean expansion of a Zel'dovich dominated unvierse is found to be independent of shear viscosity and anisotropy. Bulk viscosity and shear viscosity cause exponential decay of anisotropy, while nonlinear viscosity causes power-law decay of anisotropy.     

Behaviour of dissipative accretion flows around black holes

We investigate the behaviour of dissipative accreting matter close to a black hole, as this provides important observational features of galactic and extragalactic black hole candidates. We find a complete set of global solutions in the presence of viscosity and synchrotron cooling. We show that advective accretion flow can have a standing shock wave and the dynamics of the shock is controlled by the dissipation parameters (both viscosity and cooling). We study the effective region of the parameter space for standing as well as oscillating shock. We find that the shock front always moves towards the black hole as the dissipation parameters are increased. However, viscosity and cooling have opposite effects in deciding the solution topologies. We obtain two critical cooling parameters that separate the nature of the accretion solution.     

Expanding Universe with bulk and shear viscosity in conformally flat coordinates

Conformally flat line-elements are applied to imperfect fluids in cosmology. Explicit solutions of the field equations are given for an equation of state for which the pressure is proportional to the density. Both the isotropic case (for which the shear viscosity vanishes) and the non-isotropic case are considered and expressions derived for the appropriate coefficients of shear and bulk viscosity, as well as density.     

Extended Chaplygin gas equation of state with bulk and shear viscosities

In this note extended Chaplygin gas equation of state includes bulk and shear viscosities suggested. Bulk viscosity assumed as power law form of density and shear viscosity considered as a constant. We study evolution of dark energy density numerically for several forms of scale factor, and analytically under some assumptions corresponding to early universe. We found our model is stable for infinitesimal viscous parameters.     

Tidal dissipation in small viscoelastic ice moons: The case of Enceladus

Tidal dissipation is investigated in a viscoelastic homogeneous sphere having the orbital and physical characteristics of the icy inner satellite of Saturn, Enceladus. The dissipated power is calculated for Kelvin-Voigt and Maxwell rheologies, whose dissipation function can be expressed in terms of viscosity. Expressions for the dissipated power as a function of viscosity is calculated in both cases and compared to the expression found for a lossy elastic body. A physical law relating viscosity of water ice to temperature and grain size is introduced and the feedback between dissipated power and temperature is investigated. It is found that tidal dissipation with current orbital eccentricity alone cannot account for the surface activity observed on Enceladus, if it is composed of water ice.     

Finite Larmor radius effects on the stability of a stratified plasma

The hydromagnetic stability of a cosmical plasma interacting with neutral gas has been studied to include the effects of ion viscosity and the finiteness of the ion Larmor radius. It is first shown that the system is characterized by a variational principle. The explicit solution has then been obtained, by making use of the existence of the variational principle, for a semi-infinite plasma in which the density is stratified, exponentially, along the vertical. It is found that FLR, ion viscosity as well as neutral gas friction have all a stabilizing influence.     

The effects of parallel and perpendicular viscosity on resistive ballooning modes in line-tied coronal magnetic fields

The study of resistive ballooning instabilities in line-tied coronal magnetic fields is extended by including viscosity in the stability analysis. The equations that govern the resistive ballooning instabilities are derived and the effects of parallel and perpendicular viscosity are included using Braginskii's stress tensor. Numerical solutions to these equations are obtained under the rigid wall boundary conditions for arcades with cylindrically-symmetric magnetic fields. It is found that viscosity has a stabilizing effect on the resistive ballooning instabilities with perpendicular viscosity being more important by far than parallel viscosity. The strong stabilizing effect of perpendicular viscosity can lead to complete stabilization for realistic values of the equilibrium quantities.Research Assistant at the Belgian Fund for Scientific Research.     

Rheological structure of the mantle of a super-Earth: Some insights from mineral physics

The rheological properties of the mantle of super-Earths have important influences on their orbital and thermal evolution. Mineral physics observations are reviewed to obtain some insights into the rheological properties of deep mantles of these planets where pressure can be as high as ∼1 TPa. It is shown that, in contrast to a conventional view that the viscosity of a solid increases with pressure (at a fixed temperature), viscosity will decrease with pressure (and depth) when pressure exceeds ∼0.1 TPa. The causes for pressure-weakening include: (i) the transition in diffusion mechanisms from vacancy to interstitial mechanism (at ∼0.1 TPa), (ii) the phase transition in MgO from B1 to B2 structure (at ∼0.5 TPa), (iii) the dissociation of MgSiO₃ into MgO and SiO₂ (at ∼1 TPa), and (iv) the transition to the metallic state (at ∼1 TPa). Some (or all) of them individually or in combination reduce the effective viscosity of constituent materials in the deep interior of super-Earths. Taken together, super-Earths are likely to have low viscosity deep mantle by at least 2-3 orders of magnitude less than the maximum viscosity in the lower mantle of Earth. Because viscosity likely decreases with pressure above ∼0.1 TPa (in addition to higher temperatures for larger planets), deep mantle viscosity of super-Earths will decrease with increasing planetary mass. The inferred low viscosity of the deep mantle results in high tidal dissipation and resultant rapid orbital evolution, and affects thermal history and hence generation of the magnetic field and the style of mantle convection.     

Viscous cosmological models with particle creation in Brans-Dicke theory

The effect of bulk viscosity on the evolution of the spatially flat Friedmann-Robertson-Walker models in the context of open thermodynamical systems, which allow particle creation, is analyzed within the framework of Brans-Dicke theory. Particle creation and bulk viscosity have been considered as separated irreversible processes. To accommodate the viscous pressure and creation pressure, which is associated with creation of matter out of gravitational field, the energy-momentum tensor is modified. Dynamical behaviour of the models have been discussed.     

A gravitationally non-degenerate cosmological model with expanding and shearing viscous fluid in general relativity

The object of this paper is to investigate the behaviour of viscosity in a cosmological model, in which the coefficient of shear viscosity is assumed to be proportional to rate of expansion in the model. The behaviour of the model in the absence of shear viscosity is also discussed.     

Exploding radiating viscous spheres in general relativity

The influence of viscosity on the gravitational collapse in radiating fluid spheres is investigated. The interior solution is matched with the Vaidya metric at the boundary of the fluid distribution. Prescribing an equation of state to take into account the degree of induced anisotropy by the viscosity and using the Herrera, Jiménez and Ruggeri method, we obtain an explicit Tolman VI-like exploding model. The sphere explodes more violently when the anisotropy due to the viscosity is smaller. The shear viscosity diminishes with the expansion of the distribution of matter.     

Eddy viscosity and turbulent Schmidt number by kink-type instabilities of toroidal magnetic fields

The potential of the non-axisymmetric magnetic instability to transport angular momentum and to mix chemicals is probed considering the stability of a nearly uniform toroidal field between conducting cylinders with different rotation rates. The fluid between the cylinders is assumed as incompressible and to be of uniform density. With a linear theory, the neutral-stability maps for   m = 1  are computed. Rigid rotation must be sub-Alfvénic to allow instability, while for differential rotation also an unstable domain with faster rotation exists [azimuthal magnetorotational instability (AMRI)]. The rotational quenching of the magnetic instability is strongest for magnetic Prandtl number of the order of unity.
The effective angular momentum transport by the instability is directed outwards for subrotation. The resulting magnetic-induced eddy viscosity exceeds the microscopic values by factors of 10–100. This is only true for AMRI; in the opposite case of Tayler instability, the viscosity results are very small.
The same instability also quenches concentration gradients of chemicals by dynamic fluctuations. The corresponding diffusion coefficient always remains smaller than the magnetic-generated eddy viscosity. A Schmidt number of the order of 30 is found as the ratio of the effective viscosity and the diffusion coefficient. For not too strong magnetic fields in the radiation zone of young solar-type stars, the magnetic instability transports much more angular momentum than that it mixes chemicals.     

Imperfect fluid Friedmannian cosmology

The bulk viscosity is introduced into the frame of ordinary Friedmannian cosmology (under highly idealized assumption of the constant coefficient of bulk viscosity). Explicit solutions are given for the viscous flat universe filled with the dust-substratum and for the viscous radiative universe. The problem, how does the introduction of viscosity affect the appearance of singularity, is briefly discussed.     

Viscous fluid universe filled with stiff fluid in general relativity

We have investigated two stiff-fluid models in which the material distribution is that of viscous fluid. In the first model, the coefficient of shear viscosity is assumed to be constant while in the second model the coefficient of shear viscosity is proportional to the rate of expansion in the model. The paper also discusses some physical and geometrical aspects of the model. The behaviour of the model in absence of viscosity is also discussed.