Related papers: A Dynamical Systems Approach to an Inviscid and Th…
We present an analytic, quasi-local model for accretion discs threaded by net, vertical magnetic flux. In a simple slab geometry and ignoring stochastic mean-field dynamo effects, we calculate the large-scale field resulting from the…
Saddle fixed points are the centerpieces of complicated dynamics in a system. The one-dimensional stable and unstable manifolds of these saddle-points are crucial to understanding the dynamics of such systems. While the problem of sketching…
Analytical expressions for coordinates of stationary points and conditions for their existence in the ABC flow are received. The type of the stationary points is shown analytically to be saddle-node. Exact expressions for eigenvalues and…
Accretion disk instabilities are briefly reviewed. Some details are given to the short-wavelength thermal instabilities and the convective instabilities. Time-dependent calculations of two-dimensional advection-dominated accretion flows are…
Using existing, forward-in-time integration schemes, we demonstrate that it is possible to compute unstable, saddle-type fixed points of stiff systems of ODEs when the stable compenents are fast (i.e., rapidly damped) while the unstable…
This is an introduction to models of accretion discs around black holes. After a presentation of the non-relativistic equations describing the structure and evolution of geometrically thin accretion discs we discuss their steady-state…
We present solutions to the relativistic thin disc evolutionary equation using a modified description of the mean fluid flow within the disc. The model takes into account the effects of sub-circular velocities in the innermost disc regions,…
Two-dimensional (axially symmetric) numerical hydrodynamical calculations of accretion flows which cannot cool through emission of radiation are presented. The calculations begin from an equilibrium configuration consisting of a thick torus…
Numerical, two-dimensional, time-dependent hydrodynamical models of geometrically thick accretion discs around black holes are presented. Accretion flows with non-effective radiation cooling (ADAFs) can be both convectively stable or…
An analytic solution is presented to the three-dimensional problem of steady axisymmetric fluid flow through an accretion disk. The solution has been obtained through a systematic expansion in the small parameter epsilon =H/R (the ratio of…
The article provides an analytical solution of the Navier-Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of…
Realization of the stationary integral solutions of steady state transonic accretion flow in spherical symmetry helps to understand accretion phenomena on various astrophysical objects. In recent years, attempts have been made to study…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies…
Nonlinear time-dependent calculations have been carried out in order to study the evolution of the thermal instability for optically thick, transonic, slim accretion discs around black holes. In the present calculations we have investigated…
A new class of critical points, termed as perpetual points, where acceleration becomes zero but the velocity remains non-zero, are observed in dynamical systems. The velocity at these points is either maximum or minimum or of inflection…
Consider the 3D flow of a viscous Newtonian fluid upon a curved 2D substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a comprehensive model of the dynamics of the film, the model being…
We study the rheology of a suspension of soft deformable droplets subjected to a pressure-driven flow. Through computer simulations, we measure the apparent viscosity as a function of droplet concentration and pressure gradient, and provide…
The properties of axisymmetric accretion flows of cold adiabatic gas with zero total energy in the vicinity of a Newtonian point mass are characterized by a single dimensionless parameter, the thickness of incoming flow. In the limit of…
Using simple arguments we show that the canonical thin keplerian accretion disks cannot smoothly match any plain advection dominated flow (ADAF) model. By 'plain' ADAF model we mean the ones with zero cooling. The existence of sonic points…