Related papers: Focusing of nonlinear eccentric waves in astrophys…
We consider the evolution of a warped disc around a Kerr black hole, under conditions such that the warp propagates in a wavelike manner. This occurs when the dimensionless effective viscosity, alpha, that damps the warp is less than the…
The non-axisymmetric features observed in the discs of dwarf novae in outburst are usually considered to be spiral shocks, which are the non-linear relatives of tidally excited waves. This interpretation suffers from a number of problems.…
Warped astrophysical discs are usually treated as laminar viscous flows, which have anomalous properties when the disc is nearly Keplerian and the viscosity is small: fast horizontal shearing motions and large torques are generated, which…
Circumbinary disks are considered to exist in a wide variety of astrophysical objects, e.g., young binary stars, protoplanetary systems, and massive binary black hole systems in active galactic nuclei (AGNs). However, there is no definite…
The amplification of disk oscillations resulting from nonlinear resonant couplings between the oscillations and a disk deformation is examined. The disk is geometrically thin and general relativistic with a non-rotating central source. A…
The secular thickening of a discrete self-gravitating galactic disc is investigated using the inhomogeneous multi-component Balescu-Lenard equation. The thick WKB limit for the diffusion and drift coefficients is found using the epicyclic…
Observations of distorted discs have highlighted the ubiquity of warps in a variety of astrophysical contexts. This has been complemented by theoretical efforts to understand the dynamics of warp evolution. Despite significant efforts to…
The inspiral of a turbulent molecular cloud in the Galactic Centre may result in the formation of a small, dense and moderately eccentric gas disc around the supermassive black hole (SMBH). Such a disc is unstable to fragmentation and may…
A new description of the dynamics of warped accretion discs is presented. A theory of fully nonlinear, slowly varying bending waves is developed, involving a proper treatment of viscous fluid dynamics but neglecting self-gravitation. The…
We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative…
The Lagrange planetary equations are used to study to secular evolution of a small, eccentric satellite that orbits within a narrow gap in a broad, self-gravitating planetary ring. These equations show that the satellite's secular…
It is well known that Lagrangian dynamical systems naturally arise in describing wave front dynamics in the limit of short waves (which is called pseudoclassical limit or limit of geometrical optics). Wave fronts are the surfaces of…
We simulate the viscous evolution of an accretion disc around a spinning black hole. In general any such disc is misaligned, and warped by the Lense-Thirring effect. Unlike previous studies we use effective viscosities constrained to be…
Interaction of spiral density waves with stars in the vicinity of the inner Lindblad resonance in galactic discs is investigated using the linear perturbation theory and the leading orders in the epicyclic and WKB approximations. In analogy…
We discuss the propagation of electromagnetic waves on a rectangular lattice of polarizable point dipoles. For wavelengths long compared to the lattice spacing, we obtain the dispersion relation in terms of the lattice spacing and the…
Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered. For parameters close to the vortex limit, and for a system of spiral waves with well-separated centres, laws of motion of the…
A theory is developed for the dynamics of eccentric perturbations $[\propto \exp(\pm i\phi)]$ of a disk galaxy residing in a spherical dark matter halo and including a spherical bulge component. The disk is represented as a large number $N$…
In this paper, we study the nonlinear dispersive waves including the rarefaction and dispersive shock waves in the discrete modified KdV equation through the numerical simulations of the dispersive Riemann problems. In particular, we…
A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson…
We investigate the elastic normal modes of two-dimensional media with broken time-reversal and parity symmetries due to a Lorentz term. Our starting point is an elasticity theory that captures the low-energy physics of a diverse range of…