Related papers: Perturbation of mass accretion rate, associated ac…
This paper is mainly concerned with the inverse scattering problem of determining the unknown potential for the classical Schr\"odinger equation in two and three dimensions. We establish the increasing stability of the inverse scattering…
It is known that a localized vortex can have two specific mechanisms of interaction with the ambient flow. The first mechanism is associated with acoustic radiation, which is accompanied by a loss of energy and causes instability in the…
Accretion disc outbursts are re-occurring events observed in various astrophysical systems, including X-ray binaries and cataclysmic variables. These outbursts are characterized by a sudden increase in luminosity due to various…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
We study analytically and numerically the stability of the pressure-less, viscously spreading accretion ring. We show that the ring is unstable to small non-axisymmetric perturbations. To perform the perturbation analysis of the ring we use…
The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple scales…
In earlier work we identified a global, non-axisymmetric instability associated with the presence of an extreme in the radial profile of the key function ${\cal L}(r) \equiv (\Sigma \Omega/\kappa^2) S^{2/\Gamma}$ in a thin, inviscid,…
We study the stability of a type of stratified flows of the two dimensional inviscid incompressible MHD equations with velocity damping. The exponential stability for the perturbation near certain stratified flow is investigated in a…
On the basis of the competing cubic-quintic nonlinearity model, stability (instability) of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the…
Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…
We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, in [10] the authors have derived a pseudo-differential equation…
We study the perturbations of two classes of static black ellipsoid solutions of four dimensional vacuum Einstein equations. Such solutions are described by generic off--diagonal metrics which are generated by anholonomic transforms of…
The broad-band variability of many accreting systems displays characteristic structure; log-normal flux distributions, RMS-flux relations, and long inter-band lags. These characteristics are usually interpreted as inward propagating…
We analyse the stability of periodic, travelling-wave solutions to the Kawahara equation and some of its generalizations. We determine the parameter regime for which these solutions can exhibit resonance. By examining perturbations of…
We develop a mean-field model to examine the stability of a `quasi-2D suspension' of elongated particles embedded within a viscous membrane. This geometry represents several biological and synthetic settings, and we reveal mechanisms by…
We present a novel space-time isogeometric discretization of the acoustic wave equation in second-order formulation that is intrinsically unconditionally stable. The method relies on a variational framework inspired by [Walkington 2014],…
We initiate the study of stability of solutions of the 2D inviscid incompressible porous medium equation (IPM). We begin by classifying all stationary solutions of the inviscid IPM under mild conditions. We then prove some linear stability…
We investigate the 2D instability recently discussed by Gallet et al. (2010) and Ilin \& Morgulis (2013) which arises when a radial crossflow is imposed on a centrifugally-stable swirling flow. By finding a simpler rectilinear example of…
The effect of particles that undergo strong diffusive-shock-acceleration on the stability of the accelerating shock is investigated. A two-fluid model is employed in which the accelerated particles are treated as a fluid whose effect is…
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…