Related papers: A Dynamical Systems Approach to an Inviscid and Th…
Transonicity in a spherically symmetric accreting system has been considered in both the stationary and the dynamic regimes. The stationary flow, set up as a dynamical system, has been shown to be greatly unstable to even the minutest…
This work examines the conditions for asymptotic and exponential convergence of saddle flow dynamics of convex-concave functions. First, we propose an observability-based certificate for asymptotic convergence, directly bridging the gap…
Models of Soft X--ray Transients are presented and compared with observations. The importance of inner advection--dominated flows in quiescent transient sources is discussed, as well as the problem of global stability of the standard outer…
We have developed a three-dimensional numerical model and applied it to simulate plasma flows in semi-detached binary systems whose accretor possesses a strong intrinsic magnetic field. The model is based on the assumption that the plasma…
We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of…
We present time-dependent solutions of thin, supersonic accretion flows near a black hole and compare them with analytical solutions. Such flows of inviscid, adiabatic gas are characterized by the specific angular momentum and the specific…
We study the coupled disc-jet system around the black hole where the outflow solutions are obtained in terms of the inflow parameters. We observe that an advective accretion disc can eject outflows/jets for wide range of viscosity…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
Consideration is given to the effects of inhomogeneous shear flow (both regular and chaotic) on nematic liquid crystals in a planar geometry. The Landau--de Gennes equation coupled to an externally-prescribed flow field is the basis for the…
We introduce the Discrete Inverse Continuity Equation (DICE) method, a generative modeling approach that learns the evolution of a stochastic process from given sample populations at a finite number of time points. Models learned with DICE…
I review the observational evidence for stream-fed accretion in intermediate polars. Recent work on the discless system V2400 Oph confirms the pole-flipping model of stream-fed accretion, but this applies only to a minority of the flow. The…
We study the development of finite eccentricity in accretion disks in close binary systems using a two-dimensional grid-based numerical scheme. We perform detailed parameter studies to explore the dependence on viscosity, disk aspect ratio,…
Here we present a multiscale method to calculate the saddle point associated with the effective dynamics arising from a stochastic system which couples slow deterministic drift and fast stochastic dynamics. This problem is motivated by the…
Models and simulations of the flow of thin films of fluids have many important applications in industrial and natural processes. We consider the motion of a thin layer of an incompressible, Newtonian fluid over an arbitrary solid,…
In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of…
We consider a third order non-autonomous ODE that arises as a model of fluid accumulation in a two dimensional thin-film flow driven by surface tension and gravity. With the appropriate matching conditions, the equation describes the inner…
In this paper, we study the local behaviour of solutions near the fixed points of a reaction-diffusion equation with discontinuous nonlinearity. By employing an appropriate linearization around the fixed points, which involves the Dirac…
We study the stability of poloidal magnetic fields anchored in a thin accretion disc. The two-dimensional hydrodynamics in the disc plane is followed by a grid-based numerical simulation including the vertically integrated magnetic forces.…
In this article we consider the inviscid two-dimensional shallow water equations in a rectangle. The flow occurs near a stationary solution in the so called supercritical regime and we establish short term existence of smooth solutions for…
We develop an analytical model for the accretion and gravitational drag on a point mass that moves hypersonically in the midplane of a gaseous disk with a Gaussian vertical density stratification. Such a model is of interest for studying…