Related papers: Radially anisotropic systems with $r^{-\alpha}$ fo…
The so-called ``symplectic method'' is used for studying the linear stability of a self-gravitating collisionless stellar system, in which the particles are also submitted to an external potential. The system is steady and spherically…
We consider the dynamics of porous icy dust aggregates in a turbulent gas disk and investigate the stability of the disk. We evaluate the random velocity of porous dust aggregates by considering their self-gravity, collisions, aerodynamic…
The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed…
We investigate the linear axisymmetric viscous overstability in dense planetary rings with typical values of the dynamical optical depth $\tau\gtrsim 0.5$. We develop a granular flow model which accounts for the particulate nature of a…
We study the linear and nonlinear stability of relative equilibria in the planar N-vortex problem, adapting the approach of Moeckel from the corresponding problem in celestial mechanics. After establishing some general theory, a topological…
Magnetic fields vary in complexity for different stars. The stability of dipolar magnetic fields is known to depend on different quantities, e.g., the stellar rotation, the stratification, and the intensity of convective motions. Here, we…
Hydrodynamic instability of a gravity-driven flow down an inclined plane is investigated in the presence of a floating elastic plate which rests on the top surface of the flow. Linear instability of the system with respect to infinitesimal…
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schr\"odinger…
The magneto-rotational instability (MRI) is the most likely mechanism for transportation of angular momentum and dissipation of energy within hot, ionized accretion discs. This instability is produced through the interactions of a…
The innermost stable circular orbit (ISCO) offers a fundamental test of spacetime structure. However, its behavior in higher-dimensional black holes influenced by anisotropic energy-momentum tensors remains insufficiently explored. In this…
In the era of gravitational wave astronomy, radial oscillations hold significant potential for not only uncovering the microphysics behind the internal structure but also investigating the stability of neutron stars (NSs). We start by…
Oscillatory flows have become an indispensable tool in microfluidics, inducing inertial effects for displacing and manipulating fluid-borne objects in a reliable, controllable, and label-free fashion. However, the quantitative description…
The issues of robust stability for two types of uncertain fractional-order systems of order $\alpha \in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust…
A stable approach for integrating the impedance matrix in cylindrical, radial inhomogeneous structures is developed and studied. A Stroh-like system using the time-harmonic displacement-traction state vector is used to derive the Riccati…
Roughness and orientational order in thin films of anisotropic particles are investigated using kinetic Monte Carlo simulations on a cubic lattice. Anisotropic next-neighbor interactions between the lattice particles were chosen to mimic…
The linear dynamics and instability mechanisms of double-layered weakly viscoelastic fluid flowing over an inclined plane are analyzed in the presence of insoluble surfactant at both the free surface and interface. The constitutive equation…
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,…
This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits…
In general relativity, it has been shown that radiation-supported atmospheres exist outside the surface of a radiating spherical body close to a radius where the gravitational and radiative forces balance each other. We calculate the…
We consider circular particle motion under the action of an unspecified force in a static spherically symmetric spacetime. We derive the machinery that allows one to find the force acting on a circular particle and deduce whether its…