Related papers: On the Stability of Electrostatic Orbits
We analyze the stability of relativistic, quasi-equilibrium binary neutron stars in synchronous circular orbit. We explore stability against radial collapse to black holes prior to merger, and against orbital plunge. We apply theorems based…
The structure of the hot downstream region below a radiative accretion shock, such as that of an accreting compact object, may oscillate due to a global thermal instability. The oscillatory behaviour depends on the functional forms of the…
The different types of orbits in the classical problem of two particles with equal masses and opposite charges on a plane under the influence of a constant orthogonal magnetic field are classified. The equations of the system are reduced to…
A general study of the stability of equatorial circular orbits in static axially symmetric gravitating systems is presented. Important circular geodesics as the marginally stable orbit, the marginally bounded orbit and the photon orbit are…
We study the nonlinear classical dynamics of an electron confined in a double dot potential and subjected to a spin-orbit coupling and a constant external magnetic field. It is shown that due to the spin orbit coupling, the energy can be…
We investigate the dynamics in a galactic potential with two reflection symmetries. The phase-space structure of the real system is approximated with a resonant detuned normal form constructed with the method based on the Lie transform.…
We study a crystal composed of active units governed by self-alignment and chirality. The first mechanism acts as an effective torque that aligns the particle orientation with its velocity, while the second drives individual particles along…
We present exact closed-form expressions and complete asymptotic expansions for the electrostatic force between two charged conducting spheres of arbitrary sizes. Using asymptotic expansions of the force we confirm that even like-charged…
We study the dynamics of $N$ point vortices on a rotating sphere. The Hamiltonian system becomes infinite dimensional due to the non-uniform background vorticity coming from the Coriolis force. We prove that a relative equilibrium formed of…
Differential rotation occurs in conducting flows in accretion disks and planetary cores. In such systems, the magnetorotational instability can arise from coupling Lorentz and centrifugal forces to cause large radial angular momentum…
Two point charges are placed in a spherical dielectric core-shell embedded in a dielectric environment, one of the charges being located in the core and the other in the shell. The core, shell, and environment are characterized by different…
Instabilities and strong dynamical interactions between several giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems. In particular, dynamical instabilities would…
Since its prediction fifteen years ago, electro-osmotic instability has been attributed to non-equilibrium electro-osmosis related to the extended space charge which develops at the limiting current in the course of concentration…
In the year 2002 publications of A.V.M. Khachatourian and A.O. Wistrom were released, in which the existence of an electrostatic torque has been claimed. This moment of force should act in a three sphere configuration, where one sphere is…
We investigated the orbital evolution of satellite galaxies using numerical simulations. It has been long believed that the orbit suffers circularization due to the dynamical friction from the galactic halo during orbital decay. This…
Near a black hole or an ultracompact star, motion of particles is governed by strong gravitational field. Electrically charged particles feel also electromagnetic force arising due to currents inside the star or plasma circling around. We…
We investigate how stable circular orbits around a main compact object appear depending on the presence of a second one by using the Majumudar--Papapetrou dihole spacetime, which consists of the two extremal Reissner--Nordstr\" om black…
In classical electrodynamics for rotating with variable angular velocity charged rigid sphere are found: the exact values of electromagnetic fields, the flux of radiating energy and the exact integral equation of rotation including the…
We find an exact solution for the stability limit of relativistic charged spheres for the case of constant gravitational mass density and constant charge density. We argue that this provides an absolute stability limit for any relativistic…
Let $\Omega_0$ denote the unit ball of $\mathbb{R}^N$ ($N\ge 2$) centered at the origin. We suppose that $\Omega_0$ contains a core, given by a smaller concentric ball $D_0$, made of a (possibly) different material. We discover that,…