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We discuss the basic principles of a self-organization of a finite number of charged particles interacting via the 1/r Coulomb potential in a disk geometry. Our approach is based on the cyclic symmetry and periodicity of the Coulomb…

We have found that the minimum energy configuration of $N=395$ charges confined in a disk and interacting via the Coulomb potential, reported by Cerkaski et al. in Ref.~\cite{Cerkaski15} is not a global minimum of the total electrostatic…

The basic principles of self-organization of one-component charged particles, confined in disk and circular parabolic potentials, are proposed. A system of equations is derived, that allows us to determine equilibrium configurations for an…

We investigate the classical ground state of a large number of charges confined inside a disk and interacting via the Coulomb potential. By realizing the important role that the peripheral charges play in determining the lowest energy…

In this paper, we develop the analysis of a two-dimensional magnetohydrodynamical configuration for an axially symmetric and rotating plasma (embedded in a dipole like magnetic field), modeling the structure of a thin accretion disk around…

We use direct numerical simulations to study the evolution, or relaxation, of magnetic configurations to an equilibrium state. We use the full single-fluid equations of motion for a magnetized, non-resistive, but viscous fluid; and a…

We analyze a two dimensional viscoresistive magnetohydrodynamical (MHD) model for a thin accretion disk which reconciles the crystalline structure outlined in [Coppi(2005), Coppi and Rousseau(2006)] with real microscopic and macroscopic…

Most analytic work to date on protostellar disks has focused on those in isolation from their environments. However, observations are now beginning to probe the earliest, most embedded phases of star formation, during which disks are…

The effect of radial vibrations on the properties of one or two disks confined to a circular trap in contact with a thermal reservoir are investigated. The vibrational amplitudes and energies are assumed to be quantized, with the motions…

We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or micro-scale particles where rolling is an approximation for strong static friction. We consider the simplest possible…

Our focus is to study constellations of disjoint disks in the hyperbolic space, the unit disk equipped with the hyperbolic metric. Each constellation corresponds to a set $E$ which is the union of $m>2$ disks with hyperbolic radii $r_j>0,…

We investigate the structural properties of a two-dimensional system of ellipsoidal particles carrying a linear quadrupole moment in their center. These particles represent a simple model for a variety of uncharged, non-polar conjugated…

The exact superposition of a central static black hole with surrounding thin disk in presence of a magnetic field is investigated. We consider two models of disk, one of infinite extension based on a Kuzmin-Chazy-Curzon metric and other…

We study the ascending motion of a disk rolling on an incline when its center of mass lies outside the disk axis. The problem is suitable as laboratory project for a first course in mechanics at the undergraduate level and goes beyond…

We study the evolution of a system consisting of two protoplanets still embedded in a protoplanetary disk. Results of two different numerical approaches are presented. In the first kind of model the motion of the disk material is followed…

We consider warped equilibrium configurations for stellar and gaseous disks in the Keplerian force-field of a supermassive black hole, assuming that the self-gravity of the disk provides the only acting torques. Modeling the disk as a…

We provide a new analysis of the system of partial differential equations describing the radial and vertical equilibria of the plasma in accretion disks. In particular, we show that the partial differential system can be separated once a…

We show that a jammed packing of disks with generic radii, in a generic container, is such that the minimal number of contacts occurs and there is only one dimension of equilibrium stresses. We also point out some connections to packings…

We present a new, simple, fast algorithm to numerically evolve disks of inelastically colliding particles surrounding a central star. Our algorithm adds negligible computational cost to the fastest existing collisionless N-body codes, and…

We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction $\phi_J$. For configurations with a fixed isotropic global stress tensor, we compute the…