Related papers: Spatial Statistics of Apollonian Gaskets

We investigate turbulent gas motions in spiral galaxies and their importance to star formation in far outer disks, where the column density is typically far below the critical value for spontaneous gravitational collapse. Following the…

We develop a theory of Sobolev orthogonal polynomials on the Sierpi\'nski gasket ($SG$). These orthogonal polynomials arise through the Gram-Schmidt orthogonalisation process applied on the set of monomials on $SG$ using several notions of…

A time-dependent model for pair creation in a pulsar magnetosphere is developed. It is argued that the parallel electric field that develops in a charge-starved region (a gap) of a pulsar magnetosphere oscillates with large amplitude.…

We analyse nonequilibrium phase transitions in microcavity polariton condensates trapped in optically induced annular potentials. We develop an analytic model for annular optical traps, which gives an intuitive interpretation for recent…

For two nearby pulsars, formed close to the galactic plane, their host open stellar clusters have been found.

Water vortices are known to develop polygon structures inside their cores. The apexes of the polygonal manifestations are the result of satellite vortices attached to the parent vortex. Exploiting the analogy between the shallow water…

We develop an analytical formalism to determine the statistical properties of a system consisting of an ensemble of vortices with random position in plane interacting with a turbulent field. We calculate the generating functional by…

Series of experiments on turbulent bubbly channel flows observed bubble clusters near the wall which can change large-scale flow structures. To gain insights into clustering mechanisms, we study the interaction of a pair of spherical…

The main result of this paper is an effective count for Apollonian circle packings that are either bounded or contain two parallel lines. We obtain this by proving an effective equidistribution of closed horospheres in the unit tangent…

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.…

Galactic accretion interacts in complex ways with gaseous halos, including galactic winds. As a result, observational diagnostics typically probe a range of intertwined physical phenomena. Because of this complexity, cosmological…

Theoretical studies on the response of interstellar gas to a gravitational potential disc with a quasi-stationary spiral arm pattern suggest that the gas experiences a sudden compression due to standing shock waves at spiral arms. This…

We study the self-organization of spherical particles in an oscillating flow through experiments inside an oscillating box. The interactions between the particles and the time-averaged (steady streaming) flow lead to the formation of either…

Hierarchical structure from stellar clusters, to subgroups, to associations and star complexes is discussed in the context of the Orion stellar grouping and its origin. The analogous structure in gas clouds is also reviewed, with an…

We use a Cartesian grid to simulate the flow of gas in a barred Galactic potential and investigate the effects of varying the sound speed in the gas and the resolution of the grid. For all sound speeds and resolutions, streamlines closely…

We have now accumulated a wealth of observations of the planet-formation environment and of mature planetary systems. These data allow us to test and refine theories of gas-giant planet formation by placing constraints on the conditions and…

It is often assumed that a warped galaxy can be modeled by a set of rings. This paper verifies numerically the validity of this assumption by the study of periodic orbits populating a heavy self-gravitating warped disk. The phase space…

We study the formation and growth of equilibrium clusters in a suspension of weakly-charged colloidal particles and small non-adsorbing polymers. The effective potential is characterised by a short-range attraction and a long-range…

The energetics and stability of dislocations, vacancies and, interstitials in the one-component plasma (OCP), where the charges interact with a log potential and move on the curved surface of a cylinder have been investigated numerically.…

Recent observations show that spiral galaxies are surrounded by extended gaseous halos as predicted by the hierarchical structure formation scenario. The origin and nature of extraplanar gas is often unclear since the halo is continuously…