Related papers: Statistical Regularity of Apollonian Gaskets
Recently Usov's mechanism of pair creation on the surface of compact astrophysical objects has been revisited [1] with a conclusion that the pair creation rate was previously underestimated in the literature by nearly two orders of…
An analytic theory is developed for the density of states oscillations in quantum wells in a magnetic field which is tilted with respect to the barrier planes. The main oscillations are found to come from the simplest one or two-bounce…
We define the correlation of holes on the triangular lattice under periodic boundary conditions and study its asymptotics as the distances between the holes grow to infinity. We prove that the joint correlation of an arbitrary collection of…
Let n points be taken at random on a circle of unit circumference and clockwise ordered. Uniform spacings are defined as the clockwise arc-lengths between the successive points from this sample. We are interested in the asymptotic behavior…
We study orthogonal polynomial systems arising from general pre-Hilbert inner products on polynomial spaces, beyond the classical framework of measures. To each such inner product we associate a canonical Laplacian defined from an abstract…
In this paper we study the dynamics near the equilibrium point of a family of Hamiltonian systems in the neighborhood of a $0^2 iw$ resonance. The existence of a family of periodic orbits surrounding the equilibrium is well-known and we…
A few years ago we identified a recursion that works directly with the gaps among the generators in each stage of Eratosthenes sieve. This recursion provides explicit enumerations of sequences of gaps among the generators, which sequences…
Galaxies must form and evolve via the acquisition of gas from the intergalactic environment, however the way this gas accretion takes place is still poorly understood. Star-forming galaxies are surrounded by multiphase halos that appear to…
Polar ring galaxies are peculiar systems in which a gas rich, nearly polar ring surrounds an early-type or elliptical host galaxy. Two formation scenarios for these objects have been proposed: they are thought to form either in major galaxy…
We have developed a two-dimensional orbit averaged Fokker-Planck model of stellar clusters which expands on spherically symmetric one-dimensional models to include rotation and ellipticity. Physical effects such as collisions, finite…
The existence of the limiting pair correlation for angles between reciprocal geodesics on the modular surface is established. An explicit formula is provided, which captures geometric information about the length of reciprocal geodesics, as…
Time-dependent Stark-Zeeman systems describe the motion of an electron attracted by a proton subject to a magnetic and a time-dependent electric field. For instance the study of the dynamics of a gateway around the moon which is subject to…
It is generally assumed that gas in a galactic disk follows closely non self-intersecting periodic stellar orbits. In order to test this common assumption, we have performed MHD simulations of a galactic-like disk under the influence of a…
We carried out 2.5-dimensional resistive MHD simulations to study the formation mechanism of molecular loops observed by Fukui et al. (2006) at Galactic central region. Since it is hard to form molecular loops by uplifting dense molecular…
We describe new arithmetic invariants for pairs of torus orbits on groups isogenous to an inner form of $\mathbf{PGL}_n$ over a number field. These invariants are constructed by studying the double quotient of a linear algebraic group by a…
It is widely accepted that shell galaxies form as a result of a merger between an elliptical and a small disk galaxy. Simulations of the stellar component have shown that the shells are created either by ``phase-wrapping'' of debris on…
We demonstrate the existence of stable collective excitation in the form of "supersolitons" propagating through chains of solitons with alternating signs (i.e., Newton's cradles built of solitons) in nonlinear optical couplers, including…
We develop the theory of arrangements of spheres. Consider a finite collection of codimension-$1$ subspheres in a positive-dimensional sphere. There are two posets associated with this collection: the poset of faces and the poset of…
A Gilbert tessellation arises by letting linear segments (cracks) in the plane unfold in time with constant speed, starting from a homogeneous Poisson point process of germs in randomly chosen directions. Whenever a growing edge hits an…
Self_organization of hydrogen bubbles is reported under etching of metallic Aluminum in a weakly basic solution. The ascending gas bubbles drift to the areas with higher density of bubbles due to pressure difference. As a result, ascending…