Region of the anomalous compression under Bondi-Hoyle accretion

We investigate the properties of an axisymmetric non-magnetized gas flow without angular momentum on a small compact object, in particular, on a Schwarzschild black hole in the supersonic region near the object; the velocity of the object itself is assumed to be low compared to the speed of sound at infinity. First of all, we see that the streamlines intersect (i.e., a caustic forms) on the symmetry axis at a certain distance $r_x$ from the center on the front side if the pressure gradient is neglected. The characteristic radial size of the region, in which the streamlines emerging from the sonic surface at an angle no larger than $\theta_0$ to the axis intersect, is $\Delta r= r_x\theta^2_0/3.$ To refine the flow structure in this region, we numerically compute the system in the adiabatic approximation without ignoring the pressure. We estimate the parameters of the inferred region with anomalously high matter temperature and density accompanied by anomalously high energy release.Comment: 10 pages, 2 figure

Malmheden's theorem revisited

In 1934 H. Malmheden discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin 23 years later, it still does not seem to be widely known. In this paper we return to Malmheden's theorem, give an alternative proof of the result that allows generalization to polyharmonic functions and, also, discuss applications of his theorem to geometric properties of harmonic measures in balls in Euclidean spaces

Two-dimensional shapes and lemniscates

A shape in the plane is an equivalence class of sufficiently smooth Jordan curves, where two curves are equivalent if one can be obtained from the other by a translation and a scaling. The fingerprint of a shape is an equivalence of orientation preserving diffeomorphisms of the unit circle, where two diffeomorphisms are equivalent if they differ by right composition with an automorphism of the unit disk. The fingerprint is obtained by composing Riemann maps onto the interior and exterior of a representative of a shape in a suitable way. In this paper, we show that there is a one-to-one correspondence between shapes defined by polynomial lemniscates of degree n and nth roots of Blaschke products of degree n. The facts that lemniscates approximate all Jordan curves in the Hausdorff metric and roots of Blaschke products approximate all orientation preserving diffeomorphisms of the circle in the C^1-norm suggest that lemniscates and roots of Blaschke products are natural objects to study in the theory of shapes and their fingerprints

Glaciological and volcanological studies in the Wrangell Mountains, Alaska

There are no author-identified significant results in this report

Cold Atomic Collisions: Coherent Control of Penning and Associative Ionization

Coherent Control techniques are computationally applied to cold (1mK < T < 1 K) and ultracold (T < 1 microK) Ne*(3s,3P2) + Ar(1S0) collisions. We show that by using various initial superpositions of the Ne*(3s,3P2) M = {-2,-1,0,1,2} Zeeman sub-levels it is possible to reduce the Penning Ionization (PI) and Associative Ionization (AI) cross sections by as much as four orders of magnitude. It is also possible to drastically change the ratio of these two processes. The results are based on combining, within the "Rotating Atom Approximation", empirical and ab-initio ionization-widths.Comment: 4 pages, 2 tables, 2 figure

Neutrino emissivity under neutral kaon condensation

Neutrino emissivity from neutron star matter with neutral kaon condensate is considered. It is shown that a new cooling channel is opened, and what is more, all previously known channels acquire the greater emissivity reaching the level of the direct URCA cycle in normal matter.Comment: 7 pages, 1 figure, to be published in Phys.Rev.C, revised version: the sectioning changed and more discussion adde

Is There a Relationship between the Density of Primordial Black Holes in a Galaxy and the Rate of Cosmological Gamma-Ray Bursts?

The rate of accretion of matter from a solar-type star onto a primordial black hole (PBH) that passes through it is calculated. The probability that a PBH is captured into an orbit around a star in a galaxy is found. The mean lifetime of the PBH in such an orbit and the rate of orbital captures of PBHs in the galaxy are calculated. It is shown that this rate does not depend on the mass of the PBH. This mechanism cannot make an appreciable contribution to the rate of observed gamma-ray bursts. The density of PBHs in the galaxy can reach a critical value - the density of the mass of dark matter in the galaxy.Comment: 7 page