254 research outputs found
Spectral Asymptotics for Perturbed Spherical Schr\"odinger Operators and Applications to Quantum Scattering
We find the high energy asymptotics for the singular Weyl--Titchmarsh
m-functions and the associated spectral measures of perturbed spherical
Schr\"odinger operators (also known as Bessel operators). We apply this result
to establish an improved local Borg-Marchenko theorem for Bessel operators as
well as uniqueness theorems for the radial quantum scattering problem with
nontrivial angular momentum.Comment: 20 page
Review of scientific topics for Millimetron space observatory
This paper describes outstanding issues in astrophysics and cosmology that
can be solved by astronomical observations in a broad spectral range from far
infrared to millimeter wavelengths. The discussed problems related to the
formation of stars and planets, galaxies and the interstellar medium, studies
of black holes and the development of the cosmological model can be addressed
by the planned space observatory Millimetron (the "Spectr-M" project) equipped
with a cooled 10-m mirror. Millimetron can operate both as a single-dish
telescope and as a part of a space-ground interferometer with very long
baseline.Comment: The translation of the original article in Physics Uspekhi
http://ufn.ru/ru/articles/2014/12/c
Abstract kinetic equations with positive collision operators
We consider "forward-backward" parabolic equations in the abstract form , , where and are
operators in a Hilbert space such that , , and
. The following theorem is proved: if the operator is
similar to a self-adjoint operator, then associated half-range boundary
problems have unique solutions. We apply this theorem to corresponding
nonhomogeneous equations, to the time-independent Fokker-Plank equation , , , as well as to
other parabolic equations of the "forward-backward" type. The abstract kinetic
equation , where is injective and
satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in
the introductio
Simulations of M87 and Sgr A* imaging with the Millimetron Space Observatory on near-Earth orbits
High resolution imaging of supermassive black holes shadows is a direct way
to verify the theory of general relativity at extreme gravity conditions. Very
Long Baseline Interferometry (VLBI) observations at millimeter/sub-millimeter
wavelengths can provide such angular resolution for supermassive black holes,
located in Sgr A* and M87. Recent VLBI observations of M87 with the Event
Horizon Telescope (EHT) has shown such capabilities. The maximum obtainable
spatial resolution of EHT is limited by Earth diameter and atmospheric phase
variations. In order to improve the image resolution longer baselines are
required. Radioastron space mission has successfully demonstrated the
capabilities of Space-Earth VLBI with baselines much larger than Earth
diameter. Millimetron is a next space mission of the Russian Space Agency that
will operate at millimeter wavelengths. Nominal orbit of the observatory will
be located around Lagrangian L2 point of the Sun-Earth system. In order to
optimize the VLBI mode, we consider a possible second stage of the mission that
could use near-Earth high elliptical orbit (HEO). In this contribution a set of
near-Earth orbits is used for the synthetic space-ground VLBI observations of
Sgr A* and M87 in joint Millimetron and EHT configuration. General-relativistic
magnetohydrodynamic models (GRMHD) for black hole environment of Sgr A* and M87
are used for static and dynamic imaging simulations at 230 GHz. A comparison
preformed between ground and space-ground baselines demonstrates that joint
observations with Millimetron and EHT significantly improve the image
resolution and allow the EHT+Millimetron to obtain snapshot images of Sgr A*
probing dynamics at fast timescales.Comment: 12 pages, 6 figure
- …