1,363 research outputs found
An efficient method for calculation of cooling in Lagrange computational gas dynamics
A new method for computation of gas cooling for Lagrange approach is
suggested. The method is based on precalculation of cooling law for known
cooling function. Unlike implicit methods, this method is very efficient, it is
an one-step method which is even more accurate than implicit methods of the
same order.Comment: submitted to JCompPhys, 5 pages, 1 figur
Computation of a function of a matrix with close eigenvalues by means of the Newton interpolating polynomial
An algorithm for computing an analytic function of a matrix is described.
The algorithm is intended for the case where has some close eigenvalues,
and clusters (subsets) of close eigenvalues are separated from each other. This
algorithm is a modification of some well known and widely used algorithms. A
novel feature is an approximate calculation of divided differences for the
Newton interpolating polynomial in a special way. This modification does not
require to reorder the Schur triangular form and to solve Sylvester equations.Comment: 11 page
The Gelfand--Shilov type estimate for Green's function of the bounded solutions problem
An analog of the Gelfand--Shilov estimate of the matrix exponential is proved
for Green's function of the problem of bounded solutions of the ordinary
differential equation .Comment: 9 page
Inverse-closedness of subalgebras of integral operators with almost periodic kernels
The integral operator of the form acting in
, , is considered. It is assumed that
, , and
We prove that if the
operator is invertible, then , where
is an integral operator possessing the analogous representation.Comment: 21 page
Excitation of turbulence in accretion disks of binary stars by non-linear perturbations
Accretion disks in binary systems can experience hydrodynamic impact at inner
as well as outer edges. The first case is typical for protoplanetary disks
around young T Tau stars. The second one is typical for circumstellar disks in
close binaries. As a result of such an impact, perturbations with different
scales and amplitudes are excited in the disk. We investigated the nonlinear
evolution of perturbations of a finite, but small amplitude, at the background
of sub-Keplerian flow. Nonlinear effects at the front of perturbations lead to
the formation of a shock wave, namely the discontinuity of the density and
radial velocity. At this, the tangential flow in the neighborhood of the shock
becomes equivalent to the flow in in the boundary layer. Instability of the
tangential flow further leads to turbulization of the disk. Characteristics of
the turbulence depend on perturbation parameters, but alpha-parameter of
Shakura-Sunyaev does not exceed ~0.1.Comment: Accepted in Astronomy Report
An estimate of approximation of a matrix-valued function by an interpolation polynomial
Let be a square complex matrix, , ..., be
(possibly repetitive) points of interpolation, be analytic in a
neighborhood of the convex hull of the union of the spectrum of and the
points , ..., , and be the interpolation polynomial of ,
constructed by the points , ..., . It is proved that under these
assumptions where
.Comment: 8 pages, 1 figur
Inverse-closedness of the set of integral operators with -continuously varying kernels
Let be an integral operator of the form acting in with a measurable kernel
satisfying the estimate , where . It is
proved that if the function is continuous in the norm of
and the operator has an inverse, then
, where is an integral operator possessing
the same properties.Comment: 16 page
Computation of Green's function of the bounded solutions problem
It is well known that the equation , where is a square
matrix, has a unique bounded solution for any bounded continuous free term
, provided the coefficient has no eigenvalues on the imaginary axis.
This solution can be represented in the form \begin{equation*}
x(t)=\int_{-\infty}^{\infty}\mathcal G(t-s)x(s)\,ds. \end{equation*} The kernel
is called Green's function. In the paper, a representation of
Green's function in the form of the Newton interpolating polynomial is used for
approximate calculation of . An estimate of the sensitivity of the
problem is given.Comment: 12 pages, 2 figure
On the possible turbulence mechanism in accretion disks in non-magnetic binary stars
The arising of turbulence in gas-dynamic (non-magnetic) accretion disks is a
major issue of modern astrophysics. Such accretion disks should be stable
against the turbulence generation, in contradiction to observations. Searching
for possible instabilities leading to the turbulization of gas-dynamic disks is
one of the challenging astrophysical problems. In 2004, we showed that in
accretion disks in binary stars the so-called precessional density wave forms
and induces additional density and velocity gradients in the disk. Linear
analysis of the fluid instability of an accretion disk in a binary system
revealed that the presence of the precessional wave in the disk due to tidal
interaction with the binary companion gives rise to instability of radial modes
with the characteristic growth time of tenths and hundredths of the binary
orbital period. The radial velocity gradient in the precessional wave is shown
to be responsible for the instability. A perturbation becomes unstable if the
velocity variation the perturbation wavelength scale is about or higher than
the sound speed. Unstable perturbations arise in the inner part of the disk
and, by propagating towards its outer edge, lead to the disk turbulence with
parameters corresponding to observations (the Shakura-Sunyaev parameter ).Comment: Appeared in Phys. Us
Analytic functional calculus for two operators
Properties of the mappings \begin{align*} C&\mapsto\frac1{(2\pi
i)^2}\int_{\Gamma_1}\int_{\Gamma_2}f(\lambda,\mu)\,R_{1,\,\lambda}\,C\,
R_{2,\,\mu}\,d\mu\,d\lambda, C&\mapsto\frac1{2\pi
i}\int_{\Gamma}g(\lambda)R_{1,\,\lambda}\,C\, R_{2,\,\lambda}\,d\lambda
\end{align*} are discussed; here and are
pseudo-resolvents, i.~e., resolvents of bounded, unbounded, or multivalued
linear operators, and and are analytic functions. Several applications
are considered: a representation of the impulse response of a second order
linear differential equation with operator coefficients, a representation of
the solution of the Sylvester equation, and an exploration of properties of the
differential of the ordinary functional calculus.Comment: 49 page
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