We examine the spatial stability of spherical adiabatic Bondi accretion on to a point gravitating mass against external perturbations. Both transonic critical and subsonic subcritical accretion are shown to be stable against purely radial acoustic, vortex or entropy perturbations. In the case of non‐radial perturbations the amplitude of the perturbations grows without limit with smaller radii. Instability manifests itself only if the size of the accreting body is much less than the Bondi radius so that the inflow is highly supersonic or highly subsonic at the surface of the accretor in the case of critical or subcritical accretion respectively. These asymptotics hold and consequently the instability may develop for adiabatic index of accreting gas γ < 5/3. We suggest that this instability may lead to an essential thermalization of accreting flow thus, particularly, solving the problem of otherwise inefficient energy release in spherical accretion on to a black hole.

The evolution of a supernova remnant in a cloudy medium as a function of the volume filling factor of the clouds is studied in a three-dimensional axially symmetrical model. The model includes the mixing of heavy elements (metals) ejected by the supernova and their contribution to radiative losses. The interaction of the supernova envelope with the cloudy phase of the interstellar medium leads to nonsimultaneous, and on average earlier, onsets of the radiative phase in different parts of the supernova envelope. Growth in the volume filling factor f leads to a decrease in the time for the transition of the envelope to the radiative phase and a decrease in the envelopes mean radius, due to the increased energy losses by the envelope in the cloudy medium. When the development of hydrodynamical instabilities in the supernova envelope is efficient, the thermal energy falls as E t ∼ t −2.3 , for the propagation of the supernova remnant through either a homogeneous or a cloudy medium. When the volume filling factor is f > ∼ 0.1, a layer with excess kinetic energy andmomentumforms far behind the global shock front from the supernova, which traps the hot gas of the cavity in the central part of the supernova remnant. Metals ejected by the supernova are also enclosed in the central region of the remnant, where the initial (high) metallicity is essentially preserved. Thus, the interaction of the supernova envelope with the cloudy interstellar medium appreciably changes the dynamics and structure of the distribution of the gas in the remnant. This affects the observational characteristics of the remnant, in particularly, leading to substantial fluctuations of the emission measure of the gas with T > 10 5 K and the velocity dispersion of the ionized gas.

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The aim of this work is to construct an algorithm for visualizing a polydisperse phase of solid particles (dust) in an inhomogeneous flow of a two-phase gas-dust mixture that would allow us to see, within one plot, the degree of polydispersity of the dust phase and the difference in the spatial distributions of individual fractions of dust particles in the computational domain. The developed technique allows us to reproduce concentrations from one to three fractions of dust particles in each cell in the computational domain. Each of the three fractions of dust particles is mapped to one of the main channels of the RGB palette.The intensity of the color shade is set to be proportional to the relative concentration of dust particles in this fraction. The final image for a polydisperse mixture is obtained by adding images in each of the three color channels. To visualize the degree of polydispersity, I propose depicting the spatial distribution of the entropy of the dust mixture. The definition of the entropy of a mixture is generalized to take into account the states of a mixture with zero number of particles in the mixture. They correspond to dust-free sections of the computational domain (voids). The proposed method for visualizing the polydispersity of a mixture of particles is demonstrated using the example of dynamic numerical modeling of the spatial features of dust structures formed in turbulent gas-dust flows and in flows with shock waves.Real liquid, gas or plasma media have an inhomogeneous structure and are complex, composite systems that include microobjects of different types and different nature, such as small solid suspended particles, droplets or bubbles. There are a huge number of areas in the field of technology in which a person deals with multiphase environments, from chemical reactors to engine building and aeronautics. There are no manifestations of polyphase in nature that are less significant. Despite the small relative mass content, impurity aerosol or dust particles can play an important role in the life of planetary atmospheres, interstellar or intergalactic gas. The dust component determines the optical properties of the medium, its opacity in one interval or another of the electromagnetic spectrum. As a consequence, dust in the atmosphere or in the interstellar gas can act as a coolant, realizing the anti-greenhouse effect [1,2]. Due to their windage, dust grains can cause an effective mechanical effect of star radiation on a transparent neutral gas, accelerating under the influence of radiation pressure and accelerating the surrounding matter [3,4]. Particles of dust in the interstellar gas act as a catalyst for the process of gas molecularization [1]. Dust also serves as a building material for the formation of solid celestial bodies, such as asteroids or planets [1].Examples of space objects enriched with impure dust particles are gas-dust interstellar clouds and nebulae, protoplanetary disks, spiral arms of galaxies and gas-dust halos of galaxies. Usually, cosmic dust grains are par...

A significant reduction in the time required to obtain an estimate of the mean frequency of the spectrum of Doppler signals when seeking to measure the instantaneous velocity of dangerous near-Earth cosmic objects (NEO) is an important task being developed to counter the threat from asteroids. Spectral analysis methods have shown that the coordinate of the centroid of the Doppler signal spectrum can be found by using operations in the time domain without spectral processing. At the same time, an increase in the speed of resolving the algorithm for estimating the mean frequency of the spectrum is achieved by using fractional differentiation without spectral processing. Thus, an accurate estimate of location of the centroid for the spectrum of Doppler signals can be obtained in the time domain as the signal arrives. This paper considers the implementation of a fractional-differentiating filter of the order of 1 ⁄2 by a set of automation astatic transfer elements, which greatly simplifies practical implementation. Real technical devices have the ultimate time delay, albeit small in comparison with the duration of the signal. As a result, the real filter will process the signal with some error. In accordance with this, this paper introduces and uses the concept of a "pre-derivative" of 1 ⁄2 of magnitude. An optimal algorithm for realizing the structure of the filter is proposed based on the criterion of minimum mean square error. Relations are obtained for the quadrature coefficients that determine the structure of the filter.