Recent zbMATH articles in MSC 85https://zbmath.org/atom/cc/852021-01-08T12:24:00+00:00WerkzeugNumerical integration of celestial bodies equations with taking into account regularization and use osculating elements of major planets.https://zbmath.org/1449.850072021-01-08T12:24:00+00:00"Zausaev, Dmitriĭ Anatol'evich"https://zbmath.org/authors/?q=ai:zausaev.dmitrii-anatolevich"Solov'ev, Leonid Aleksandrovich"https://zbmath.org/authors/?q=ai:solovev.leonid-aleksandrovichSummary: The regular differential equations for a problem of perturbed motion are received. The computing algorithm and the program of numerical integration of the equations of celestial motion by a method of Everhart taking into account regularization and use osculating of elements of major planets is developed.Multiscale radiative transfer in cylindrical coordinates.https://zbmath.org/1449.850142021-01-08T12:24:00+00:00"Sun, Wenjun"https://zbmath.org/authors/?q=ai:sun.wenjun"Jiang, Song"https://zbmath.org/authors/?q=ai:jiang.song"Xu, Kun"https://zbmath.org/authors/?q=ai:xu.kunSummary: The radiative transfer equations in cylindrical coordinates are important in the application of inertial confinement fusion. In comparison with the equations in Cartesian coordinates, an additional angular derivative term appears in the cylindrical case. This term adds great difficulty for a numerical scheme to keep the conservation of total energy. In this paper, based on weighting factors, the angular derivative term is properly discretized, and the interface fluxes in the radial \(r\)-direction depend on such a discretization as well. A unified gas kinetic scheme (UGKS) with asymptotic preserving property for the gray radiative transfer equations is constructed in cylindrical coordinates. The current UGKS can naturally capture the radiation diffusion solution in the optically thick regime with the cell size being much larger than photon's mean free path. At the same time, the current UGKS can present accurate solutions in the optically thin regime as well. Moreover, it is a finite volume method with total energy conservation. Due to the scale-dependent time evolution solution for the interface flux evaluation, the scheme can cover multiscale transport mechanism seamlessly. The cylindrical hohlraum tests in inertial confinement fusion are used to validate the current approach, and the solutions are compared with implicit Monte Carlo result.Mathematical modeling of close encounters of solar system small bodies with major planets and the Moon.https://zbmath.org/1449.850092021-01-08T12:24:00+00:00"Abramov, V. V."https://zbmath.org/authors/?q=ai:abramov.vladimir-viktorovichSummary: We establish the choice of numerical integration method for the motion equations of solar system small bodies in moments of close encounters with major planets and the Moon. The performed research shows that the multi-step Adams-Moulton method with preliminary chosen smaller step and increased order of approximation is more preferable for these moments. The modeling of moments of encounters using the one-step Everhart method with variable step sufficiently increases the global time of numerical process and requires the following optimization of step change criterion.Thermal equations of the radiation dominated universe evolution.https://zbmath.org/1449.830102021-01-08T12:24:00+00:00"Dolgopolov, Mikhaĭl Vyacheslavovich"https://zbmath.org/authors/?q=ai:dolgopolov.mikhail-vyacheslavovich"Petrova, Elena Yur'evna"https://zbmath.org/authors/?q=ai:petrova.elena-yurevnaSummary: The equations of the evolution of the Universe in Friedmann model are considered using thermodynamic functions and temperature as function of time. The exit for frameworks of the standard model is carried out, the influence of dark energy is considered.Mathematical modeling of motion of the asteroid 99942 Apophis on the basis of Adams methods with a variable step size.https://zbmath.org/1449.850102021-01-08T12:24:00+00:00"Abramov, V. V."https://zbmath.org/authors/?q=ai:abramov.vladimir-viktorovichSummary: The choice of Adams methods with divided differences has been validated for solving of the equations of motion of small bodies of the Solar system. The numerical integration with a variable step size of differential equations of motion of the asteroid 99942 Apophis has been carried out with the help of these methods. The moments of closest approaches to major planets and the Moon by this minor planet has been determined. The evolution of its orbit has been investigated on 600 years time interval.Integration of equations of solar system small bodies motion with osculating elements method.https://zbmath.org/1449.850042021-01-08T12:24:00+00:00"Zausaev, A. F."https://zbmath.org/authors/?q=ai:zausaev.anatolii-fedorovich"Zausaev, D. A."https://zbmath.org/authors/?q=ai:zausaev.dmitrii-anatolevichSummary: Algorithm of osculating elements method for numerical integration of equations of Solar system small bodies' motion is introduced.Software development for automating the process of creation database of asteroids' orbital evolution.https://zbmath.org/1449.850012021-01-08T12:24:00+00:00"Denisov, Sergeĭ Sergeevich"https://zbmath.org/authors/?q=ai:denisov.sergei-sergeevichSummary: This paper describes the software system that automates the process of calculating the asteroids orbital evolution. These applications allow automatically calculating on multiple computers simultaneously. Also the optimization of the algorithms implementation was done.Study of the cosmic rays transport problems using second order parabolic type partial differential equation.https://zbmath.org/1449.850132021-01-08T12:24:00+00:00"Gil, Agnieszka"https://zbmath.org/authors/?q=ai:gil.agnieszka"Alania, Michael V."https://zbmath.org/authors/?q=ai:alania.michael-vSummary: It has been exactly 100 years since Hess's historical discovery: an extraterrestrial origin of cosmic rays [\textit{E. N. Parker}, ``Dynamics of the interplanetary gas and magnetic fields'', Astrophys. J. 128, 664--676 (1958; \url{doi:10.1086/146579})]. Galactic cosmic rays (GCR) being charged particles, penetrate the heliosphere and are modulated by the solar magnetic field. The propagation of cosmic rays is described by Parker's transport equation [\textit{V. F. Hess}, ``Über Beobachtungen der durchdringenden Strahlung bei sieben Freiballonfahrten'', Phys. Z. 13, 1084--1091 (1912)], which is a second order parabolic type partial differential equation. It is time dependent 4-variables (with \(r\), \(\theta\), \(\varphi\), \(R\), meaning: distance from the Sun, heliolatitudes, heliolongitudes and particles' rigidity, respectively) equation which is a well known tool for studying problems connected with solar modulation of cosmic rays. Transport equation contains all fundamental processes taking place in the heliosphere: convection, diffusion, energy changes of the GCR particles owing to the interaction with solar wind's inhomogeneities, drift due to the gradient and curvature of the regular interplanetary magnetic field and on the heliospheric current sheet.
In our paper we investigate a topic of the 27-day variation of the galactic cosmic rays intensity, which is connected with solar rotation. We numerically solve the Parker's transport equation involving in situ measurements of solar wind and magnetic field.Using the database of coordinates of the major planets for the numerical integration of the equations of celestial bodies motion.https://zbmath.org/1449.850022021-01-08T12:24:00+00:00"Radchenko, Vladimir Pavlovich"https://zbmath.org/authors/?q=ai:radchenko.vladimir-pavlovich"Zausaev, Dmitriĭ Anatol'evich"https://zbmath.org/authors/?q=ai:zausaev.dmitrii-anatolevichSummary: Databases of major planets coordinates are created on the basis of the numerical theory of movement of planets DE405. Numerical integration of the motion equations of small bodies of Solar system is realized using the received databanks. Extra efficiency of usage of databanks of major planets coordinates is shown at numerical integration of motion equations of celestial bodies.Electronic catalogue of orbital evolution of small bodies of the solar system: database and web-site development.https://zbmath.org/1449.850082021-01-08T12:24:00+00:00"Abramov, V. V."https://zbmath.org/authors/?q=ai:abramov.vladimir-viktorovichSummary: The main stages of development of the electronic catalogue of orbital evolution of small bodies of the Solar system are introduced. The short description of the web site architecture, its structure and interface has been given. Guidelines for web-site users are described.Extension of the Lorentz symmetry up to conformal in the limit of ultrahigh energies.https://zbmath.org/1449.830022021-01-08T12:24:00+00:00"Vernigora, Irina Aleksandrovna"https://zbmath.org/authors/?q=ai:vernigora.irina-aleksandrovna"Rudoĭ, Yuriĭ Grigor'evich"https://zbmath.org/authors/?q=ai:rudoi.yurii-grigorevichSummary: The group-theoretical justification is presented for the original approach by \textit{D. A. Kirzhnits} and \textit{V. A. Chechin} [``Ultra-high energy cosmic rays and possible generalization of the relativistic theory'', Yadern. Fiz. 15, No. 5, 1051--1059 (1972)] which allows for the primary protons of ultra-high energy cosmic rays to overcome the energetic limit (about 50 EeV) of Greisen-Zatsepin-Kuzmin remaining in the scope of the usual ideas about the nature of the extra-galactic sources of the cosmic rays. It is shown that the explicit form of the factor deforming the Lorentz invariant in the energy-momentum space may be found on the grounds of the approximate transition from Lorentz symmetry to the conformal values of the Lorentz-factor of the order \(10^{10} \div 10^{11}\).Photons as carriers of ultra-high energy in cosmic space.https://zbmath.org/1449.830012021-01-08T12:24:00+00:00"Buyanova, Elena Alekseevna"https://zbmath.org/authors/?q=ai:buyanova.elena-alekseevna"Molchatskiĭ, Lev Solomonovich"https://zbmath.org/authors/?q=ai:molchatskii.lev-solomonovichSummary: Absorbing process of ultrahigh-energy gamma-quanta in a cosmic space is investigated. It is shown that the main absorbing mechanism is the reactions arising at collisions of cosmic-ray photons with microwave and radio background ones. Estimate of the mean free path of a photon for different energies gives evidence that gamma-quanta with energies \(E > 10^{19}\) eV running from Active Galactic Nuclei seem to reach the Earth vicinity. This result is in agreement with the recent observations of extensive air shower array experiments realized by AGASA and Yakutsk.A study of the orbital evolution of 10 short-period comets by solving differential equations of motion obtained on the basis of a new principle of interaction.https://zbmath.org/1449.850112021-01-08T12:24:00+00:00"Zausaev, A. F."https://zbmath.org/authors/?q=ai:zausaev.anatolii-fedorovichSummary: The research of the orbital evolution of 10 short-period comets on the time interval of 400 years (1800--2200) is made by solving the differential equations of motion based on the new principle of mutual interaction of material bodies. The results are compared with the orbital elements, calculated by solving the motion equations with regard to gravitational effect and relativistic effect. It is shown that the results of calculations obtained by two different methods are in agreement within acceptable inaccuracy.Research of effect of initial data displacement on results of calculation of orbits evolution for short-period comets.https://zbmath.org/1449.830032021-01-08T12:24:00+00:00"Zausaev, A. A."https://zbmath.org/authors/?q=ai:zausaev.a-aSummary: We study the problems of stability of solution and the effect of initial data errors on the results of calculation of orbits evolution for short-period comets on the time intervals within the order of 100 years.Numerical modelling of major planets movement on the new interaction principle basis.https://zbmath.org/1449.850062021-01-08T12:24:00+00:00"Zausaev, Anatoliĭ Fëdorovich"https://zbmath.org/authors/?q=ai:zausaev.anatolii-fedorovichSummary: Numerical integration of the equations of movement of major planets, on the basis of a new principle of interaction is spent. Elements of orbits of major planets on large time interval (1602---2200) are calculated. Results of calculations are compared with elements of the orbits defined according to coordinates and speeds by numerical theory DE405. It is shown that elements of orbits of the exterior planets, found on new algorithm, will well be coordinated with dates DE405. For internal planets Venus, the Earth and Mars have insignificant discrepancies in secular offsets of perihelions in comparison with dates DE405.Research of dynamics of Aten asteroids in vicinity of resonance with inner planets.https://zbmath.org/1449.850122021-01-08T12:24:00+00:00"Zausaev, A. F."https://zbmath.org/authors/?q=ai:zausaev.anatolii-fedorovich"Altynbaev, F. Kh."https://zbmath.org/authors/?q=ai:altynbaev.f-khSummary: In the time interval from 1800 to 2200 we research the dynamics of Aten in vicinity of resonance with inner planets. It is shown that 238 among 320 Aten asteroids move in vicinity of resonance with one, two or three inner planets.Interpolation methods used to obtain orbit coordinates and elements of the solar system large planets and small bodies.https://zbmath.org/1449.850032021-01-08T12:24:00+00:00"Zausaev, A. F."https://zbmath.org/authors/?q=ai:zausaev.anatolii-fedorovich"Zausaev, D. A."https://zbmath.org/authors/?q=ai:zausaev.dmitrii-anatolevichSummary: Various methods of interpolation for receiving coordinates, velocities and elements of large planets and small bodies orbits of the Solar system are studied. New osculating elements method is introduced. This method has proved to be the most effective in comparison with trapezium and parabola methods.The numerical integration of the equation of small bodies of the solar system with use of osculating elements.https://zbmath.org/1449.850052021-01-08T12:24:00+00:00"Zausaev, A. F."https://zbmath.org/authors/?q=ai:zausaev.anatolii-fedorovich"Zausaev, D. A."https://zbmath.org/authors/?q=ai:zausaev.dmitrii-anatolevichSummary: The numerical integration of the equations of the Solar system small bodies motion is carried out with application of osculating elements of the larger planets. This method proves to be highly efficient for small bodies that do not approach close to the Earth.