Recent zbMATH articles in MSC 83https://zbmath.org/atom/cc/832021-01-08T12:24:00+00:00WerkzeugRolling regime in the Higgs model with friction.https://zbmath.org/1449.830042021-01-08T12:24:00+00:00"Piskovskiĭ, Evgeniĭ Viktorovich"https://zbmath.org/authors/?q=ai:piskovskii.evgenii-viktorovichSummary: The Higgs model with friction is considered. The hyperbolic analog of the Krylov-Bogoliubov averaging method is used to obtain an approximate solution. The obtained solution is compared to a numerical solution of the considered equation.Cauchy problem for the wave equation on non-globally hyperbolic manifolds.https://zbmath.org/1449.352832021-01-08T12:24:00+00:00"Groshev, Oleg Viktorovich"https://zbmath.org/authors/?q=ai:groshev.oleg-viktorovichSummary: We consider Cauchy problem for wave equation on two types of non-global hyperbolic manifolds: Minkowski plane with an attached handle and Misner space. We prove that the classical solution on a plane with a handle exists and is unique if and only if a finite set of point-wise constraints on initial values is satisfied. On the Misner space the existence and uniqueness of a solution is equivalent to much stricter constraints for the initial data.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.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.On nonlocal cosmological equations on half-line.https://zbmath.org/1449.830062021-01-08T12:24:00+00:00"Aref'eva, Irina Yaroslavna"https://zbmath.org/authors/?q=ai:arefeva.irina-ya"Volovich, Igor' Vasil'evich"https://zbmath.org/authors/?q=ai:volovich.igor-vSummary: A system of nonlocal cosmological equations where the time variable runs over a half-line is considered. These equations are more suitable for description of the Universe than the previously discussed cosmological equations on the whole line since the Friedmann metric contains a singularity at the beginning of time. Definition of the exponential operator includes a new arbitrary function which is absent in the equations on the whole line. It is shown that this function could be choosen in such a way that one of the slow roll parameters in the chaotic inflation scenario can be made arbitrary small. Solutions of the linearized nonlocal equations on the half-line are constructed.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.Spherically-symmetric non-linear sigma model: the exact solutions obtained with isometrical embedding method.https://zbmath.org/1449.830092021-01-08T12:24:00+00:00"Chervon, Sergeĭ Viktorovich"https://zbmath.org/authors/?q=ai:chervon.sergei-viktorovich"Svistunova, Yuliya Aleksandrovna"https://zbmath.org/authors/?q=ai:svistunova.yuliya-aleksandrovnaSummary: The method to generate exact cosmological solutions in the frame of the spherically-symmetric non-linear sigma model offered in the present paper. This method is based on the isometrical embeddings of the target space (non-linear sigma-model fields chiral space) into space-time. Also the method application to two- and three-component chiral spaces embedded into space-time was considered. The exact cosmological solutions were obtained in the frame of the several special cases of the two- and three-component spherical-symmetric non-linear sigma-model. The obtained cosmological solutions were also investigated.The exact cosmological solutions for tachyon fields.https://zbmath.org/1449.830082021-01-08T12:24:00+00:00"Chervon, Sergeĭ Viktorovich"https://zbmath.org/authors/?q=ai:chervon.sergei-viktorovich"Panina, Ol'ga Gennad'evna"https://zbmath.org/authors/?q=ai:panina.olga-gennadevna"Sami, M."https://zbmath.org/authors/?q=ai:sami.mariagiovanna|sami.mustapha|sami.muhammadSummary: The application of the method of super-potential to the solution of the problems of cosmology with the tachyon fields is examined. The classes of exact solutions are found and the periods of time with the predominance of dark energy are established.The effect of the mass transfer along the cosmic string.https://zbmath.org/1449.810332021-01-08T12:24:00+00:00"Talalov, Sergeĭ Vladimirovich"https://zbmath.org/authors/?q=ai:talalov.sergei-vladimirovichSummary: The caption of massive quantum particle by the infinite string is considered. It is demonstrated that the appearance of the cuspidal point on the string leads to the collapse of particle wave function in this point.Three dimensional near-horizon metrics that are Einstein-Weyl.https://zbmath.org/1449.530112021-01-08T12:24:00+00:00"Randall, Matthew"https://zbmath.org/authors/?q=ai:randall.matthewThe paper investigates three-dimensional near-horizon metrics \(g=2dydr+2rh(x)dxdy+r^2f(x)dy^2+dx^2\) whose associate conformal structure is Einstein-Weyl. This means that there exists a symmetric connection \(D\) preserving the structure \([g]\) and such that \(\operatorname{Ric}_D^{sym}=\Lambda g\) for some function \(\Lambda\). By imposing a certain ansatz on the covector field \(g^{-1}Dg\) the author finds several classes of solutions, among which two are particular remarkable: one that is defined by some solutions of the dispersionless Kadomtsev-Petviashvili equation and one that is defined by some solutions of the dispersionless Hirota type, also known as hyper-CR. The work is well written and is of interest for both communities studying near horizon geometries and studying Einstein-Weyl geometry and dispersionless integrable systems.
Reviewer: Boris S. Kruglikov (Tromsø)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.On the fractional Newton and wave equation in one space dimension.https://zbmath.org/1449.354512021-01-08T12:24:00+00:00"Velasco, M. P."https://zbmath.org/authors/?q=ai:velasco.maria-pilar"Vázquez, L."https://zbmath.org/authors/?q=ai:vazquez.luis|vazquez.luis-a|vazquez.l-v|vazquez.leonorSummary: We consider the new mathematical scenarios in the framework of the Fractional Calculus. In this context, we study the generalized fractional virial theorem as well as the fractional plane wave solutions and the fractional dispersion relations for the fractional wave equation.On the Hartman effect and velocity of propagating the electromagnetic wave in the tunneling process.https://zbmath.org/1449.810352021-01-08T12:24:00+00:00"Chuprikov, Nikolaĭ Leonidovich"https://zbmath.org/authors/?q=ai:chuprikov.nikolai-lSummary: A new approach to the problem of scattering the plane electromagnetic TE wave on a homogeneous dielectric layer is presented, which does not predict, unlike the standard model, the Hartman effect for the tunneling time in the case of scattering the TE wave in the regime of a frustrated total internal refection (FTIR). The basic idea of this approach is that a correct definition of the tunneling velocity and time is possible if only the dynamics of both its subprocesses -- transmission and reflection -- is known at all stages of the scattering process investigated. It is shown that the Wigner (group) tunneling time was introduced without taking into account of this requirement, and, as a consequence, both this characteristic itself and the associated with it Hartman effect have no relation to transferring the light energy through the layer. The dwell transmission time, which is directly related to it, does not lead to the Hartman effect.Representation of Friedmann equation solution in form of generalized Dirichlet series.https://zbmath.org/1449.830112021-01-08T12:24:00+00:00"Kuryanovich, Èduard Anatol'evich"https://zbmath.org/authors/?q=ai:kuryanovich.eduard-anatolevichSummary: The cosmological Friedmann equation for the Universe, filled by scalar field with the quadratic potential, is reduced to the system of two first-order equations, one having the separable variables. The boundary-value problem with data at infinity is formulated for the second equation. The solution of this problem is represented in form of generalized Dirichlet series. The existence of classical solution in this form at the neighborhood of infinity is proved.Mathematical modeling of particle aggregation and sedimentation in the inclined tubes.https://zbmath.org/1449.760652021-01-08T12:24:00+00:00"Baranets, V."https://zbmath.org/authors/?q=ai:baranets.v-o"Kizilova, N."https://zbmath.org/authors/?q=ai:kizilova.n-mSummary: Sedimentation of the aggregating particles of different technical suspensions, blood and nanofluids in the gravity is investigated. The dependence of the sedimentation rate on the angle of inclination is considered. The two phase model of the aggregating particles is generalized to the inclined tubes. In the suggestion of small angles of inclination the equations are averaged over the transverse coordinate and the obtained hyperbolic system of equations is solved by the method of characteristics.Noncommutative geometry and structure of space-time.https://zbmath.org/1449.580012021-01-08T12:24:00+00:00"Chamseddine, Ali H."https://zbmath.org/authors/?q=ai:chamseddine.ali-hSummary: I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the Standard Model and the reasons behind the particular form of gauge fields, Higgs fields and fermions as well as the origin of symmetry breaking. It also points that at high energies the Standard Model is a truncation of Pati-Salam unified model of leptons and quarks. The same conclusions are arrived at uniquely without making any assumptions except for an axiom which is a higher form of Heisenberg commutation relations quantizing the volume of space-time. We establish the existence of two kinds of quanta of geometry in the form of unit spheres of Planck length. We provide answers to many of the questions which are not answered by other approaches, however, more research is needed to answer the remaining challenging questions.The exact cosmological solutions for phantom fields.https://zbmath.org/1449.830072021-01-08T12:24:00+00:00"Chervon, Sergeĭ Viktorovich"https://zbmath.org/authors/?q=ai:chervon.sergei-viktorovich"Panina, Ol'ga Gennad'evna"https://zbmath.org/authors/?q=ai:panina.olga-gennadevnaSummary: The application of the method of super-potential to the solution of the problems of cosmology with phantom fields is examined. The classes of exact solutions are found and the periods of time with the predominance of dark energy are established.Accretion of dark energy onto black holes.https://zbmath.org/1449.830052021-01-08T12:24:00+00:00"Babichev, Evgeniĭ Olegovich"https://zbmath.org/authors/?q=ai:babichev.evgenii-olegovich"Dokuchaev, Vyacheslav Ivanovich"https://zbmath.org/authors/?q=ai:dokuchaev.vyacheslav-i"Eroshenko, Yuriĭ Nikolaevich"https://zbmath.org/authors/?q=ai:eroshenko.yurii-nikolaevichSummary: The stationary accretion of dark energy onto black holes is studied. General expressions are derived for the accretion rate of an ideal fluid with an arbitrary equation of state and for scalar fields. The black hole mass was found to decrease for the accretion of phantom energy with \(p+\rho<0\). We also study the back reaction of accreting matter onto the metrics of a black hole in a perturbative way. The general expressions for corrections to the metric coefficients are found.