Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of the perfect fluid with one-parametric equation of state (EOS) p = p(ε). For linear EOS p = κε we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS (κ = 1) we obtain ''monopole + dipole'' and ''monopole + quadrupole'' axially symmetric solutions. We also found some nonlinear EOSs that admit analytic solutions

The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state

A small viscosity approach to discontinuous flows is discussed in relativistic hydrodynamics with a general (possibly, non-convex) equation of state that typically occurs in the domains of phase transitions. Different forms of criteria for the existence and stability of relativistic shock waves, such as evolutionarity conditions, entropy criterion and corrugation stability conditions are compared with the requirement of the existence of shock viscous profile. The latter is shown to be most restrictive in case of a single-valued shock adiabat expressed as a function of pressure. One-dimensional numerical simulations with artificial viscosity for a simple piecewise-linear equation of state are carried out to illustrate the criteria in the case of planar and spherical shock waves. The effect of a phase transition domain on the shock amplitude in the process of a hydrodynamical spherical collapse is demonstrated.Обговорюється підхід малої в’язкости до розривних потоків у релятивістичній гідродинаміці із загальним (можливо, неопуклим) рівнянням стану, яке характерне для области фазових переходів. Різні форми критеріїв існування та стійкости релятивістичних ударних хвиль — умови еволюційности, ентропійний критерій та умови складчастої стабільности — порівнюються з вимогою існування ударного в’язкісного профілю. Показано, що останній критерій є більш обмежуючим у випадку ударної адіябати, яка виражається як однозначна функція тиску. Для ілюстрування цих критеріїв у випадку плоских та сферичних ударних хвиль проведено одновимірне числове моделювання зі штучною в’язкістю для простого кусково–лінійного рівняння стану. Продемонстровано вплив области фазових переходів на ударну амплітуду у процесі гідродинамічного сферичного колапсу

Observations of Sy2 galaxy NGC 3281 by XMM-Newton and INTEGRAL satellites

We present the results of the analysis of X-ray properties of the Seyfert 2 galaxy NGC 3281, based on the observational data obtained by XMM-Newton and INTEGRAL within the energy ranges 0.2-12 keV and 20-150 keV, respectively. The XMM-Newton spectrum of this object is presented for the first time. We show that fitting the X-ray spectrum of this galaxy with models based on the reflection from the disc with infinite column density yields non-physical results. A more appropriate fit takes into account both transmitted and reflected emission, passed through a gas-dust torus-like structure. Keeping this in mind, to model the inhomogeneous clumpy torus, we used the MYTorus model. Hence, we conclude that the torus of NGC 3281 is not a continuous structure, but rather consists of separate clouds, which is in a good agreement with the results of near-IR observations. Using this assumption, we found that the torus inclination angle and the hydrogen column density are 66.98⁺²˙⁶³ ₋₁.₃₄ degrees and 2.08⁺⁰˙³⁵₋₀.₁₈ × 10²⁴ cm⁻², respectively. Also, emissions of hot diffuse gases with temperature ∼ 590 eV, and warm absorption, were detected

Gravitational lens equation: critical solutions and magnification near folds and cusps

We study approximate solutions of the gravitational lens equation and corresponding lens magnification factor near the critical point. This consideration is based on the Taylor expansion of the lens potential in powers of coordinates and an introduction of a proximity parameter characterising the closeness of a point source to the caustic. Second-order corrections to known approximate solutions and magnification are found in case of a general fold point. The first-order corrections near a general cusp are found as well

Microlensing effects and structure of gravitational lens systems

A study of gravitational microlensing of distant objects is presented. We performed simulations of light curves and trajectories of the image centroid of an extended source in the Chang–Refsdal lens with shear and continual dark matter. Various brightness distributions over the source (Gaussian, power-law, Shakura–Synyaev accretion disc) have been studied. We considered in detail approximate relations and corresponding algorithms used to fit observational data on high amplification events (HAE). The results are applied to interpretation of HAE observed by OGLE and GLITP groups. The source size and caustic crossing moment are estimated from these data, however, the determination of the brightness profile is statistically not reliable

Search for the astrophysical sources of the Fly's Eye event with the highest to date cosmic ray energy E=3.2·10²⁰ eV

Among the registered extremely high energy cosmic rays (EHECR, E > 10²⁰ eV) an event with the highest to date energy of E = 3.2 · 10²⁰ eV was detected by the Fly's Eye experiment (FE event) in 1991. With the use of the back-tracking method for the calculation of the EHECR trajectories in Galactic and extragalactic magnetic fields, we show that the galaxies UGC 03574 and UGC 03394 are the most promising candidates among the nearby extragalactic sources for the cases of iron and C-N-O group primary nucleus respectively. The most likely accelerating mechanisms are the newly-born millisecond pulsars, magnetar ares and tidal disruption events in these galaxies

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by families of point transformations. A class of variable coefficient (1+1)-dimensional semilinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u_x)_x+h(x)u^m$ ($m\ne0,1$) is studied from the symmetry point of view in the framework of the approach proposed. The singular subclass of the equations with $m=2$ is singled out. The group classifications of the entire class, the singular subclass and their images are performed with respect to both the corresponding (generalized extended) equivalence groups and all point transformations. The set of admissible transformations of the imaged class is exhaustively described in the general case $m\ne2$. The procedure of classification of nonclassical symmetries, which involves mappings between classes of differential equations, is discussed. Wide families of new exact solutions are also constructed for equations from the classes under consideration by the classical method of Lie reductions and by generation of new solutions from known ones for other equations with point transformations of different kinds (such as additional equivalence transformations and mappings between classes of equations).Comment: 40 pages, this is version published in Acta Applicanda Mathematica

Study of doubly strange systems using stored antiprotons

Bound nuclear systems with two units of strangeness are still poorly known despite their importance for many strong interaction phenomena. Stored antiprotons beams in the GeV range represent an unparalleled factory for various hyperon-antihyperon pairs. Their outstanding large production probability in antiproton collisions will open the floodgates for a series of new studies of systems which contain two or even more units of strangeness at the P‾ANDA experiment at FAIR. For the first time, high resolution γ-spectroscopy of doubly strange ΛΛ-hypernuclei will be performed, thus complementing measurements of ground state decays of ΛΛ-hypernuclei at J-PARC or possible decays of particle unstable hypernuclei in heavy ion reactions. High resolution spectroscopy of multistrange Ξ−-atoms will be feasible and even the production of Ω−-atoms will be within reach. The latter might open the door to the |S|=3 world in strangeness nuclear physics, by the study of the hadronic Ω−-nucleus interaction. For the first time it will be possible to study the behavior of Ξ‾+ in nuclear systems under well controlled conditions