Opava, Czech Republic

Silesian University in Opava

Opava, Czech Republic

Silesian University in Opava, is one of the youngest universities in the Czech Republic, established in 1989.Silesian University in Opava should not be confused with a similarly named university in Polish-administered part of Silesia .Silesian University had about 4 000 students in 2006. Wikipedia.

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Kolos M.,Silesian University in Opava | Stuchlik Z.,Silesian University in Opava
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2013

Current-carrying string-loop dynamics is studied in the Kerr spacetimes. With attention concentrated to the axisymmetric motion of string loops around the symmetry axis of both black-hole (BH) and naked singularity (NS) spacetimes, it is shown that the resulting motion is governed by the presence of an outer tension barrier and an inner angular momentum barrier that are influenced by the BH or NS spin. We classify the string dynamics according to properties of the energy boundary function (effective potential) for the string loop motion. We have found that for NS there exist new types of energy boundary function, namely those with off-equatorial minima. Conversion of the energy of the string oscillations to the energy of the linear translational motion has been studied. Such a transmutation effect is much more efficient in the NS spacetimes because of lack of the event horizon. For BH spacetimes efficiency of the transmutation effect is only weakly spin dependent. Transition from the regular to chaotic regime of the string-loop dynamics is examined and used for explanation of the string-loop motion focusing problem. Radial and vertical frequencies of small oscillations of string loops near minima of the effective potential in the equatorial plane are given. These can be related to high-frequency quasiperiodic oscillations observed near black holes. © 2013 American Physical Society.

Stuchlik Z.,Silesian University in Opava | Schee J.,Silesian University in Opava
Classical and Quantum Gravity | Year: 2010

We study optical phenomena related to the appearance of Keplerian accretion discs orbiting Kerr superspinars predicted by string theory. The superspinar exterior is described by standard Kerr naked singularity geometry breaking the black hole limit on the internal angular momentum (spin). We construct local photon escape cones for a variety of orbiting sources that enable us to determine the superspinars silhouette in the case of distant observers. We show that the superspinar silhouette depends strongly on the assumed edge where the external Kerr spacetime is joined to the internal spacetime governed by string theory and significantly differs from the black hole silhouette. The appearance of the accretion disc is strongly dependent on the value of the superspinar spin in both their shape and frequency shift profile. Apparent extension of the disc grows significantly with the growing spin, while the frequency shift grows with the descending spin. This behaviour differs substantially from the appearance of discs orbiting black holes enabling thus, at least in principle, to distinguish clearly the Kerr superspinars and black holes. In vicinity of a Kerr superspinar the non-escaped photons have to be separated to those captured by the superspinar and those being trapped in its strong gravitational field leading to self-illumination of the disc that could even influence its structure and cause self-reflection effect of radiation of the disc. The amount of trapped photons grows with descending superspinar spin. We thus can expect significant selfillumination effects in the field of Kerr superspinars with near-extreme spin a ∼ 1. © 2010 IOP Publishing Ltd.

Stuchlik Z.,Silesian University in Opava | Schee J.,Silesian University in Opava
Classical and Quantum Gravity | Year: 2012

String theory indicates the existence of primordial Kerr superspinars, extremely compact objects with exterior described by the Kerr naked-singularity geometry. The primordial superspinars have to be converted to a black hole due to accretion, but they could survive to the era of high-redshift quasars. We discuss observational phenomena caused by the primordial Kerr superspinars in this era, considering the properties of corotating Keplerian accretion discs orbiting such superspinars and the optical phenomena modified by their presence. The potential well around a near-extreme superspinar with spin a very close to the extreme black hole value a = 1 is very deep so that the efficiency of the accretion process reaches 157.7%, influencing thus significantly the spectral continuum of corotating Keplerian discs and giving a signature of near-extreme superspinars. Such superspinars can also serve as an efficient accelerator for extremely high-energy collisions. Phenomena enabling a clear distinction of primordial Kerr superspinars and black holes are related to the disc oscillations with the radial and vertical epicyclic frequencies and the most profound could be differences implied by the profiled spectral lines generated in the innermost parts of the corotating Keplerian discs. © 2012 IOP Publishing Ltd.

Stuchlik Z.,Silesian University in Opava | Kolos M.,Silesian University in Opava
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2012

We study acceleration of current-carrying string loops governed by the presence of an outer tension barrier and an inner angular momentum barrier in the field of Schwarzschild-de Sitter black holes. We restrict attention to the axisymmetric motion of string loops with energy high enough, when the string loop can overcome the gravitational attraction and escape to infinity. We demonstrate that string loops can be scattered near the black hole horizon, and the energy of string oscillations can be efficiently converted to the energy of their linear motion. Such a transmutation effect can potentially represent acceleration of jets in active galactic nuclei and microquasars. We give the conditions limiting energy available for conversion onto the jetlike motion. Surprisingly, we are able to show that string loops starting from rest can be accelerated up to velocities v∼c even in the field of Schwarzschild black holes, if their angular momentum parameter is low enough. Such loops could serve as an explanation of highly relativistic jets observed in some quasars and active galactic nuclei. The cosmic repulsion becomes important behind the so-called static radius where it accelerates the linear motion of the string loops up to velocity v=c that is reached at the cosmic horizon of the Schwarzschild-de Sitter spacetimes independently of the angular momentum parameter of the strings. © 2012 American Physical Society.

Stuchlik Z.,Silesian University in Opava | Schee J.,Silesian University in Opava
Classical and Quantum Gravity | Year: 2013

Kerr naked singularities (superspinars) have to be efficiently converted to a black hole due to accretion from Keplerian discs. In the final stages of the conversion process the near-extreme Kerr naked singularities (superspinars) provide a variety of extraordinary physical phenomena. Such superspinning Kerr geometries can serve as an efficient accelerator for extremely high-energy collisions enabling direct and clear demonstration of the outcomes of the collision processes. We shall discuss the efficiency and visibility of the ultra-high-energy collisions in the deepest parts of the gravitational well of superspinning near-extreme Kerr geometries for the whole variety of particles freely falling from infinity. We demonstrate that the ultra-high-energy processes can be obtained with no fine tuning of the motion constants and the products of the collision can escape to infinity with both directional and energetical efficiency significantly higher than in the case of the near-extreme black holes. The strongest efficiency of the collision process is reached for particles falling along trajectories with maximally acceptable negative angular momentum. © 2013 IOP Publishing Ltd.

Vodova J.,Silesian University in Opava
Nonlinearity | Year: 2013

In 1993, P Rosenau and J M Hyman introduced and studied Kortewegde- Vries-like equations with nonlinear dispersion admitting compacton solutions, ut+D3x (un)+Dx(u m) = 0, m, n > 1, which are knownas the K(m, n) equations. In this paper we consider a slightly generalized version of the K(m, n) equations for m = n, namely, ut = aD3x (um) + bDx(um), where m, a, b are arbitrary real numbers. We describe all generalized symmetries and conservation laws thereof for m ≠ -2, -1/2, 0, 1; for these four exceptional values of m the equation in question is either completely integrable (m = -2,-1/2) or linear (m = 0, 1). It turns out that for m ≠ -2,-1/2, 0, 1 there are only three symmetries corresponding to x- and t-translations and scaling of t and u, and four non-trivial conservation laws, one of which expresses the conservation of energy, and the other three are associated with the Casimir functionals of the Hamiltonian operator D = aD 3x + bDx admitted by our equation. Our result provides inter alia a rigorous proof of the fact that the K(2, 2) equation has just four conservation laws from the paper of P Rosenau and J M Hyman. © 2013 IOP Publishing Ltd & London Mathematical Society.

Stuchlik Z.,Silesian University in Opava | Kolos M.,Silesian University in Opava
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2014

Small oscillations of current-carrying string loops around stable equilibrium positions corresponding to minima of the effective potential in the equatorial plane of the Kerr black holes are studied using the perturbation method. In the lowest approximation, two uncoupled harmonic oscillators are obtained that govern the radial and vertical oscillations; the higher-order terms determine nonlinear phenomena and transition to chaotic motion through quasiperiodic stages of the oscillatory motion. The radial profiles of frequencies of the radial and vertical harmonic oscillations that are also relevant in the quasiperiodic stages of the oscillatory motion are given, and their properties, independent of the spin of the black holes and the angular momentum and tension of the string loops, are determined. It is shown that the radial profiles differ substantially from those corresponding to the radial and vertical frequencies of the geodetical epicyclic motion; however, they have the same mass scaling and their magnitude is of the same order. Therefore, we are able to demonstrate that, assuming the relevance of resonant phenomena of radial and vertical string-loop oscillations at their frequency ratio 32, the oscillatory frequencies of string loops can be related to the frequencies of the twin high-frequency quasiperiodic oscillations (HF QPOs) observed in the microquasars GRS 1915+105, XTE 1550-564, GRO 1655-40. We can conclude that oscillating current-carrying string loops have to be considered as one of the possible explanations of the HF QPOs occurring in the field of compact objects. © 2014 American Physical Society.

Cremaschini C.,Silesian University in Opava | Stuchlik Z.,Silesian University in Opava
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2013

Current-carrying string loops are adopted in astrophysics to model the dynamics of isolated flux tubes of magnetized plasma expected to arise in the gravitational field of compact objects, such as black holes. Recent studies suggest that they could provide a framework for the acceleration and collimation of jets of plasma observed in these systems. However, the problem remains of the search of physical mechanisms which can consistently explain the occurrence of such plasma toroidal structures characterized by nonvanishing charge currents and are able to self-generate magnetic loops. In this paper, the problem is addressed in the context of Vlasov-Maxwell theory for nonrelativistic collisionless plasmas subject to both gravitational and electromagnetic fields. A kinetic treatment of quasistationary axisymmetric configurations of charged particles exhibiting epicyclic motion is obtained. Explicit solutions for the species equilibrium phase-space distribution function are provided. These are shown to have generally a non-Maxwellian character and to be characterized by nonuniform fluid fields and temperature anisotropy. Calculation of the relevant fluid fields and analysis of the Ampere equation then show the existence of nonvanishing current densities. As a consequence, the occurrence of a kinetic dynamo is proved, which can explain the self-generation of both azimuthal and poloidal magnetic fields by the plasma itself. This mechanism can operate in the absence of instabilities, turbulence, or accretion phenomena and is intrinsically kinetic in character. In particular, several kinetic effects contribute to it, identified here with finite Larmor radius, diamagnetic and energy-correction effects together with temperature anisotropy, and non-Maxwellian features of the equilibrium distribution function. © 2013 American Physical Society.

Kordulova P.,Silesian University in Opava
Nonlinear Analysis: Real World Applications | Year: 2011

The paper is devoted to the investigation of a parabolic equation with the Preisach operator under the time derivative. The model equation appears in the context of soil water hysteresis. Under suitable assumptions an existence result is obtained by using an implicit time discretization scheme, a priori estimates and passage to the limit in the convexity domain of the Preisach operator. © 2011 Elsevier Ltd. All rights reserved.

Hasik K.,Silesian University in Opava
Journal of Mathematical Biology | Year: 2010

In this paper a Gause type model of interactions between predator and prey population is considered. We deal with the sufficient condition due to Kuang and Freedman in the generalized form including a kind of weight function. In a previous paper we proved that the existence of such weight function implies the uniqueness of limit cycle. In the present paper we give a new condition equivalent to the existence of a weight function (Theorem 4.4). As a consequence of our result, it is shown that some simple qualitative properties of the trophic function and the prey isocline ensure the uniqueness of limit cycle. © Springer-Verlag 2009.

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