595 research outputs found

    Heating and Cooling of Hot Accretion Flows by Non Local Radiation

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    We consider non-local effects which arise when radiation emitted at one radius of an accretion disk either heats or cools gas at other radii through Compton scattering. We discuss three situations: 1. Radiation from the inner regions of an advection-dominated flow Compton cooling gas at intermediate radii and Compton heating gas at large radii. 2. Soft radiation from an outer thin accretion disk Compton cooling a hot one- or two-temperature flow on the inside. 3. Soft radiation from an inner thin accretion disk Compton cooling hot gas in a surrounding one-temperature flow. We describe how previous results are modified by these non-local interactions. We find that Compton heating or cooling of the gas by the radiation emitted in the inner regions of a hot flow is not important. Likewise, Compton cooling by the soft photons from an outer thin disk is negligible when the transition from a cold to a hot flow occurs at a radius greater than some minimum Rtr,minR_{tr,min}. However, if the hot flow terminates at R<Rtr,minR < R_{tr,min}, non-local cooling is so strong that the hot gas is cooled to a thin disk configuration in a runaway process. In the case of a thin disk surrounded by a hot one-temperature flow, we find that Compton cooling by soft radiation dominates over local cooling in the hot gas for \dot{M} \gsim 10^{-3} \alpha \dot{M}_{Edd}, and R \lsim 10^4 R_{Schw}. As a result, the maximum accretion rate for which an advection-dominated one-temperature solution exists, decreases by a factor of 10\sim 10, compared to the value computed under an assumption of local energy balance.Comment: LaTeX aaspp.sty, 25 pages, and 6 figures; to appear in Ap

    Discrete Maximum Principle for Nonsmooth Optimal Control Problems with Delays

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    We consider optimal control problems for discrete-time systems with delays. The main goal is to derive necessary optimality conditions of the discrete maximum principle type in the case of nonsmooth minimizing functions. We obtain two independent forms of the discrete maximum principle with transversality conditions described in terms of subdifferentials and superdifferentials, respectively. The superdifferential form is new even for non-delayed systems and may be essentially stronger than a more conventional subdifferential form in some situations

    The Approximate Maxium Principle in Constrained Optimal Control

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    The paper concerns optimal control problems for dynamic systems governed by a parametric family of discrete approximations of control systems with continuous time. Discrete approximations play an important role in both qualitative and numerical aspects of optimal control and occupy an intermediate position between discrete-time and continuous-time control systems. The central result in optimal control of discrete approximations is the Approximate Maximum Principle (AMP), which is justified for smooth control problems with endpoint constraints under certain assumptions without imposing any convexity, in contrast to discrete systems with a fixed step. We show that these assumptions are essential for the validity of the AMP, and that the AMP does not hold, in its expected (lower) subdifferential form, for nonsmooth problems. Moreover, a new upper subdifferential form of the AMP is established in this paper for both ordinary and time-delay control systems. This solves a long-standing question about the possibility to extend the AMP to nonsmooth control problems

    Trans-sonic propeller stage

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    We follow the approach used by Davies and Pringle (1981) and discuss the trans-sonic substage of the propeller regime. This substage is intermediate between the supersonic and subsonic propeller substages. In the trans-sonic regime an envelope around a magnetosphere of a neutron star passes through a kind of a reorganization process. The envelope in this regime consists of two parts. In the bottom one turbulent motions are subsonic. Then at some distance rsr_\mathrm{s} the turbulent velocity becomes equal to the sound velocity. During this substage the boundary rsr_\mathrm{s} propagates outwards till it reaches the outer boundary, and so the subsonic regime starts. We found that the trans-sonic substage is unstable, so the transition between supersonic and subsonic substages proceeds on the dynamical time scale. For realistic parameters this time is in the range from weeks to years.Comment: 8 pages with figures, submitted to Astron. Astroph. Transaction

    Vacuum Breakdown near a Black Hole Charged by Hypercritical Accretion

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    We consider a black hole accreting spherically from the surrounding medium. If accretion produces a luminosity close to the Eddington limit the hole acquires a net charge so that electrons and ions can fall with the same velocity. The condition for the electrostatic field to be large enough to break the vacuum near the hole horizon translates into an upper limit for the hole mass, M6.6×1020g.M\sim 6.6\times 10^{20} {\rm g}. The astrophysical conditions under which this phaenomenon can take place are rather extreme, but in principle they could be met by a mini black hole residing at the center of a star.Comment: 6 pages, accepted for publication in the Astrophysical Journa

    Physical properties of Tolman-Bayin solutions: some cases of static charged fluid spheres in general relativity

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    In this article, Einstein-Maxwell space-time has been considered in connection to some of the astrophysical solutions as previously obtained by Tolman (1939) and Bayin (1978). The effect of inclusion of charge into these solutions has been investigated thoroughly and also the nature of fluid pressure and mass density throughout the sphere have been discussed. Mass-radius and mass-charge relations have been derived for various cases of the charged matter distribution. Two cases are obtained where perfect fluid with positive pressures give rise to electromagnetic mass models such that gravitational mass is of purely electromagnetic origin.Comment: 15 pages, 12 figure

    Fixed Volume Effect on Polar Properties and Phase Diagrams of Ferroelectric Semi-ellipsoidal Nanoparticles

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    For advanced applications in modern industry it is very important to reduce the volume of ferroelectric nanoparticles without serious deterioration of their polar properties. In many practically important cases fixed volume (rather than fixed size) corresponds to realistic technological conditions of nanoparticles fabrication. The letter is focused on the theoretical study of the behavior of ferroelectric polarization, paramagnetoelectric coefficient and phase diagrams of semi-ellipsoidal nanoparticles with fixed volume V. Our approach combines the Landau-Ginzburg-Devonshire phenomenology, classical electrostatics and elasticity theory. Our results show that the size effects of the phase diagrams and polarization of semi-ellipsoidal BiFeO3 nanoparticles nontrivially depends on V. These findings provide a path to optimize the polar properties of nanoparticles by controlling their phase diagrams at a fixed volume.Comment: 15 pages, 5 figures, we added the section IV. Paramagnetoelectric (PME) coefficient at fixed volume in this version and changed title and abstract accordingl
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