595 research outputs found
Heating and Cooling of Hot Accretion Flows by Non Local Radiation
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 . However, if the hot flow terminates at
, 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 , 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
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
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
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
the turbulent velocity becomes equal to the sound velocity.
During this substage the boundary 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
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, 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
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
Recommended from our members
From discrete to continuum models of three-dimensional deformations in epithelial sheets
International audienceEpithelial tissue, in which cells adhere tightly to each other and to theunderlying substrate, is one of the four major tissue types in adultorganisms. In embryos, epithelial sheets serve as versatile substratesduring the formation of developing organs. Some aspects of epithelialmorphogenesis can be adequately described using vertex models, in which thetwo-dimensional arrangement of epithelial cells is approximated by apolygonal lattice with an energy that has contributions reflecting theproperties of individual cells and their interactions. Previous studieswith such models have largely focused on dynamics confined to two spatialdimensions and analyzed them numerically. We show how these models can beextended to account for three-dimensional deformations and studiedanalytically. Starting from the extended model, we derive a continuumplate description of cell sheets, in which the effective tissue properties,such as bending rigidity, are related explicitly to the parameters of thevertex model. To derive the continuum plate model, we duly take intoaccount a microscopic shift between the two sublattices of the hexagonalnetwork, which has been ignored in previous work. As an application of thecontinuum model, we analyze tissue buckling by a line tension applied alonga circular contour, a simplified set-up relevant to several situations inthe developmental context. The buckling thresholds predicted by thecontinuum description are in good agreement with the results of directstability calculations based on the vertex model. Our results establish adirect connection between discrete and continuum descriptions of cellsheets and can be used to probe a wide range of morphogenetic processes inepithelial tissues
Fixed Volume Effect on Polar Properties and Phase Diagrams of Ferroelectric Semi-ellipsoidal Nanoparticles
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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