865 research outputs found
Asymptotic models of meridional flows in thin viscous accretion disks
We present the results of numerical integrations yielding the structure of
and meridional flow in axisymmetric thin viscous accretion disk models. The
solutions are obtained by simplifying and approximating first the equations,
using systematic asymptotic expansions in the small parameter ,
measuring the relative disk thickness. The vertical structure is solved
including radiative transfer in the diffusion approximation. Carrying out the
expansion to second order in we obtain, for low enough values of the
viscosity parameter , solutions containing {\em backflows}. These
solutions are similar to the results first found by Urpin (1984), who used
approximations that are only valid for large radii and the asymptotic
analytical solutions of Klu\'zniak & Kita (1997), valid only for polytropic
disks. Our results may be important for several outstanding issues in accretion
disk theory.Comment: 5 figure
A weakly nonlinear analysis of the magnetorotational instability in a model channel flow
We show by means of a perturbative weakly nonlinear analysis that the
axisymmetric magnetorotational instability (MRI) of a viscous, resistive,
incompressible rotating shear flow in a thin channel gives rise to a real
Ginzburg-Landau equation for the disturbance amplitude. For small magnetic
Prandtl number (), the saturation amplitude is and the resulting momentum transport scales as , where is the {\em hydrodynamic} Reynolds number. Simplifying
assumptions, such as linear shear base flow, mathematically expedient boundary
conditions and continuous spectrum of the vertical linear modes, are used to
facilitate this analysis. The asymptotic results are shown to comply with
numerical calculations using a spectral code. They suggest that the transport
due to the nonlinearly developed MRI may be very small in experimental setups
with .Comment: Accepted to Physical Review Letters - Nov. 30, 2006. In final for
Grover's search with faults on some marked elements
Grover's algorithm is a quantum query algorithm solving the unstructured
search problem of size using queries. It provides a
significant speed-up over any classical algorithm \cite{Gro96}.
The running time of the algorithm, however, is very sensitive to errors in
queries. It is known that if query may fail (report all marked elements as
unmarked) the algorithm needs queries to find a marked element
\cite{RS08}. \cite{AB+13} have proved the same result for the model where each
marked element has its own probability to be reported as unmarked.
We study the behavior of Grover's algorithm in the model where the search
space contains both faulty and non-faulty marked elements. We show that in this
setting it is indeed possible to find one of non-faulty marked items in
queries.
We also analyze the limiting behavior of the algorithm for a large number of
steps and show the existence and the structure of limiting state .Comment: 17 pages, 6 figure
Non-exponential hydrodynamical growth in density-stratified thin Keplerian discs
The short time evolution of three dimensional small perturbations is studied.
Exhibiting spectral asymptotic stability, thin discs are nonetheless shown to
host intensive hydrodynamical activity in the shape of non modal growth of
initial small perturbations. Two mechanisms that lead to such behavior are
identified and studied, namely, non-resonant excitation of vertically confined
sound waves by stable planar inertia-coriolis modes that results in linear
growth with time, as well as resonant coupling of those two modes that leads to
a quadratic growth of the initial perturbations. It is further speculated that
the non modal growth can give rise to secondary strato-rotational instabilities
and thus lead to a new route to turbulence generation in thin discs
Revised research about chaotic dynamics in Manko et al. spacetime
A recent work by Dubeibe et al. [Phys. Rev. D 75, 023008 (2007)] stated that
chaos phenomenon of test particles in gravitational field of rotating neutron
stars which are described by Manko, Sanabria-Gomez, and Manko (Manko et al.)
metric can only occur when the stars have oblate deformation. But the chaotic
motions they found are limited in a very narrow zone which is very close to the
center of the massive bodies. This paper argues that this is impossible because
the region is actually inside of the stars, so the motions cannot exist at this
place. In this paper, we scan all parameters space and find chaos and unstable
fixed points outside of stars with big mass-quadrupole moments. The
calculations show that chaos can only occur when the stars have prolate
deformation. Because real deformation of stars should be oblate, all orbits of
test particles around the rotating neutron stars described by Manko et al.
solutions are regular. The case of nonzero dipolar magnetic moment has also
been taken into account in this study.Comment: 6 pages, 5 figure
Hydrodynamic response of rotationally supported flows in the Small Shearing Box model
The hydrodynamic response of the inviscid small shearing box model of a
midplane section of a rotationally supported astrophysical disk is examined. An
energy functional is formulated for the general nonlinear problem.
It is found that the fate of disturbances is related to the conservation of
this quantity which, in turn, depends on the boundary conditions utilized:
is conserved for channel boundary conditions while it is not
conserved in general for shearing box conditions. Linearized disturbances
subject to channel boundary conditions have normal-modes described by Bessel
Functions and are qualitatively governed by a quantity which is a
measure of the ratio between the azimuthal and vertical wavelengths. Inertial
oscillations ensue if - otherwise disturbances must in general be
treated as an initial value problem. We reflect upon these results and offer a
speculation.Comment: 6 pages, resubmitted to Astronomy and Astrophysics, shortened with
references adde
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