5,005 research outputs found
Preimage problems for deterministic finite automata
Given a subset of states of a deterministic finite automaton and a word
, the preimage is the subset of all states mapped to a state in by the
action of . We study three natural problems concerning words giving certain
preimages. The first problem is whether, for a given subset, there exists a
word \emph{extending} the subset (giving a larger preimage). The second problem
is whether there exists a \emph{totally extending} word (giving the whole set
of states as a preimage)---equivalently, whether there exists an
\emph{avoiding} word for the complementary subset. The third problem is whether
there exists a \emph{resizing} word. We also consider variants where the length
of the word is upper bounded, where the size of the given subset is restricted,
and where the automaton is strongly connected, synchronizing, or binary. We
conclude with a summary of the complexities in all combinations of the cases
Magnetically Arrested Disk: An Energetically Efficient Accretion Flow
We consider an accretion flow model originally proposed by Bisnovatyi-Kogan &
Ruzmaikin (1974), which has been confirmed in recent 3D MHD simulations. In the
model, the accreting gas drags in a strong poloidal magnetic field to the
center such that the accumulated field disrupts the axisymmetric accretion flow
at a relatively large radius. Inside the disruption radius, the gas accretes as
discrete blobs or streams with a velocity much less than the free-fall
velocity. Almost the entire rest mass energy of the gas is released as heat,
radiation and mechanical/magnetic energy. Even for a non-rotating black hole,
the efficiency of converting mass to energy is of order 50% or higher. The
model is thus a practical analog of an idealized engine proposed by Geroch and
Bekenstein.Comment: 4 pages, 2 figure, new refs added, in print in PAS
Accretion Disks Phase Transitions: 2-D or not 2-D?
We argue that the proper way to treat thin-thick accretion-disk transitions
should take into account the 2-D nature of the problem. We illustrate the
physical inconsistency of the 1-D vertically integrated approach by discussing
a particular example of the convective transport of energy.Comment: 4 pages, 2 figure
Self-Similar Accretion Flows with Convection
We consider height-integrated equations of an advection-dominated accretion
flow (ADAF), assuming that there is no mass outflow. We include convection
through a mixing length formalism. We seek self-similar solutions in which the
rotational velocity and sound speed scale as R^{-1/2}, where R is the radius,
and consider two limiting prescriptions for the transport of angular momentum
by convection. In one limit, the transport occurs down the angular velocity
gradient, so convection moves angular momentum outward. In the other, the
transport is down the specific angular momentum gradient, so convection moves
angular momentum inward. We also consider general prescriptions which lie in
between the two limits.
When convection moves angular momentum outward, we recover the usual
self-similar solution for ADAFs in which the mass density scales as rho ~
R^{-3/2}. When convection moves angular momentum inward, the result depends on
the viscosity coefficient alpha. If alpha>alpha_{crit1} ~ 0.05, we once again
find the standard ADAF solution. For alpha<alpha_{crit}, however, we find a
non-accreting solution in which rho ~ R^{-1/2}. We refer to this as a
"convective envelope" solution or a "convection-dominated accretion flow".
Two-dimensional numerical simulations of ADAFs with values of alpha<0.03 have
been reported by several authors. The simulated ADAFs exhibit convection. By
virtue of their axisymmetry, convection in these simulations moves angular
momentum inward, as we confirm by computing the Reynolds stress. The
simulations give rho ~ R^{-1/2}, in good agreement with the convective envelope
solution. The R^{-1/2} density profile is not a consequence of mass outflow.Comment: 22 pages, 4 figures, final version accepted for publication in ApJ, a
new appendix was added and 3 figs were modifie
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