1,652 research outputs found
On Generators and Congenerators
The question of the existence of generators and cogenerators
i n a category is of i n t e r e s t i n view of the special
adjoint functor theorem. ISBELL has given an example (unpublished)
which shows t h a t the existence of a cogenerator
i s a necessary part of the hypothesis of the special
adjoint functor theorem. This example also shows t h a t the
category of groups has no cogenerator. (Clearly the f r e e
group on one element i s a generator i n the category of
groups.) It is well known t h a t there e x i s t generators and
cogenerators i n the categories of commutative groups,
Comrnutative Lie algebras (over a f i e l d ) and commutative
r e s t r i c t e d Lie algebras, because a l l of these categories
are module categories. By ISBELL1s r e s u l t when one drops
the condition of cornmutativity for the category of commut
a t i v e groups there i s no longer a cogenerator. We have
Proved similar r e s u l t s for the categories of commutative
Lie algebras and commutative r e s t r i c t e d Lie algebras. The
r e s u l t s are summarized i n the l i s t below where we have
included some r e l a t e d categories
The bulk kinetic power of the jets of GRS 1915+105
We calculate the minimum value of the power in kinetic bulk motion of the
galactic superluminal source GRS 1915+105. This value far exceeds the Eddington
luminosity for accretion onto a black hole of 10 solar masses. This large value
severely limits the possible carriers of the kinetic luminosity at the base of
the jet, and favours a jet production and acceleration controlled by a magnetic
field whose value, at the base of the jet, exceeds Gauss. The Blandford
and Znajek process can be responsible of the extraction of the rotational
energy of a Kerr black hole, if lasting long enough to provide the required
kinetic energy. This time, of the order of a day, implies that the process must
operate in a stationary, not impulsive, mode.Comment: 5 pages, Latex, accepted for publication in MNRAS as a lette
A five-wave HLL Riemann solver for relativistic MHD
We present a five-wave Riemann solver for the equations of ideal relativistic
magnetohydrodynamics. Our solver can be regarded as a relativistic extension of
the five-wave HLLD Riemann solver initially developed by Miyoshi and Kusano for
the equations of ideal MHD. The solution to the Riemann problem is approximated
by a five wave pattern, comprised of two outermost fast shocks, two rotational
discontinuities and a contact surface in the middle. The proposed scheme is
considerably more elaborate than in the classical case since the normal
velocity is no longer constant across the rotational modes. Still, proper
closure to the Rankine-Hugoniot jump conditions can be attained by solving a
nonlinear scalar equation in the total pressure variable which, for the chosen
configuration, has to be constant over the whole Riemann fan. The accuracy of
the new Riemann solver is validated against one dimensional tests and
multidimensional applications. It is shown that our new solver considerably
improves over the popular HLL solver or the recently proposed HLLC schemes.Comment: 15 pages, 19 figures. Accepted for Publication in MNRA
Linear and nonlinear evolution of current-carrying highly magnetized jets
We investigate the linear and nonlinear evolution of current-carrying jets in
a periodic configuration by means of high resolution three-dimensional
numerical simulations. The jets under consideration are strongly magnetized
with a variable pitch profile and initially in equilibrium under the action of
a force-free magnetic field. The growth of current-driven (CDI) and
Kelvin-Helmholtz (KHI) instabilities is quantified using three selected cases
corresponding to static, Alfvenic and super-Alfvenic jets.
During the early stages, we observe large-scale helical deformations of the
jet corresponding to the growth of the initially excited CDI mode. A direct
comparison between our simulation results and the analytical growth rates
obtained from linear theory reveals good agreement on condition that
high-resolution and accurate discretization algorithms are employed.
After the initial linear phase, the jet structure is significantly altered
and, while slowly-moving jets show increasing helical deformations, larger
velocity shear are violently disrupted on a few Alfven crossing time leaving a
turbulent flow structure. Overall, kinetic and magnetic energies are quickly
dissipated into heat and during the saturated regime the jet momentum is
redistributed on a larger surface area with most of the jet mass travelling at
smaller velocities. The effectiveness of this process is regulated by the onset
of KHI instabilities taking place at the jet/ambient interface and can be held
responsible for vigorous jet braking and entrainment.Comment: 14 pages, 11 figure
Jet stability, dynamics and energy transport
Relativistic jets carry energy and particles from compact to very large
scales compared with their initial radius. This is possible due to their
remarkable collimation despite their intrinsic unstable nature. In this
contribution, I review the state-of-the-art of our knowledge on instabilities
growing in those jets and several stabilising mechanisms that may give an
answer to the question of the stability of jets. In particular, during the last
years we have learned that the limit imposed by the speed of light sets a
maximum amplitude to the instabilities, contrary to the case of classical jets.
On top of this stabilising mechanism, the fast growth of unstable modes with
small wavelengths prevents the total disruption and entrainment of jets. I also
review several non-linear processes that can have an effect on the collimation
of extragalactic and microquasar jets. Within those, I remark possible causes
for the decollimation and decelleration of FRI jets, as opposed to the
collimated FRII's. Finally, I give a summary of the main reasons why jets can
propagate through such long distances.Comment: For the proceedings of High Energy Phenomena in Relativistic Outflows
III (HEPRO III, IJMPD, accepted). 12 page
On gauge fixing in the Lagrangian formalism of superfield BRST quantization
We propose a modification of the gauge-fixing procedure in the Lagrangian
method of superfield BRST quantization for general gauge theories which
simultaneously provides a natural generalization of the well-known BV
quantization scheme as far as gauge-fixing is concerned. A superfield form of
BRST symmetry for the vacuum functional is found. The gauge-independence of the
S-matrix is established.Comment: 8 pages, LATEX Includes additional Reference and relation to i
Neutral and ionic dopants in helium clusters: interaction forces for the and
The potential energy surface (PES) describing the interactions between
and and an extensive
study of the energies and structures of a set of small clusters,
, have been presented by us in a previous series of
publications [1-3]. In the present work we want to extend the same analysis to
the case of the excited and of the
ionized Li moiety. We thus show here calculated
interaction potentials for the two title systems and the corresponding fitting
of the computed points. For both surfaces the MP4 method with cc-pV5Z basis
sets has been used to generate an extensive range of radial/angular coordinates
of the two dimensional PES's which describe rigid rotor molecular dopants
interacting with one He partner
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