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 ISBELL has given an example (unpublished) which shows t h a t the existence of a cogenerator i s a necessary part of the hypothesis of the special adjoint functor theorem.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 $10^8$ 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 Li2(a3Σu+)−HeLi_2(a^3\Sigma_u^+)-He and Li2+(X2Σg+)−HeLi_2^+(X^2\Sigma_g^+)-He

The potential energy surface (PES) describing the interactions between $\mathrm{Li_{2}(^{1}\Sigma_{u}^{+})}$ and $\mathrm{^{4}He}$ and an extensive study of the energies and structures of a set of small clusters, $\mathrm{Li_{2}(He)_{n}}$, 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 $\mathrm{Li_{2}}(a^{3}\Sigma_{u}^{+})$ and of the ionized Li$_{2}^{+}(X^{2}\Sigma_{g}^{+})$ 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