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

Addendum to `Fake Projective Planes'

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.Comment: A more refined classification is given in the new versio

Was the Cosmic Web of Protogalactic Material Permeated by Lobes of Radio Galaxies During the Quasar Era?

Evidence for extended active lifetimes (> 10^8 yr) for radio galaxies implies that many large radio lobes were produced during the `quasar era', 1.5 < z < 3, when the comoving density of radio sources was 2 -- 3 dex higher than the present level. However, inverse Compton losses against the intense microwave background substantially reduce the ages and numbers of sources that are detected in flux-limited surveys. The realization that the galaxy forming material in those epochs was concentrated in filaments occupying a small fraction of the total volume then leads to the conclusion that radio lobes permeated much of the volume occupied by the protogalactic material during that era. The sustained overpressure in these extended lobes is likely to have played an important role in triggering the high inferred rate of galaxy formation at z > 1.5 and in the magnetization of the cosmic network of filaments.Comment: 5 pages, 0 figures, submitted to ApJ Letters; uses emulateapj

Path Planning in the Presence of Dynamically Moving Obstacles with Uncertainty

In this paper, the problem of path-planning with dynamically moving elliptical obstacles is addressed. A new analytical result for computing the axes aligned bounding box for the ellipses with bounded uncertainty in the position of the centre and the orientation is presented. Genetic algorithm is utilised for finding the shortest path from the initial to goal position avoiding the moving obstacles.Defence Science Journal, 2010, 60(1), pp.55-60, DOI:http://dx.doi.org/10.14429/dsj.60.10