33,711 research outputs found
Afterglow lightcurves, viewing angle and the jet structure of gamma-ray bursts
Gamma ray bursts are often modelled as jet-like outflows directed towards the
observer; the cone angle of the jet is then commonly inferred from the time at
which there is a steepening in the power-law decay of the afterglow. We
consider an alternative model in which the jet has a beam pattern where the
luminosity per unit solid angle (and perhaps also the initial Lorentz factor)
decreases smoothly away from the axis, rather than having a well-defined cone
angle within which the flow is uniform. We show that the break in the afterglow
light curve then occurs at a time that depends on the viewing angle. Instead of
implying a range of intrinsically different jets - some very narrow, and others
with similar power spread over a wider cone - the data on afterglow breaks
could be consistent with a standardized jet, viewed from different angles. We
discuss the implication of this model for the luminosity function.Comment: Corrected typo in Eq. 1
Shape maps for second order partial differential equations
We analyse the singularity formation of congruences of solutions of systems
of second order PDEs via the construction of \emph{shape maps}. The trace of
such maps represents a congruence volume whose collapse we study through an
appropriate evolution equation, akin to Raychaudhuri's equation. We develop the
necessary geometric framework on a suitable jet space in which the shape maps
appear naturally associated with certain linear connections. Explicit
computations are given, along with a nontrivial example
Can Modus Vivendi Save Liberalism from Moralism? A Critical Assessment of John Gray’s Political Realism
This chapter assesses John Gray’s modus vivendi-based justification for liberalism. I argue that his approach is preferable to the more orthodox deontological or teleological justificatory strategies, at least because of the way it can deal with the problem of diversity. But then I show how that is not good news for liberalism, for grounding liberal political authority in a modus vivendi undermines liberalism’s aspiration to occupy a privileged normative position vis-à -vis other kinds of regimes. So modus vivendi can save liberalism from moralism, but at cost many liberals will not be prepared to pay
Deformed Double Yangian Structures
Scaling limits when q tends to 1 of the elliptic vertex algebras A_qp(sl(N))
are defined for any N, extending the previously known case of N=2. They realise
deformed, centrally extended double Yangian structures DY_r(sl(N)). As in the
quantum affine algebras U_q(sl(N)), and quantum elliptic affine algebras
A_qp(sl(N)), these algebras contain subalgebras at critical values of the
central charge c=-N-Mr (M integer, 2r=ln p/ln q), which become Abelian when
c=-N or 2r=Nh for h integer. Poisson structures and quantum exchange relations
are derived for their abstract generators.Comment: 16 pages, LaTeX2e Document - packages amsfonts,amssymb,subeqnarra
On the Quasi-Hopf structure of deformed double Yangians
We construct universal twists connecting the centrally extended double
Yangian DY(sl(2))_c with deformed double Yangians DY_r(sl(2))_c, thereby
establishing the quasi-Hopf structures of the latter.Comment: 11 page
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